global investment management prof bruno solnik 1

Global Investment Management

Prof Bruno Solnik 1

• Asset Allocation• Portfolio Construction• Risk Management• Performance Evaluation

Prof Bruno Solnik 2

Objective of Portfolio Management

• Maximize return for a given level of risk• Minimize risk for a set objective of

return.

This is all about risk management: Eliminate bad risks, diversify risks, and take risks that will generate extra returns.

Prof Bruno Solnik 3

Strategic Asset Allocation

• Decide of an asset allocation over the long run

• Often takes the form of a benchmark

• Based on Long-term Capital market expectations

• Based on risk estimates

Prof Bruno Solnik 4

Tactical Asset Allocation

• Strategic is the long-term anchor (say many years)

• Based on current market conditions and revisions in expectations/risks, managers apply “tactical” revisions (shorter-term).

Prof Bruno Solnik 5

Asset Allocation Principles

An optimal strategic asset allocation is derived based on:

• CME (Capital Market Expectations)• Investment objectives• Investor’s risk tolerance • Investor’s investment constraints • Investor’s liabilities• Risk estimates

Prof Bruno Solnik 6

Optimization

• Investment firms use an optimizer• The basic one is the Mean-Variance

optimizer). This is a quadratic program with constraints.

• Some more sophisticated versions are sometimes used (shortfall risk, Bayesian updates, Tail risk, etc..).

• We will talk about tail risk later. For the time-being, it is useful to think in terms of Mean-Variance optimization as all asset management companies mostly do.

Prof Bruno Solnik 7

Prof Bruno Solnik

Some Mathematics (for specialists)

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Prof Bruno Solnik

Optimization: Efficient frontier

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Optimization

• Risk measures (volatility, correlation,..) are rather stable and can be easily updated.

• Expected returns are difficult to asses and the most difficult part of the asset allocation optimization.

Prof Bruno Solnik 10

Strategic Asset Allocation

1. Derive “neutral” market expectations, meaning expected returns that are implied by market equilibrium.

2. Update those based on some beliefs of the portfolio manager (CME or Capital Market Expectations)

3. Construct an asset allocation based on those CME and a risk optimization.


Three Major Methods

There are three major methods used to derive neutral CME:

1. Use Historical returns for neutral expected return

2. Derive neutral expected return from CAPM

3. Derive neutral expected return from reverse optimization (Black-Litterman)


1. Long Term Capital Market Expectations: Historical

Historical records for mean returns, volatility, and correlation can simply be projected to repeat in the future. BUT:

• Economic conditions in the past, especially the distant past, may not be relevant for the future. A market that has done exceptionally well (or poorly) in the past because of some specific events (e.g., liberalization of the economy) may not do so in the future because that specific event will not repeat.


Long Term Capital Market Expectations: Historical

The exceptional equity risk premium in the twentieth century (6 percent for U.S. stocks) was caused by two factors:

• Earnings per share grew steadily.• Valuation multiples, such as the price /

earnings ratio, grew dramatically over time.


Long Term Capital Market Expectations: Historical

Stock prices went up in part because of real growth, but more importantly, because valuation multiples rose impressively until 2000. To expect a similar equity risk premium in the future, an analyst must make the assumption that valuation multiples will continue upward to unprecedented levels.


Prof Bruno Solnik

Exhibit 13.4: Stocks, Bonds, Bills, Inflation:The Global Record (1900-2000)

(Nominal returns in local currency in %: means calculated using geometric mean)

Source: Dimson Marsh and Staunton (2002) MAR: Mean Annual Return SD: Standard Deviation

CountryEquity Bonds Bills Inflation

MAR SD MAR SD MAR SD MAR SD

Australia 11.9 18.0 5.7 13.0 4.5 4.2 4.0 5.5

Canada 9.7 16.8 4.9 9.0 4.9 3.7 3.1 4.9

Denmark 10.4 22.6 7.0 10.6 7.0 4.5 4.1 6.6

France 12.3 24.7 6.9 8.8 4.3 2.3 8.0 14.6

Germany 9.9 36.4 2.8 13.6 4.6 3.4 5.2 15.8

Italy 12.1 34.4 6.7 9.1 4.7 3.3 9.2 36.8

Japan 13.1 30.5 6.1 15.1 5.5 1.9 7.7 40.4

The Netherlands 9.1 22.7 4.1 7.6 3.7 2.4 3.0 5.0

Sweden 12.2 23.7 6.1 9.2 5.8 3.1 3.7 6.8UK 10.2 21.9 5.4 12.6 5.1 3.9 4.1 6.9US 10.3 20.0 4.7 8.1 4.3 2.8 3.2 5.0

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Update for Equity Risk Premium (1900-2010)


2. Long Term Capital Market Expectations:Forward-Looking (UBS and some others)

This method 2 is primarily used for asset allocation across asset classes (equity, bonds, real estate, etc..)

• Calculate an updated covariance matrix (volatility and correlation of asset classes).

• Infer expected returns for each asset class using the CAPM.

• Adjust expected returns for possible market segmentation and illiquidity.


Recap of CAPM in matrix notations

• By transformation


0 0 or ( ) ( )i i M i i ME R r E R r

Prof Bruno Solnik

Exhibit 13.5: The Reward for Risk for Conventional & Alternative Investments

Source: Terhaar, Staub and Singer (2003)

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Long Term Equilibrium CME is the sum of:

• Cash Return (Expected real rate plus inflation)

• Market Risk Premium (à la CAPM)• Illiquidity/Segmentation Risk Premium• Non-Normality Risk Premium (hedge

funds)

See UBS documents


Strategic Allocation

After optimization the SAA is derived with targets and range as in the example below:


Prof Bruno Solnik

Example: UBS Global Perspectives Fall 2009

• Neutral/Equilibrium SAA

• Tactical deviations based on misvaluation model.

• The model is more complex than briefly described in the document. The idea is that UBS derives an over/undervaluation of each asset class and assume convergence in three years. Hence an expected return that will deviate from the long-term expectations.

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3. Black & Litterman (Goldman Sachs & others)

This method 3 is primarily used for allocation within

equity class.

The Black-Litterman model starts with equilibrium

expected returns.

• According to the Capital Asset Pricing Model

(CAPM), prices will adjust until the expected returns

of all assets in equilibrium are such that if all

investors hold the same belief, the demand for these

assets will exactly equal the outstanding supply.

This set of expected returns is the neutral reference

point of the Black-Litterman model.

• The investor then can express her views about the

markets. Prof Bruno Solnik 24

Steps of Black-Litterman Portfolio Optimisation

Step Action

1 Define the equilibrium market weights and covariance matrix

2 Calculate the equilibrium-expected excess returns through reverse optimisation

3 Express investor views and confidence level of view

4 Compute combined equilibrium view adjusted expected returns

5 Run mean variance optimisation


Reverse Optimization (see Efficient frontier equations)


Prof Bruno Solnik

Inputting Investor’s Views (Bayesian)source J.P. Morgan

• Views are incorporated in the form of matrices as inputs into the model.

Market View Confidence Level

MSCI EMU will have an absolute excess return of 6.50% 50%

MSCI Far East will out-perform MSCI North America by 0.40% 60%

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Impact on Portfolio Weights source J.P. Morgan


The Whole Process source J.P. Morgan


http://www.jpmorgan.com/cm/ContentServer?c=TS_Images&pagename=jpmorgan/wss/TS_Images/TS_Image&cid=1290554926156

Conclusions

• Method 2 is primarily used for allocation across

asset classes.

• Method 3 is primarily used for allocation within the

equity asset class.

• They both rely on some theoretical foundations and

are preferable to a simple mean-variance

optimization which is too sensitive to the expected

returns inputs and can yield extreme results.

• Of course, a simple alternative to Method 3 is simply

a passive investment in international index funds.



Prof Bruno Solnik

Key Takeaways: Asset Allocation 1

• Markets are very efficient, we only play at margin.

• Risk Allocation/Management is crucial in portfolio management.

• We build a neutral/strategic allocation inspired by market considerations (CAPM)

• We deviate tactically based on current views.

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Prof Bruno Solnik

Key Takeaways: Asset Allocation 2

In allocation optimization we have three vectors:– E (expected returns)– X (allocation weights) – V (covariance matrix)

1. Given V and E

2. Given V and X E implied returns• Traditional optimization uses 1. and typically derives

returns from history, CAPM and various personal inputs.

• Reverse optimization uses 2. Derives equilibrium returns, adjust them by personal input and redo a direct optimization.

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CLASS 1:

Markets and Major Players

- Equity (stocks)- Bonds - Others


Investment Markets

Stock Markets


Historical Differences in Trading Procedures – Price-Driven vs. Order Driven Markets

• Automated trading systems have followed two different paths:– A market organization dominated by dealers

making the market (also known as a price driven or quote driven market).

– A market organization with brokers acting as agents in an auction system (also known as an order driven market).



Price-Driven Systems (Dealer Markets)

• For example, NASDAQ, Forex• Market makers stand ready to buy or sell at

posted prices.• The bid and ask quotes are firm commitments

by the market maker to transact at those prices for a specified transaction size.

• Only American stock markets have retained a price driven model.

• This system is useful for trading large blocks. Also for small stocks to provide liquidity. But is costly for “average trades”.



Price-Driven Systems (Dealer Markets)

• Advantages:– Easier to execute large block trades than an

order-driven system.– Provides liquidity for “small” (illiquid) stocks.

• Disadvantages:– More expensive to operate than the order

driven markets.– Requires more human intervention.



Order-Driven Systems (Auction Markets)

• For example, Paris, Frankfurt, Tokyo and elsewhere

• Traders publicly post their orders and the transaction price is the result of the equilibrium of supply and demand.

• Most markets (including emerging markets) have adopted this system.

• All buy and sell orders are entered in a central order book and a new order is immediately matched with the book of limit orders previously submitted.

• To improve liquidity, most have retained periodic call auctions.



Example on order book


• LVMH (Moët Hennesy Louis Vuitton) is a French firm listed on the Paris Bourse. You can access the central limit order book directly on the Internet and find the following information (the limit prices for sell orders are ask prices and those for buy orders are bid prices):

Sell Orders Buy Orders

Quantity Limit Limit Quantity

1,000 58 49 2,000

3,000 54 48 500

1,000 52 47 1,000

1,000 51 46 2,000

500 50 44 10,000


Order-Driven Systems (Auction Markets)

• Advantages:– Requires little human intervention.– Less costly to operate.– Markets with lesser transaction volumes

have found it more efficient to adopt.• Disadvantages:

– The absence of developing market making (orders with no price limits).

– Difficulty in executing large trades.



Risks in Order-Driven and Price-Driven

• In Price-Driven, dealers stand a risk of being “picked up”.

• In Order-Driven, limit orders stand a risk of being “picked up”.



What about the NYSE?

• The NYSE has developed a hybrid market that combines traditional floor-trading and electronic auction trading.

• The automated platform is based on the Archipelago system.

• The electronic system allows one to find the best transaction price on the NYSE or elsewhere.

• BUT competing markets have developed in the USA, especially for large trades.



BUT competing markets have developed in the USA, especially for large trades.


What about Hong Kong? • In 1891 the first formal securities market, the Association of Stockbrokers

in Hong Kong, was established. A few decades later it was renamed the Hong Kong Stock Exchange (HKSE) or the Stock Exchange of Hong Kong (SEHK). A second exchange, the Hong Kong Stockbrokers' Association was opened in 1921. The two exchanges merged to form the Hong Kong Stock Exchange in 1947.

• The HKSE also merged with other four national exchanges in the end of the 20th century. The new exchange started trading through a computer-assisted system on 2 April 1986. The unified exchange had 570 participating organizations.

• In 1993, the Exchange launched the Automatic Order Matching and Execution System (AMS) that was replaced by the third generation system (AMS/3) in October 2000. The new system enabled the exchange participants to trade from their offices.

• The HKSE launched its traded stock options market in 1995. In 1999, the HKSE opened the Growth Enterprise Market (GEM) that made the access to the capital market easier for riskier businesses. Finally, the Stock Exchange of Hong Kong together with Hong Kong Futures Exchange Ltd. established in 1976 and Hong Kong Securities Clearing Company Ltd. incorporated in 1989 merged to form a unified company Hong Kong Exchanges and Clearing Limited (HKEx) in 2000.


Market Sizes of Stock Markets (in billion US$, End 2014, right column is “largest regional markets”)


Americas 30,269 NYSE 19,351 NASDAQ 6,979 Canada 2,093 Brazil 843 Mexico 480

Asia-Pacific 21,081 Tokyo 4,377 Shanghai 3,932 Hong Kong 3,233 Shenzhen 2,072 India 1,558 Australia 1,288 Korea 1,212 Taiwan 850 Singapore 752

Europe-AME 16,190 London 4,012 Euronext 3,319 Germany 1,738 Switzerland 1,495 Noridc 1,196 Spain 992 Johannesburg 933

Total 67,540

Evolution of Market Share

• Total World market cap end 2014: US$ 67 trillion• Total World market cap early 1975: US$ 1 trillion• Reached US$ 63 trillion end-2007• The relative market capitalization of national equity

markets has changed dramatically over time. • The share of the U.S. equity markets moved from two-

thirds of the world market in the early 1970s to only one-third by the early 1990s, when Japan had about the same market size as the United States.

• In 2014, American equity markets represented 45% of the world market cap, with Asia-Pacific accounting for approximately 31% and Europe 24%.


Cross-Holding: An Overevaluation of Market Cap

• Company A is founded with 100 shares worth 1.

• Company B is founded with 100 shares worth 1.

Total market capitalization is = 100 + 100

• Then, each company issue 100 new shares and swap them.

• So company A controls 50% of company B, and company B controls 50% of company A.

Total market capitalization = ?


Prof Bruno Solnik

Balance Sheet before new share issue

A Assets A Equity

100 100

B Assets B Equity

100 100

49

Prof Bruno Solnik

Balance Sheet after new share issue

A Assets A Equity

100200

Shares B:

100

B Assets B Equity

100200

Shares A:

100

50

Cross-holding artificially inflates market capitalization

• This is frequent in Asia (Korean Chaebol,

Japanese keiretsu, Family groups in HK, etc… )

• An adjustment has to be made by subtracting

crossholdings.

Adjusted free float = value of total outstanding

shares − value of shares held by other companies

of the Group


Cross-holding Adjustments – An Example

• Question

Company A owns 40% of Company B

Company B owns 30% of Company C

Company C owns 20% of Company A

Each company has a total market capitalization of 200 million. You wish to adjust for cross-holding to reflect the weights of these companies in a market weighted index. What adjustment would you make to reflect the free float?


Cross-holding Adjustments – An Example

• Solution:

The apparent market cap of these three companies taken together is 600 million.

But the “float” (shares available to investors outside the Group) of Company A should be reduced by the 20% held by Company C: 200 – 20% × 200 = 160

The adjusted market capitalization is:

160 + 120 + 140 = 420 million


Formula to compute Free Float

Adjusted free float = value of total outstanding shares in company i − value of shares held by other companies of the Group

• Examples:– Adjusted market value of company A

= 200 − 20% × 200 = 160– Adjusted market value of company B

= 200 − 40% × 200 = 120– Adjusted market value of company C

= 200 − 30% × 200 = 140


Liquidity

• Turnover ratio is computed as transaction volume relative to market capitalization.

• Sometimes called “share turnover velocity”.• Illiquidity tends to imply higher transaction

costs.• Depending on the years observed, comparison

of national market liquidity based on turnover ratio can lead to different conclusions.


Liquidity: Annual Turnover on Major Stock Markets

Turnover Ratio

0%

50%

100%

150%

200%

250%

300%


Concentration

• Investors need to know whether a national market is made up of a diversity of firms or concentrated in a few large firms.

• A market that is dominated by a few large firms provides fewer opportunities for risk diversification and active portfolio strategies.

• On the NYSE and Tokyo Stock Exchange, the top 10 firms represent less than 20% of total market cap.

• Conversely, in Switzerland, the top 10 firms account for approx. 70% of total market cap.

• In Finland, Nokia was larger than the sum of all the other Finnish companies.


Concentration: Share of the Ten Largest Listed Companies in the National Market

capitalization

0%

10%

20%

30%

40%

50%

60%

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80%

NY

SE

Japa

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Nas

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U.K

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Sw

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rlan

d

OM

X

Aus

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Ital

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Chi

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Kor

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Indi

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Tax Aspects

• Taxes can be applied in:– Investor’s country– Investment’s country– Transactions, capital gains and income

• The international convention on taxing income is to make certain that taxes are paid by the investor in at least one country, which is why withholding taxes are levied on dividend payments.

• Hong Kong does not have tax treaty with many countries, but that is changing.


Formula for Tax paid at home: Dividends

• Net dividend received in foreign currency

DR= Dividend per share in foreign currency × no. of shares × (1 − dividend withholding tax rate)

• Gross Taxable Dividend income to be declared at home

DI = Dividend per share in foreign currency × no. of shares × exchange rate

• Tax credit to be claimed at home:

TC = Dividend per share in foreign currency × no. of shares × exchange rate × withholding tax

• If t is your home tax rate on dividends, tax to be paid

= DI × t - TC


Formula for Tax paid at home: Capital Gains


• Capital gains are not taxed in foreign country• Capital gains in home currency

= Sale of shares in local currency − Purchase of shares in local currency

Apply your home capital-gain tax rate. Capital gains are not taxed in foreign country

Example

• The shares of Volkswagen trade on the Frankfurt stock exchange. A U.S. investor purchased 1,000 shares of Volkswagen at €56.91 each, when the exchange rate was €1 = $0.9790 (this is the value of one euro, or €/$, or $ per €). Three months later, the investor received a dividend of €0.50 per share, and the investor decided to sell the shares at the then prevailing price of €61.10 per share. The exchange rate was €1 = $0.9810. The dividend withholding tax rate in Germany is 15% and there is a tax treaty between the U.S. and Germany to avoid double taxation.

- How much did the U.S. investor receive in dividends in dollars, net of tax?

- What were the capital gains from the purchase and sale of Volkswagen’s shares?

- How would the dividend income be declared by the investor in the U.S. tax returns?


Solution1. Net dividend in Euros, after deducting withholding tax = €0.50

per share × 1,000 shares × (1 – 0.15) = €425. So, the net dividend in dollars = €425 × $0.9810/€ = $416.93.

2. The investor bought the shares for €56.91 per share × 1,000 shares = €56,910, or €56,910 × $0.9795/€ = $55,743.35.

The investor sold the shares for €61.10 per share × 1,000 shares = €61,100, or €61,100 × $0.9810/€ = $59,939.1.

Thus capital gains = 59,939.1 – 55,743.35 = $4,195.75.3. The investor would need to declare the total dividends, that

is, without deducting the withholding tax, as dividend income. So, the dividend income to be declared is €0.50 per share × 1,000 shares × $0.9810/€ = $490.50.

Note that because of the tax treaty between the U.S. and Germany, however, the investor can deduct from income tax a tax credit for the dividends withheld in Germany; the tax credit is 490.50 – 416.93 = $73.57. (The tax credit can be computed alternatively as €0.50 per share × 1,000 shares × 0.15 × $0.9810/€ = $73.57.)


Execution Costs

• Execution costs can reduce the expected return and diversification benefits of an international strategy.

• Best execution refers to executing client transactions so that the total cost is most favorable to the client under the particular circumstances at the time.


Execution Costs

• We can look at three costs (listed in order of decreasing reliability of estimation):– Commissions, Fees and Taxes.

• Explicit and easily measurable.– Market Impact.

• Dependent on order size, market liquidity for the security and the speed of execution desired by the investor.

– Opportunity Costs.• Loss (or gain) incurred as the result of

delay in completion of, or failure to complete in full, a transaction following an initial decision to trade.


Estimation and Uses of Execution Costs

• Global Surveys: These give market averages for a typical trade

in each country. Total execution cost is a function of

transaction size and market depth.• VWAP (volume-weighted average price):

The difference between the actual trade price and the VWAP benchmark price is an indication of execution costs.

• Implementation Shortfall: Difference between the value of the executed

portfolio (or share position) and the value of the same portfolio at the time the trading decision was made.


For “small” Orders

• Measure the bid-ask spread as quoted by Dealer or as implicit in the Order Book.

• Execution costs:– Commission & Tax – Half the bid-ask spread (assumes that the

“true” market value is the mid-point)


Prof Bruno Solnik

Execution Costs in Basis Points (2010)

0

10

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30

40

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80

Aus

tral

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Aus

tria

Bel

gium

Bra

zil

Can

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Chi

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Den

mar

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Fin

land

Fra

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Ger

man

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Hon

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Indi

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Indo

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Isra

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Ital

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Japa

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Sou

th K

orea

Mal

aysi

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Mex

ico

Net

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New

Zea

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Nor

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Pol

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Rus

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Sin

gapo

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Sou

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fric

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Sw

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Sw

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Tai

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Tha

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Tur

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Commissions Fees Market Impact

68

Using Expected Execution Costs

• The annual expected return net of execution costs is measured as:

Net expected return = E(R) − Turnover ratio × Execution costs


Impact of Execution Costs – an example

• Question: Basil Richards follows an active international asset allocation strategy and observes the following data. The average execution cost for a buy or a sell order is forecasted at 0.75 percent. The portfolio has a turnover ratio of 1.2 times a year. The annual expected return before transaction costs is 11%. What is the annual expected return net of execution costs?


Impact of Execution Costs – an example

• Solution:

Net expected return = E(R) − Turnover ratio × Execution costs

Net expected return = 11% − 1.2 × 1.5% = 9.2%


Bond Markets: for comparison purposes


World Bond Market

The World bond market is made up of three different types of markets:− Domestic Markets− Foreign bonds− International bonds (formerly known as

Eurobonds)


World Bond Market Capitalization (all maturities)

• Total market cap as of 2013: around US$ 90 trillion− National Markets (incl. foreign bonds): US$ 65

trillion − International bonds: US$ 25 trillion


Other Markets

• Derivatives: futures, forward, options• Alternative investments (detailed later)


Major Players

- Private investors- Institutional Investors- Investment Professionals


Private Investors


Number and Financial assets of HNWIs, 2014 World Wealth Report, CapGemini-RBC Wealth Management

• In 2014, there were some 14 million HNWIs (financial wealth over $1 million).

• Their wealth around $53 trillion.• Ultra-HNWIs (financial wealth over $30 million)

own some $17 trillion. They are 1% of the HNWI population but 35% of the wealth.

• The financial assets of high net worth individuals (HNWI) are huge and present an attractive market for investment professionals.

• Asia, Europe and North America have approximately equal wealth of 12 to 15 trillion. The rest is in the Middle East, Latin America and Russia.


Total Wealth of HNWI, CapGemini-RBC


Asset Allocation

• The investment behavior of individual investors is somewhat different from that of institutional investors described below.

• Individuals tend to invest relatively more in non-tradable assets such as real estate, hedge funds or structured products. But there are also marked differences in the profile and behavior of HNWI across regions.



HNWI’s Allocation of Financial Assets

Institutional Investors


Institutional Investors

• Mutual Funds (unit trusts)• Pension Funds (called Retirement Schemes,

MPF in HK)• Insurance Companies (Life and P&C)• Endowment and Foundation


Mutual funds

• Open-end funds (vast majority):– NAV– Redemption (different clauses, games)– Fees– ETF, see later

• Closed-end funds

See Global Investments


Pension Systems

• Various types:– PYG (pay as you go): current workers

contribute for benefits (pension) of current retirees.

– Capitalized: current workers invest (contribute) in savings (pension fund) that will pay benefits when they retire.


HONG KONG

• Two types of retirement schemes:- In December 2000 was launched a Mandatory

Provident Fund (MPF) system, providing retirement based on mandatory and voluntary contributions by employers. Around 40 MPF providers (schemes) with AUM over HK$540 billion in 2014.

- Prior to it, voluntary ORSO (Occupational Retirement Schemes Ordinance). Each scheme can be different. AUM around HK$290.

- There are some statutory pension or provident funds (civil servants, public school teachers,…).


Pension Funds• The investment approach of pension funds is

greatly affected by the way future benefits are planned.

• There are basically two plan types and a combination thereof:−A defined benefit pension plan (DB) which

promises to pay beneficiaries a defined income after retirement. The benefit depends on factors such as the workers’ salary and years of service.

−A defined contribution plan (DC) where the amount of contributions paid is set, usually as a percentage of wages, but future benefits are not fixed.


Pension Funds — Types

• In a traditional pension fund, all contributions are pooled and the total money is managed collectively. A board of Trustees sets the investment policy of the fund.

• A recent trend is to give more investment decision power to each employee. (E.g., 401(k) plans in the U.S., or MPF in HK)


Institutional Investors: Endowments and Foundations

• Concerned about total return in the long run.• Capital gains and income on the assets can be

used to meet budgetary needs.• Tend to have great investment freedom,

because they operate under few regulatory constraints.

• Often the most aggressive institutional investors, with many having extensive global and alternative investments.


Institutional Investors: Insurance Companies

• Collect premiums on life insurance and on property and casualty insurance, which are invested until claims are paid.

• Heavily regulated in each country and state in which they operate.

• Tend to adopt conservative investment policies.

• Tend to focus on fixed income assets, in order to assure their claim-paying ability.

• This is a financial intermediary with large AUM.


The Economics of an Insurance Company

• Business profits come from combined ratio:

• Financial profits come from return on invested premiums

Incurred Losses + ExpensesCombined Ratio

Earned Premiums=


Example of Zurich Group, in US$ billion, June 2007

Assets Liabilities Investment Portfolio 310 Equity 27 Other assets 64 Various obligations 348 Total 374 Total 374


A simple illustration of the importance of ALM

• Typical Balance Sheet with total assets & liabilities of 100.

• Investment portfolio of 75 made up of 15 in equity and 60 in bonds

• Shareholder’s equity 10


Prof Bruno Solnik

A simple illustration of the importance of ALM

94

Typical balance sheet1 of an insurance company(excluding unit-linked business)

• Asset Allocation: 20% Equities of Group Investments or 15% of total assets

• Interest Rate Mismatch

Modified Duration:- Fixed Income: 5 years- Insurance Liabilities: 7 years

25

70

10

20

60

15

100

Assets Liabilities

Shareholders’Equity

Gro

up Invest

ments

FixedIncome

InsuranceLiabilities

OtherAssets

OtherLiabilities

100

Equities

Reminder on Bonds and Duration

• There is an inverse relationship between the price of a bond and changes in interest rates.

• If the bond's cash flows are fixed, the price is solely a function of the market yield. Practitioners usually define interest rate sensitivity, or duration, as the approximate percentage price change for a 100 basis points (1%) change in market yield. Mathematically, the duration D can be written as:

where P/P is the percentage price change induced by a small variation r in yield.

rD

P

P


Negative equity markets can have a significant impact on shareholders’ equity


Typical balance sheet1 of an insurance company (excluding unit-linked business)

94

Assets Liabilities

94

Balance sheet1 after a 40% decrease in equity markets

25

70

10

20

60

15

100

Assets Liabilities


Gro

up Invest

ments

FixedIncome


OtherAssets

OtherLiabilities

100

Equities

-40%equities

1 Balance sheet on an economic basis

25

60

9

20

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In addition falling interest rates lead to a further deterioration of economic capital


25

80

9

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Balance sheet1 after a fall of interest rates by 2%

100

Assets Liabilities

100

Balance sheet1 after a 40% decrease in equity markets



OtherLiabilities

Gro

up Invest

ments

FixedIncome

OtherAssets

Equities

Assets Liabilities

9494

-2%interestrates

25

60

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20

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1 Balance sheet on an economic basis

First step is to model liabilities

• Depending on the type of contract (Life insurance, P&C, ...), the model can be quite different.

• While a Bond-like model is a first approximation for each type of liability, there are some optional contract clauses to be incorporated.

• Typically the liabilities can be summarized in a bond-like benchmark with some average duration. This will be the “risk-free” benchmark.


Insurance Company: Asset Allocation Optimization Principles

• Economic: We value assets and liabilities at market value and perform asset liability optimization.

• Accounting: Some securities are “held to maturity” and hence not marked to market. Present value of insurance liabilities are not frequently revalued. Hence a focus on the “accounting” net income from investments.

• Regulatory: Regulators have their own views of risk. They use (and so do insurance companies) Risk Based Capital.


Major Players: Investment Professionals


• Investment Managers• Brokers• Consultants and Advisers• Custodians


Investment Managers

• Range from the asset management department of banks to independent asset management boutiques specializing in offering specific investment products. Hedge funds are a recent breed of investment managers.

• Some asset managers cater to retail clients as well as institutional clients, while others serve the needs of one type of client.


Brokers

• Play an important role in terms of implementing security trades and in research of companies and markets.

• Sell-side analysts: work for brokerage firms and make recommendations to clients.

• All CFA® charter holders and CFA candidates must follow the CFA Institute® Code of Ethics and Standards of Professional Conduct, wherever they work and invest.


Consultants and Advisers

• Better known for their work with pension funds, but they also work with private clients and other types of investors.

• Play a major role in the asset management industry.

• Independent consulting firms have traditionally advised U.S. pension funds, while actuaries played a similar role in the U.K.

• Consultants also focus on services such as recommending asset allocation, selecting investment managers and monitoring performance, and giving tax and legal advice.

• Their most sensitive role is the process of selecting, hiring and firing external managers.


Custodians• Securities owned by investors are deposited

with a custodian, which often uses a global network of sub-custodians.

• Information technology is an important component of custodial services

• With the high development costs of software, many banks have sold their custodial activities, and further consolidation is expected in the future, because economies of scale can be significant in this business.


Prof Bruno Solnik

Key Takeaways: Major Markets and Players 1

• Financial markets are diverse. A good understanding of their mechanisms can help get better trading prices.

• Market Cap is important because many investors benchmark to market indices. Need to better understand free float.

• Execution costs are of great importance and should be focused on.

• Explained how global taxes work.

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Prof Bruno Solnik

Key Takeaways: Major Markets and Players 2

• Investors are diverse and we reviewed some of their asset allocation.

• To better understand how some institutional investors act, we spent time on one of the lesser-known but huge investor type, insurance companies. Stressed the importance of ALM

• This also provides a link to the next topic : asset allocation

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From Asset Allocation to Portfolio Management

• Equity• Fixed Income (Brief, see Module 6)


Global Equity Investment

I. Passive approach (ETF)II. Factor Models (Roll &

Ross, BARRA)

109Prof Bruno Solnik

Global Investment Philosophies

• An investment management organization must make certain major choices in structuring its global decision process, based on:

Its view of the world regarding security price behavior

Its strengths, in terms of research and management

Cost aspects

Its location and prospective domestic / global marketing strategy


From Passive to Very Active

Asset Allocation:• Strategic Asset Allocation• Active Asset Allocation (TAA)• Index Funds (ETF, trackers etc…)

Portfolio construction:• Managing/Selecting Risk Exposures• Looking for Alphas (individual

securities)• “Deals”


Prof Bruno Solnik

From Passive to Very Active

Portfolio Management is about taking risks:- Avoid bad risks- Diversify risks (free lunch)- Take some bets (good risks)

A passive index is usually assigned as benchmark. - Increase/reduce the risk exposure (betas) of

the portfolio opportunistically - Try to generate alphas by selecting

undervalued securities.

Note: We do not do company valuation here (see Module 6)

112112

Risk-Adjusted measure: Asset Allocation

• From an Asset allocation viewpoint, one looks at the total risk taken and compare return to a no-risk investment (risk-free asset).

• The total risk is simply the sigma (s) and the risk-adjusted return is the Sharpe ratio:

Where R0 is the risk-free rate.

0R R


Risk-Adjusted measure: Portfolio

• Looking at an asset class (say US equity), one looks at the risk taken relative to the benchmark (tracking error) measured as the standard deviation of excess returns.

• Then one compares the realized excess return over the risk taken (tracking error).

More in Class 6


I. Global Investment Philosophies: Passive Approach

• This approach simply attempts to reproduce a market index of securities (index fund approach).

• It is an extension of modern portfolio theory, which claims that the market portfolio should be efficient.

• The trend toward global indexing is strongly felt among institutional investors.


Global Investment Philosophies: Passive Approach

• Various indexing methods can be used:– Full replication– Stratified sampling– Optimization sampling– Synthetic replication


Index Funds

• Mutual Fund

• ETF (Exchange Traded Fund or Trackers). The big names are BlackRock (iShares), State Street Global Advisors (Spiders), Vanguard..

There are many ETF traded in Hong Kong, and Singapore or elsewhere.


Fund Management Fees

Investment companies charge fees, some as one-time charges and some as annual charges.

- For managed funds, loads are simply sales commissions charged at purchase (front-end) as a percentage of the investment. A redemption fee (back-end load) is a charge to exit the fund. Redemption fees discourage quick trading turnover and are often set up so that the fees decline the longer the shares are held (in this case, the fees are sometimes called contingent deferred sales charges). Loads and redemption fees provide sales incentives but not portfolio management performance incentives.


Fund Management Fees

Investment companies charge fees, some as one-time charges and some as annual charges.

- Annual charges are composed of operating expenses including management fees, administrative expenses, and continuing distribution fees.

- Typical example for active stock portfolio could be: Load of 3%, expense ratio of 1.5% (1% management fee, 0.25% administrative expenses, 0.25% distribution fee).


What are Exchange Traded Funds (ETFs)

• They are shares of a portfolio, not of an individual company.

• ETFs are index-based investment products that allow investors to buy or sell exposure to an index through a single financial instrument.

• The market maker commits to bid and ask prices around the index value. For active ETFs the bid-ask spread is small. (See detailed description in Global Investments textbook)


Exchange Traded Funds (ETFs)

• ETF is a special case of a fund that tracks some market index but that is traded on a stock market as any common share.



Exhibit 8.1 Creation/Redemption Process of Exchange Traded Funds

II. Factor Models

1 1 2 2 3 3 ...

is factor

is exposure to factor

k k

i

i

R f f f f

f i

i


• The factors are measured as the return on some index portfolio representative of the factor (“mimicking portfolios”). For example, the oil industry factor could be proxied by the return on a global stock index of oil firms. Various statistical techniques can be used to optimize the factor structure.


• The exposure can be assessed a priori by using information on the company studied. This usually leads to a 0/1 exposure. For example, Exxon would have a unitary exposure to the oil industry factor and zero exposures to all other industry factors, because it is an oil company.

• The exposure can be estimated using a multiple regression approach. The exposures would then be the estimated betas in a time-series regression.


• Macro factor: Roll-Ross APT

• Attribute factor: Barra


II a) Roll & Ross APT

- Confidence factor- Time horizon factor- Inflation factor- Business cycle factor- Market-timing factor


Roll & Ross (APT)

• Confidence factor (ƒ1).

This factor is measured by the difference in return on risky corporate bonds and on government bonds.

The default-risk premium required by the market to compensate for the risk of default on corporate bonds is measured as the spread between the yields on risky corporate bonds and government bonds. A decrease in the default-risk spread will give a higher return on corporate bonds and implies an improvement in the investors’ confidence level.


Roll & Ross (APT)

• Confidence factor (ƒ1) continued•

Confidence risk focuses on the willingness of investors to undertake risky investments. Most stocks have a positive exposure to the confidence factor (1 > 0), so their prices tend to rise when the confidence factor is positive (ƒ1 > 0).


• Time horizon factor (ƒ2)

This factor is measured as the difference between the return on a 20-year government bond and a one-month Treasury bill.

A positive difference in return is caused by a decrease in the term spread (long minus short interest rates). This is a signal that investors require a lesser premium to hold long-term investments.


• Time horizon factor (ƒ2) continued

Growth stocks are more exposed (higher 2) to time horizon risk than income stocks. The underlying idea is to view the stock price as the discounted stream of its future cash flows. The present value of growth stocks is determined by the long-term prospects of growing earnings while current earnings are relatively weak (high PE ratio). An increase in the market-required discount rate will penalize the price of growth stocks more than the price of value stocks.


• Inflation factor (ƒ3).

This factor is measured as the difference between the actual inflation for a month and its expected value, computed the month before, using an econometric inflation model.

An unexpected increase in inflation tends to be bad for most stocks (3 < 0), so they have a negative exposure to this inflation surprise (ƒ3 > 0). Luxury goods stocks tend to be most sensitive to inflation risk, whereas firms in the sectors of foods, cosmetics, or tires are less sensitive to inflation risk. Real estate holdings benefit from increased inflation.


• Business cycle factor (ƒ4).

This factor is measured by the monthly variation in a business activity index.

Business cycle risk comes from unanticipated changes in the level of real activity. The business cycle factor is positive (ƒ4 > 0) when the expected real growth rate of the economy has increased. Most firms have a positive exposure to business cycle risk (4 > 0). Retail stores are more exposed to business cycle risk than are utility companies, because their business activity (sales) is much more sensitive to recession or expansion.


• Market-timing factor (ƒ5).

This factor is measured by the part of the Benchmark total return (e.g. S&P 500 for US) that is not explained by the first four factors.

It captures the global movements in the market that are not explained by the four macroeconomic factors. The inclusion of this market-timing factor makes the CAPM a special case of the APT. If all relevant macroeconomic factors had been included, it would not be necessary to add this market-timing factor.


How to use Factor Models

• Factor models are linear. Hence the betas (exposures) of a portfolio are simply the weighted-average betas of the stocks in the portfolio

• The benchmark (market index) has some exposure to the various factors. A difference between the portfolio betas and the benchmark betas implies that the future return on the portfolio is going to be different from the return on the benchmark.

• A manager takes bets on the various factors to try to beat the benchmark.


Prof Bruno Solnik

A Simple ExampleRisk Factor Exposures

Tata Ltd Exposures SuperMark

Exposures S&P 500

Confidence Risk

0.7 0.1 0.3

Time Horizon Risk

0.8 0.9 0.6

Inflation Risk

-0.5 -0.1 -0.3

Business Cycle Risk

4.2 0.8 1.7

Market Timing Risk

1.5 0.6 1.0

1) Discuss the various exposure (start with S&P 500)2) What are the exposures of a portfolio invested half in Tata and half in

SuperMark.3) You believe that confidence and business activity will improve without

affecting inflation. Which company would you overweight?

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Prof Bruno Solnik

A Simple Example: solution 2) & 3)

Risk Factor Exposures Tata Ltd

Exposures SuperMark

Exposures Portfolio

Confidence Risk

0.7 0.1 0.4

Time Horizon Risk

0.8 0.9 0.85

Inflation Risk

-0.5 -0.1 -0.3

Business Cycle Risk

4.2 0.8 2.5

Market Timing Risk

1.5 0.6 1.05

3) If confidence and business activity will improve without affecting inflation, I should overweight Tata.

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II b) BARRA Models (BIM, etc…)

• World factor• Country factor• Industry factor• Style factor (Size, value, Momentum)

inspired by Fama and French model• Other factors (leverage, volatility)• Currency


Styles or Attributes

• Value stocks do not behave like growth stocks. A value stock is a company whose stock price is “cheap” in relation to its book value, or in relation to the cash flows it generates (low stock price compared to its earnings, cash flows, or dividends). A growth stock has the opposite attribute, implying that the stock price capitalizes growth in future earnings. This is known as the value effect.


Styles or Attributes

• Small firms do not exhibit the same stock price behavior as large firms. The size of a firm is measured by its stock market capitalization. This is known as the size effect.

• Winners tend to repeat. In other words, stocks that have performed well (or badly) in the recent past, say in the past six months, will tend to be winners (or losers) in the next six months. This is known as the momentum, success or relative strength effect.


Currency Factor

• See article FT: Multinationals drive US rally on weak dollar, Oct 2, 2007.“2007 will go down as the year the rest of the world saved America,” said Joseph Quinlan, chief investment strategist at Bank of America. “The belief that the dollar is going to weaken further is prompting investors to own int’l large-cap stocks.”…Companies with large overseas operations have been at the forefront of the rally. Since the Dow’s previous record – on July 19 – eight of the top ten performers have been multinational companies, led by P&G but also including Hewlett-Packard, Johnson & Johnson and McDonald’s.The weakness in the dollar, which has hit a series of all-time lows against major currencies, benefits multinational companies in two ways: it makes their US-made products cheaper on international markets and increases the dollar value of their overseas earnings.


A Hot Topic: Smart Beta

Smart Beta strategies attempt to deliver a better risk and return trade-off than conventional market cap weighted indices by using alternative weighting schemes (rules) based on measures such as volatility or various fundamental factors. Usually a very passive approach.

• The basic idea is that you can construct non-market-cap-weighted portfolio with better return and lower volatility than a typical market index.

• There are many variants of Smart Beta strategies from simple (equal-weighting) to complex (factor/fundamental investing). All require some periodic rebalancing (transaction costs) and do not work all the time.


Low Volatility is a typical strategy that avoid the index concentration in big cap stocks that induce high volatility. An equal-weighted index has lower volatility than a market-cap-weighted index. The claim is that such portfolio (with a bias toward small cap) delivers similar or better performance with less risk.

• One can go beyond equal-weighting to minimize volatility.• S&P DJ, Russell, MSCI, … all provide low volatility indices

and ETF have been created to match them. Invesco PowerShares are an example of the “intelligent” ETFs.

• Low volatility strategies have done quite well but have also underperformed during significant periods of time


Factor or Fundamental Investing allocates to various factors (value, size, momentum, Book Value, Free Cash Flow, Total Sales, Total Cash Dividend..) while controlling volatility.

• The claim is that you can generate better return/risk performance than a typical market-cap-weighted index or ETF.

• For example Research Affiliates provide a RAFI fundamental index used in FTSE RAFI Low Volatility and Russell Fundamental indices.

• This leads to a semi-passive approach tilting the portfolio away from market-cap indices based on factor exposures. But the exposures can be dynamically tilted.


Fixed Income Investment Management


• Yield curves• Yield play (ride,…)• Duration• Multi-currency• Dual currency, currency option



U.S. dollar Yield Curve, Summer 2007

0

1

2

3

4

5

6

3 M

on

th

6 M

on

th

2 Y

ea

r

5 Y

ea

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7 Y

ea

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10

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ar

20

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30

Ye

ar

Maturity (years)

Yie

ld i

n %

Prof Bruno Solnik

Interest Rate Forecast

• Remember the “duration” relation:

*PD r

P

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Interest Rate Forecast – Example

• On the U.S. dollar yield curve, the current (mid-2007) yields are 4.6% for both five-year and ten-year. You expect the yields to drop uniformly to 4.1% in the near future.

What should you do on your U.S. bond portfolio?


Prof Bruno Solnik

Interest Rate Forecast – Solution

• The approximate capital gain for both maturities are:

Five-year:

Ten-year:

5 ( 0.5%) 2.5%

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10 ( 0.5%) 5%

Interest Rate Forecast – Example

• On the U.S. dollar yield curve, the current (mid-2007) yields are 4.6% for both five-year and ten-year. You expect the yields to drop to 3.1% for 5-year and 3.9% for 10-year in the near future.

What should you do on your U.S. bond portfolio?


Prof Bruno Solnik

Interest Rate Forecast – Solution

• The approximate capital gain for both maturities are:

Five-year:

Ten-year:

5 ( 1.5%) 7.5%

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10 ( 0.7%) 7%


Exhibit 7.7: Yield curves in different currencies in 2007

0

1

2

3

4

5

63

Mo

nth

6 M

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2 Y

ea

r

5 Y

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7 Y

ea

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20

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30

Ye

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Maturity (years)

Yie

ld in

%

£

US$

Yen

Euro

Prof Bruno Solnik

Currency Forecast

• “Break-even” or “Implied” Forward exchange rate:

• Where:S is spot rate e.g. $1.5 per €Ft is the implied forward for

maturity tr is the interest rate for the quoted

currency (€), e.g., 4%r* is the interest rate for the

measurement currency ($), e.g., 5%

*(1 )

(1 )

tt

t tt

rF S

r

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Currency Forecast

• For one-year forward euro we get:

F = 1.5000 x (1.05)/(1.04) = 1.5144

• If euro is above $1.5144 a year from now, an investor in one-year euro bond is better off.

• If euro is below $1.5144 a year from now, an investor in dollar bond is better off.


Prof Bruno Solnik

Currency Forecast - Example

• For example, the 5-year yields given on the previous Exhibit are 4.6% in dollars and 1.25% in yen. The Spot exchange rate is ¥120 per $. The quoted currency is the $ and the measurement currency is the ¥. The implied 5-year forward exchange rate, or breakeven exchange rate, is equal to:

• Which amounts to a 15% depreciation of the dollar.• If your expectations for the next 5 year is that the

dollar would depreciate by more than 20%, then Yen bonds look attractive. But bonds in other currencies could look even more attractive.

* 5

5

(1 ) (1.0125)120 101.98

(1 ) (1.046)

tt

t tt

rF S

r

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Prof Bruno Solnik

Key Takeaways: Portfolio Management

• Portfolio Management is about taking risks:- Avoid bad risks- Diversify risks (free lunch)- Take some bets (good risks)

• A passive index is usually assigned as benchmark. - Increase/reduce the risk exposure (betas) of the

portfolio opportunistically - Try to generate alphas by selecting undervalued

securities.• To manage an equity portfolio, one uses a factor

model (BARRA, Sungard APT, Axioma, Northfield,…). • Factor models are either ‘macro factors’ model or

‘attribute factors’ models, or some (difficult) mix.

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Prof Bruno Solnik

CLASS 3Should We Hedge Currency

Risk in Global Asset Management ?

162

Prof Bruno Solnik Prof Bruno Solnik

Structure

1. Some General Considerations

2. Hedging with Currency

FUTURES/FORWARD

3. Optimal Currency Hedging

4. The Contribution of Behavioral Finance

5. Currency Overlay Managers

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Prof Bruno Solnik

1. Currency Risks: Some General Considerations

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Prof Bruno Solnik

Currency risk can be significant in the short run.

- For example, an American investor who decided not to hedge currency risk would have incurred a currency loss of some 40% on its eurozone assets from late 1998 to late 2000.

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Prof Bruno Solnik

Currency risk can be significant in the short run.

Let’s look at a Japanese investor:

- The dollar was 260 yen per dollar 20 years ago, 85 ten years ago, 135 early 2002, 75 in late 2012, 115 in Nov 2014.

- The euro was introduced in 1999 at 130 yen, two years later it was down to 90 yen, went to 167 in July 2007, 100 in late 2012, 144 in Nov 2014.

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Prof Bruno Solnik Prof Bruno Solnik167

Prof Bruno Solnik

Currency Risks

• There are many current and expected variables (Purchasing power, deficits, interest rates, growth, politics...) that influence exchange rates at different times.

• Short term variations of exchange rates are extremely hard to predict.

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My Model for the ¥/€ Exchange Rate

0 Yen / € log ty

tX Z e dt

Xt is the number of bottles of Cognac drunk in Tokyo at time t

Z is the number of tries scored by the Japanese team in the Rugby World Cup

yt is the probability of a typhoon in Japan, divided by the probability of an earthquake in Europe

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Prof Bruno Solnik

• Currency changes are quite volatile.• Currency risk can be cheaply hedged.• Currency risk is relatively small in well-

diversified global equity portfolios. But very high in global bond portfolios.

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Prof Bruno Solnik

Unrelated Parenthesis:

My Personal thoughts on the euro

Prof Bruno Solnik171


Currency Considerations• The return and risk of an asset depend on the currency

used. For example, the dollar value of an asset is equal to its local currency value (V ) multiplied by the exchange

rate (S) (number of dollars per local currency):

• The rate of return over the period is:

where

R = return in local currency

s = percentage exchange rate movement

*V V S

*R R s R s R s


Illustration

• You are US investor and invest $20,000 in British equity. The exchange rate is 1£ = $2.

• The British market goes up by 10% and the new exchange rate is 1£ = $2.1 (5% appreciation of the £).

• What is your return in $?


British market goes up 10% and £ goes up 5%

Return

The new value is $23,100

or a dollar return of 15.5% =

(23,100 – 20,000)/20,000

The rate of return is 15.5% =

10% (capital gain in £)

+ 5% (currency gain on initial capital)

+ 0.5% (currency gain on capital gain)


Prof Bruno Solnik

2. HEDGING with CURRENCY FUTURES/FORWARD

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Table of Content

• Definition• Quotation• Gain/Loss at maturity• Valuation Principles• Use in Hedging a Portfolio

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Definition

A Forward or Futures contract is a commitment to purchase (buyer) or deliver (seller) a specified quantity of an underlying asset on a designated date in the future, for a price (“futures/forward price”) determined competitively when the contract is transacted.

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Prof Bruno Solnik

Definition

For example, suppose that today’s spot exchange rate is S = 1 dollar per euro.

An investor could buy forward 100,000 euros for delivery on December 10, at a Forward price F = 1.01 dollars per euro.

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Prof Bruno Solnik

Forward and Futures Contracts

• FORWARD contract: A private contract between two parties (one is usually a bank). Nothing happens till maturity. A margin is usually deposited.

• FUTURES contract: A standardized contract transacted on a futures exchange. Standardized in terms of size, delivery date. With a marking-to-market procedure.

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Prof Bruno Solnik Prof Bruno Solnik181

Prof Bruno Solnik

Quotation

• Simply quote the Futures/Forward price

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Prof Bruno Solnik

Gain/loss at Maturity: Straightforward

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Valuation Principles

• The Futures price F is linked to the Spot price S by arbitrage.

• The “cost of carry” of the arbitrage is simple.

• Example:

S = 1 dollar per euro

R$ = 5%

R€ = 4%

F = ?

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Prof Bruno Solnik


Example:

S = 1 dollar per euro

R$ = 5%

R€ = 4%

F = ?

185

$

€

1 1.051 1.0096 dollars per euro

1 1.04

rF S

r

Prof Bruno Solnik

Use in Hedging

• The “naïve” approach is simply sell the foreign currency for an amount equal to the portfolio position in the foreign currency.

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Hedged Portfolio - Example

An Italian investor owns a portfolio of U.S. stocks worth US $10 million. The current spot rate and one-month forward exchange rates are €1 per $. Interest rates are equal in both countries. The investor sells forward $10 million to hedge currency risk because he is concerned about the outcome of the US elections. A week later, the US stock portfolio has gone up to $10,350,000, and the spot and forward exchange rates are now €0.94 per $. Analyze the return on the hedged portfolio.

187



• The U.S. stock portfolio went up by 3.5%, but the dollar lost 6 percent relative to the euro. If the portfolio had not been hedged, its return in euros would have been:

10,350,000 0.94 10,000,000 12.71%

10,000,000 1

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Prof Bruno Solnik


As per equation 11.3, the profit on the hedge portfolio in euros is:

Profit = 10,350,000 x 0.94 – 10,000,000 x 1 – 10,000,000 x (0.94 – 1)

Profit = 329,000

The rate of return on the hedged portfolio is 329,000/10,000,000 = 3.29%

Or we could directly apply Equation 11.4:Return = – 2.71% + 6% = 3.29%

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Prof Bruno Solnik

3. Optimal Currency Hedging: The traditional

approach (MV)

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Minimum-Variance Hedge Ratio

• One objective is to search for minimum variability in the value of the hedged portfolio.

• Investors would like to set the hedge ratio, h, so as to minimize the variance of the return on the hedged portfolio.

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Minimum Variance Hedge Ratio

Where R* = rate of return on the original portfolio (unhedged)

RF = % times change in futures price , approximately equal to exchange rate variation = s

REMEMBER: Here * means in the investor’s currency, no * means in the asset local currency.

* ( ) (1 )H FR R h R R s h s R h s

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Derivation of Optimal Hedge Ratio

Minimize relative to h

Hence

𝑑𝜎𝐻2

h𝑑=−2 (1−h )𝜎𝑠

2 −2𝑐𝑜𝑣 (𝑅 ,𝑠)=0

h=1+𝑐𝑜𝑣 (𝑅 ,𝑠 )

𝜎 𝑠2

Prof Bruno Solnik

Minimum Variance Hedge Ratio

The minimum-variance hedge ratio is equal to:

where

translation risk hedge is:

economic risk hedge is:

The optimal hedge ratio is sometimes called the regression hedge ratio

194

h=1+𝑐𝑜𝑣 (𝑅 ,𝑠 )

𝜎 𝑠2

h1=1

h2=𝑐𝑜𝑣 (𝑅 ,𝑠 )

𝜎 𝑠2

Prof Bruno Solnik

Translation Risk

• Translation risk comes from the translation of the value of the asset from the foreign currency to the domestic currency.

• A hedge ratio of 1 will minimize translation risk.

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Prof Bruno Solnik

Economic Risk

• Economic risk comes when the foreign currency value of a foreign investment reacts systematically to an exchange rate movement.

• If an investor worries about the total influence of a foreign exchange rate depreciation on her portfolio value, measured in domestic currency, she should hedge both translation and economic currency risk.

196


Economic Risk

• The hedge ratio required to minimize economic risk can be estimated by:

• This is the slope that we would get on a regression of the foreign currency return of the asset on the exchange rate movement.

2

),cov(

s

sR

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Prof Bruno Solnik

Illustrations

• Individual firms• Stock indexes developed• Stock indexes emerging• Bonds

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Prof Bruno Solnik

A Global Survey of Institutional Investors

What is the typical currency hedging benchmark of institutional investors?

- Very diverse!

199


Distribution of Accounts by Base Currency and Hedge Ratio Russell Mellon

Hedge USD AUD YEN EUR GBP Others Total0% 113 36 13 26 17 13 21850% 111 31 15 10 2 20 189

100% 37 3 14 11 3 12 80Others 43 14 1 5 5 8 76Total 304 84 43 52 27 53 563

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

USA(304)

Australia(84)

Japan(43)

Euro (52)

U.K.(27)

Others(53)

Total(563)

Others

100%

50%

0%

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4. The Contribution of Behavioral Finance

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Behavioral Finance: The Early Days

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Behavioral Finance

• It has long been recognized that a source of judgment and decision biases is that cognitive resources such as time, memory, and attention are limited. Since human information processing capacity is finite, there is a need for imperfect decision-making procedures, or heuristics, that arrive at reasonably good decisions cheaply.

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Behavioral Finance

• However, there are other possible reasons for systematic decision errors. Feeling or emotion-based judgments can explain mood effects (market sentiment).

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Behavioral Finance: Examples

Overreaction A cognitive bias (investor overreaction to

a long series of bad/good news) could produce predictable mispricing of stocks; DeBondt and Thaler (1985).

ExtrapolationInvestors use past performance as an indicator of future performance in mutual fund and stock purchase decisions; Sirri and Tufano (1998), Grinblatt et al. (1995), Carhart, (1997).

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Behavioral Finance: Examples

Overconfidence Individuals trade too much,

overconfidently thinking that they can pick winners, whereas the stocks they buy do worse than the stocks they sell; Odean (1998, 1999), Barber and Odean (2000).

Disposition effectInvestors are reluctant to sell losers (and mentally “declare” the loss), even though tax considerations should make them prefer selling a loser to selling a winner; Shefrin and Statman (1985), Odean (1998).

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Reactions to Behavioral Finance

Traditional Finance Professor

It is a collection of ad-hoc stories. Small anecdotes of little general value.

Psychology produces too many answers and no theory.

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Reactions to Behavioral Finance

PractitionersIt is not really useful. Cannot make money on anomalies:- Many “anecdotes” apply to minuscule

market value.- all attempts on “January effect”, “day of

the week effect”, etc, have been unsuccessful.

- For example, private investors are overconfident, so what!

Does not tell me how to structure a portfolio. Little implications for investment choices.

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Regret Theory

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Nobel Prize Thinking

“I should have computed the historical covariance of the asset classes and drawn an efficient frontier. Instead I visualized my grief if the stock market went way up and I wasn’t in it-or if it went way down and I was completely in it. My intention was to minimize my future regret, so I split my [pension scheme] contributions 50/50 between bonds and equities.”

- Harry Markowitz.As quoted in Jason Zweig, "How the Big Brains Invest at TIAA-CREF", Money, 27(1), p114, January 1998

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Regret

• Regret is defined as a cognitively-mediated emotion of pain and anger when, with hindsight, we observe that we took a bad decision in the past and could have taken one with better outcome. Ex post, one compares the investment outcome with the best outcome that could have been achieved.

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Regret

• Contrary to mere disappointment (prospect Theory), which is experienced when a negative outcome happens relative to prior expectations, regret is experienced relative to the best outcome of alternative choices that could have been made (foregone alternatives).

• As the opening quote suggests, the anticipation of future regret was strong enough to turn Harry Markowitz away from his very own portfolio allocation theory when faced with a financial decision on his pension plan.

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Regret (2)

• Regret is very present in life (“missed opportunities”)

• Regret influences investment choices. We look at the performance of peers (competitors). It is more than looking at passive benchmarks.

• As stressed by Statman (2005), currency hedging is a dimension where regret clearly applies.

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Prof Bruno Solnik

Currency Hedging is a Dimension where Regret Applies

The euro was introduced in 1999 at 130 yen, two years later it was down to 90 yen, went to 167 in July 2007, 100 in November 2012, 144 in Nov 2014.• For example, a Japanese investor who

decided not to hedge currency risk would have incurred a currency loss of some 30% on its eurozone assets from 1999 to 2001, with a vast regret of not having fully hedged.

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Currency Hedging is a Dimension where Regret Applies

• Conversely a fully-hedged Japanese investor would have missed the huge appreciation of the euro from late 2001 to late 2007. Again, a vast regret of not having taken the "right" hedging decision (90 to 167).

• But an unhedged Japanese investor would have lost a huge amount on the currency side from 2007 to 2012.

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The 50% Hedging Rule is Not New Among Investment Managers

"A partial hedging policy – such as 50/50 or 70/30 – means the investor won’t ever experience the major highs of an unhedged portfolio, but won’t be subject to the lowest returns either.“

"To Hedge or not to hedge", Simon Segal, SuperReview.com.au, 21 march 2003

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"The 50% hedge benchmark is gaining in popularity around the world as it offers specific benefits. It avoids the potential for large underperformance that is associated with "polar" benchmark, i.e. being fully unhedged when the Canadian dollar is strong or being fully hedged when it is weak. This minimizes the "regret" that comes with holding the wrong benchmark in the wrong conditions.“

"Managing Currency Risk: A Canadian Perspective", Gregory Chrispin, State Street Global Advisor, Essays and Presentations, March 23, 2004.

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• The 50% hedge ratio is the simplest currency hedging policy that attempts to deal with regret.

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Prof Bruno Solnik

• In a recent paper (Michenaud-Solnik, 2008), we apply regret theory to the determination of optimal currency hedging. This is a tough mathematical task.

• Investors care about the portfolio expected return and volatility (as in mean variance) but also about expected regret.

• We find optimum hedging depending on the level of risk aversion and of regret aversion of the investors.

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• 100%• - regret term• + speculative term• + covariance term

With large regret aversion, the optimal hedge ratio nears 50%.

But regret aversion does not necessarily dominates traditional risk aversion.

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In Practice: Use the Model to Derive Optimal Hedging

- Expected currency return (currency risk premium?)

- Correlation between asset and currency return

- Regret aversion compared to risk aversion

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Using Currency Options

• Currency options allow to « insure » the portfolio rather than « hedge ».

• But there is the cost of the premium.

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Key Takeaways: Currency Hedging

• Using currency futures/forward to hedge is easy.• The “naïve” approach is simply to sell the foreign

currency for an amount equal to the portfolio position in the foreign currency (hedge ratio = 1 or 100%).

• The minimum-variance hedge ratio takes into account translation risk (hedge ratio of 1) but also economic risk (the sensitivity of the local-currency asset price to exchange rate movements).

• Investors have very different hedging policy. So there is not obvious one-fits-all optimal policy.

• Regret theory is often used for currency hedging decisions.

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Module 4 – Prof Bruno Solnik 224

The Eurozone Crisis and Implications for Investment ManagementSome Provocative Views

• This is not a Euro crisis but a Eurozone crisis• Financial markets and Politicians have different

objective functions• A fixed exchange rate system is explosive as shown

historically• Past research has shown that brutal medicine is often

better than lingering sickness • There are REAL problems and NOMINAL ones. The

Eurozone has primarily real problems.• In a crisis, there is always some serious underlying

cause but it needs a trigger:– 2007-2008: too much leverage in households and banks;

trigger: subprime. – 2011-2012: too much leverage of governments; trigger: Greek

creative accounting.


What Determines Exchange Rates• Real Aspects (competitiveness)

– Purchasing Power Parity (CPI, unit labor costs)– Current Account – Expected growth

• Nominal Aspects– Monetary policy

• Investments Aspects– Financial attractiveness (return and risk)



The Euro is not under gigantic speculative pressure

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Current Eurozone: 17 out of 27 EU countries


Austria Italy Belgium Luxemburg Cyprus Malta Estonia Netherlands Finland Portugal France Slovakia Germany Slovenia Greece Spain Ireland

Fixed parity: History• Historically, a regime of fixed exchange rate has

always been unsustainable because the speculative tensions and moral hazard built into the system.

• The system is asymmetric. Small countries must be stronger than big countries. But that has a cost too (Hong Kong)


What is specific to the Eurozone• There is a fixed parity with strong disparity among

countries. • Following the introduction of the euro, some countries

(esp PIIGS) got huge subsidies 1) from EU and 2) from increased borrowing capacity (who wants to lend in risky escudos or drachmas?).

• But rather than seizing this opportunity to engage in structural reforms to lift the country to international standards and competitiveness, several countries got into free spending.

• This was aggravated by the politicians’ plans to offset the 2008 credit/liquidity crisis resulting in wild spending.

• The “trigger” was the discovery of Greek creative accounting.

Note that each country has some specific problems (e.g. Spain engaged in huge real estate bubble sponsored by regions, cities and banks)


Real Problems: Competitivity


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Situation is not really improving Eurozone-wide

• France current account deficit in 2011: $55 billion• France current account deficit in 2012: $63 billion• France current account deficit in 2013: $59 billion

• Germany current account surplus 2011: $224 billion• Germany current account surplus 2012: $239 billion• Germany current account surplus 2013: $257 billion

• But situation is somewhat slowly improving in Southern Europe.


Real Problem: Down to Earth

“A decade ago, France was more price-competitive than Germany; today it is the other way around. That's evident in the macroeconomic numbers as well as on the ground. France used to produce as much asparagus as Germany, but these days Germany cultivates more than four times as much. Labor is the biggest cost in the asparagus business, and German seasonal workers cost half as much as their French counterpart."

Time magazine, 16 July, 2012, page 27.


How can a country remain competitive when it borrows @ 3% when others @ 1% and a debt level above 100% of GDP


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Government 10-year bond yield 30 January 2015

Eurozone Yield

Germany 0.3%

France 0.5%

Italy 1.6%

Spain 1.4%

Netherlands 0.4%

Portugal 2.6%

Greece 10.8%


Other Aspects: Monetary Policy and Financial Attractiveness• Eurozone countries have no monetary independence.

So they cannot adjust disparity among member countries by monetary policy.

• If you want to invest in Euro, would you consider investing in countries like Greece or Portugal given the social unrest and the risks involved? Hence such countries have both a current account deficit, because they are not competitive, and a potentially-large financial account problem that will not offset the current account deficit as in the U.S. case.


How can the PIIGS problems be solved• Devaluation and foreign debt restructuring, leading to

inflation and domestic debt devaluation (deemed politically impossible: Eurozone).

• Default (called debt restructuring) without devaluation (politically difficult and creates problems for banks, reduces past debt but not current or future needs).

• Belt tightening and structural solutions (long-term solution, burden is borne unevenly, local politics make it very difficult if not impossible: no government can survive on this program).

• Non-PIIGS taxpayers keep financing PIIGS (the easy politician’s solution: thank you Germany, thank you ECB).


The structural problems are not fully addressed because:

1) politicians are politicians guided by elections not the long-term good.

2) very painful to do structural adjustments very fast; a devaluation is so much easier. Past research has shown that brutal medicine is better than lingering sickness

3) So resort to tricks (ECB buys sovereign bonds and finance banks to take them). EuroBonds with guarantee from all Eurozone governments….

4) Without severe structural changes, the sickness will linger for many years. The major adjustment can be through deflation. But how popular is reducing drastically pension benefits, civil servant wages,… Drastic reforms are not compatible with political will and electoral cycles in Southern countries.


• Implosion (divorce)

• Lingering sickness (prozac)


Implications for Financial Markets :Two Scenarios

Foreign Exchange• The Eurozone will implode or linger sick. The sooner it

implodes the better (I wish they had done it early 2010 rather than wasting trillions). Several countries (many) will leave the euro and only the strong Northern countries (and some satellite) will keep it.

• A devaluation of some of Eurozone countries is the least-bad solution to the real problem, not the cause of the problem

• The uncertainty will be bad for the euro exchange rate.• But only the strong countries will retain the euro, so its

fundamental value should increase.• Unless South keeps the euro and North the DM.• The question is what will happen to the existing sovereign

debt (restructuring?). And the private debt?


Financial markets: Bonds• Before the euro implosion

– Bond yield will rise in most countries (e.g. France). But how can you sustain such huge differential in financing cost with Germany. The trigger of the euro implosion might be some elections somewhere. Triggers are hard to predict. Could happen in Greece, Portugal, Spain, Italy, France…

– Many government bonds are more risky than corporate bonds. But only large corporations have access to the bond market; smaller corporation have difficult time borrowing from banks, adding to the recession. There is no corporate/loan bond market in Europe like in the US and European banks are deleveraging.

– One has to be very selective with sovereign and credit exposure


• After the euro implosion– There will be more “emerging” currencies and

huge spreads.


Financial markets: Equity

• A divorce is usually very messy. Prozac is no better.• Recession can be bad in many European countries

and will affect the rest of the world to some extent.• But many real assets will retain real value.• A short-lived crisis addressing fundamentals is better

than being on Prozac while the problems get worse and worse (note that Greece still borrows @10%).

• Governments will have learnt to be more thrifty, although new politicians will quickly forget and politicians’ objective function will remain the same.


Europe Stocks vs U.S. Stocks, past 5 years


One has to be selective• Exposure to the European “political” risks vary

greatly among European companies.• Some sectors are more exposed than others• Some European companies have less European

exposure. In the short run they followed the market index. In the long run their profits will be quite different.

• Example of Peugeot vs BMW• There are no fire sales, but…


Prof Bruno Solnik Module 4 – Prof Bruno Solnik

CLASS 4:OPTIONS IN INVESTMENT

MANAGEMENT

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Module 4 – Prof Bruno Solnik

INSURING with OPTIONS

I. The Basics: Insuring with Options

II. Use of Options

III. Using Options to Manage Currency Risk

IV. Currency overlay

V. Introduction to Structured Products

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I. The Basics of Options (reminder)

• Definition• Quotation• Gain/Loss at maturity• Valuation Principles• Use in Insuring a Portfolio

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Definition

In general, an option gives the buyer the right, but not the obligation, to buy or sell an asset, and the option seller must respond accordingly. Many types of option contracts exist in the financial world. The two major types of contracts traded on organized options exchanges are calls and puts.

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Definition

A call gives the buyer of the option contract the right to buy a specified number of units of an underlying asset at a specified price, called the exercise price or strike price, on or before a specified date, called the expiration date or strike date.

A put gives the buyer the right to sell a specified number of units of an underlying asset at a specified price on or before a specified date.

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Definition

In all cases, the seller of the option contract, the writer, is subject to the buyer’s decisions, and the buyer exercises the option only if it is profitable to him or her. The buyer of a call benefits if the price of the asset is above the strike price at expiration. The buyer of a put benefits if the asset price is below the strike price at expiration.

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Wonderful!!!!!!!!!!

The buyer of an option can only win and never loses!

- Example of a car insurance

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Quotation

• The terms of the option are FIXED

• Quote the Option Price or Premium

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Gain/Loss at Maturity

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• The Premium p is linked to the Spot price S by arbitrage.

• The Premium p is equal to the intrinsic value plus the time value.

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Call Option Intrinsic Value, as a Function of Asset Price (S)

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Call Option Intrinsic Value, as a Function of Asset Price (S)

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Determinants of Option Premium

• Asset Price relative to Strike Price• Volatility • Time to expiration• Interest rate(s)

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II. Use of Options

• Speculation (with limited risk)• Insuring a portfolio

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Example of Speculation with Futures on HSI

• Futures on HSI, multiplier HK$10 IndexThis is Mini-HSI contract. Full is HK$50 times index• Quote for December Futures is 30,000. • ASSUME that the margin is set at

HK$15,000 per contract (1,500 per index).You believe that the market will go down.- What can you do using HSI futures? - Look at the result for ONE contract, if the

HSI is equal to 40,000; 35,000; 30,000; 25,000; and 20,000 in December.

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Example of Speculation with Futures on HSI

• Short futures

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HSI Gain / Loss

40,000 -100,000

35,000 -50,000

30,000 0

25,000 50,000

20,000 100,000


Example of Speculation with OPTIONS on HSI

• OPTIONS on mini-HSI, multiplier HK$10Index

• HSI is at 30,000• December CALL at the money

(K=30,000) quote at 2,000 per index.• December PUT at the money (K=30,000)

also quote at 2,000 per index.

You believe that the market will go down.

- What can you do using HSI options?- Look at the result for ONE contract, if

the HSI is equal to 40,000; 35,000; 30,000; 25,000; and 20,000 in December.

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Example of Speculation with OPTIONS on HSI

• Long put

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HSI Gain / Loss

40,000 -20,000

35,000 -20,000

30,000 -20,000

25,000 30,000

20,000 80,000


Insuring a Portfolio: Example of Stock Portfolio

A portfolio manager has an allocation of €4 million to French equity. The French portfolio is well diversified and tracks the local CAC stock index. The manager believes that the French market offers excellent returns prospects. However, the manager is worried that French elections taking place next month (April) could lead to a severe market correction. Although the probability of such an outcome is quite small, the manager wishes to insure against it. The current value of the CAC index is 4,000. Futures on the CAC with maturity in June also trade at 4,000.

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Put options with maturity in June trade as follows:

Strike Price Premium (€ per unit of index)

3,900 30

4,000 100

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CAC options and futures have a multiple of €10 times the index. Thus, the total premium for one put with exercise price €3900 is 30 x €10 = €300, for example. The manager hesitates between selling 100 futures contracts, buying 100 puts with a strike of 3,900, or buying 100 puts with a strike of 4,000.

1. Calculate the outcome of each strategy if the CAC is equal to 3,500, 4,000, or 4,500 at expiration of the contracts in June.

2. Recommend a strategy to the portfolio manager.

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Solution

1. The value of the portfolio under the various strategies is given below:

Value of CAC at expiration

Initial Portfolio (No Futures or Options)

Portfolio Hedged with Futures

Portfolio Insured with Puts 3,900

Portfolio Insured with Puts 4,000

3,500 3,500,000 4,000,000 3,870,000 3,900,000

4,000 4,000,000 4,000,000 3,970,000 3,900,000

4,500 4,500,000 4,000,000 4,470,000 4,400,000

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Solution

2. Hedging with futures provides the best protection in case of a drop in the market, but it deprives the manager of any profit potential. Buying puts provided protection in case of a market drop while keeping most of the upside potential (the put premium is deducted from the portfolio value). Given the manager’s expectations, buying puts is a natural strategy. Out-of-the-money puts are cheaper, so they are more attractive in case of an up-movement, but offer less protection in case of a down-movement. To get the best downside protection while retaining upside potential, the portfolio manager should buy 100 puts with a strike price of 4,000.

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III. Insuring Currency risk with Options

The difficulty with currency option is to pick the correct option as an exchange rate implies two currencies.

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An Example

You are a U.S. investor holding a portfolio of European assets worth €1 million. The current spot exchange rate is $1=1 euro but you fear a depreciation of the euro in the short term. The three-month forward exchange rate is $0.9960 = 1 euro. You are quoted the option premiums for calls euro and puts euro with a three-month maturity. These are options to buy (call) or sell (put) on euro at the dollar exercise price mentioned for each option. The contract size on the CME is €125,000.

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Another Example

The quotations are as follows:

Euro Options (All Prices in U.S. Cents per Euro)

Strike Call Euro Put Euro

105 0.50 6.50

100 2.10 3.00

95 6.40 0.50

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Another Example

You decide to use options to insure your portfolio.

1. Should you buy (or sell) calls (or puts)? What quantity?

2. You decide to buy at-the-money options (strike price of 100 U.S. cents) for €1 million. Suppose that you can borrow the necessary amount of dollars to buy these options at a zero interest rate. Calculate the result at maturity of your strategy, assuming that the euro value of your portfolio remains at €1 million.

3. You have the choice of three different strike prices. What is the relative advantage of each option? What is the advantage relative to hedging, using forward currency contracts?

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Solution

1. To insure, you need to buy options. Here, you want to be able to translate euros at a fixed exchange rate, so you should buy euro puts for €1 million, or eight contracts.

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Solution

2. You buy at-the-money puts on €1 million. The cost (premium) is equal to €1,000,000 x $0.03 / € = $30,000

• If the euro rises in value, the put will expire worthless.

• If the euro depreciates, you gain exercise the put and get $1,000,000 minus the option premium of $30,000, or $970,000.

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Solution

The simulation of the dollar value of the position for a different value of the exchange rate at maturity is given in the first column of the following table. The portfolio is insured for down movements in the euro and benefits from up movements. But the cost of the insurance premium has to be deducted in all cases.

Exchange Rate at Maturity (US cents per Euro)

Using Puts 100

Using Puts 105

Using Puts 95

Hedging with Forward

110 1,070,000 1,035,000 1,095,000 996,000

105 1,020,000 985,000 1,045,000 996,000

100 970,000 985,000 995,000 996,000

95 970,000 985,000 945,000 996,000

90 970,000 985,000 945,000 996,000

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Solution

3. The preceding table simulates the results of using the various options as well as the forward. An “expensive” option (in-the-money, put 105) gives better downside protection at the expense of a lesser profit potential in case of an appreciation of the euro. A “cheap” option (out-of-the-money, put 95) provides less downside protection but a larger profit potential. Using forward contracts freezes the value of the portfolio at $996,000. You are well protected on the downside, but you cannot benefit from an appreciation of the euro.

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Solution

You will decide on the strategy, depending on your scenario for the euro exchange rate. If a depreciation of the euro seems very likely, you will hedge; if a depreciation seems very unlikely, you will buy out-of-the-money options, which are the cheapest. The other two strategies lie in between.

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General Comment

To find the exchange rate that will be relevant when insurance is needed (option exercised) you compute the “all-in-cost/revenue”:

1. If the direction of quotation requires to buy a put, the relevant exchange rate (‘you receive’) is:

Strike price – put premiumIn the example you receive an exchange rate of

0.97

2. If the direction of quotation requires to buy a call the relevant exchange rate (‘you pay’) is:

Strike price + call premium



IV. Currency Overlay Managers

• Delegation of Currency Position: Management of Currency Risk Profile

• Currency as an Asset Class

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Management of Currency Risk Profile

• Technical Approach

• Fundamental Approach

• “Currency for alpha” funds

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V. Using Structured Products in Global Asset Management

1. A Deal: Example of LTCM-UBS

2. Structure Notes

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1. Example of LTCM-UBS

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2. Other Example: Structured Notes

A structured note is a bond issued with some unusual option-like clause. These notes are bonds issued by a name of good credit standing and can therefore be purchased as investment-grade bonds by most institutional investors, even those that are prevented by regulations from dealing in derivatives. Another attraction for investors is that these structured notes offer some long-term options that are not publicly traded. Structured notes with equity participation are in strong demand in many countries, especially in Europe, where they are sometimes called guaranteed notes.

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Guaranteed notes with equity participation are bonds having guaranteed redemption of capital and a minimum coupon; in addition, some participation in the price movement of a selected index is offered if this price movement is positive.

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An Example

For example, let’s consider a two-year note that guarantees

the initial capital (redemption at 100%) plus an annual

coupon of 3 percent and offers a 50 percent participation

rate in the percentage price appreciation in the Japanese

Nikkei index over the two years. At time of issue, the yield

curve was flat at 8 percent. The 50 percent participation

rate works as follows: If the stock index goes up by x

percent, the investor will get 50 percent of x. For example, if

the Nikkei stock index goes up by 30 percent from the time

of issue to the time of redemption, the option will yield a

profit of 15 percent and the bond will be redeemed for 115

percent. The participation rate is, in effect, the percentage

of a call option on the index obtained by the investor.

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In summary, the structured note can be viewed by investors as the sum of

- a straight bond with a coupon of 3 percent- plus 50 percent of an at-the-money call

option on the Nikkei

• All of these bonds can be analyzed as the sum of a straight bond with a low coupon plus an option play

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Problem

1. Value the call option implicit in the bond.

2. Assume that you offer a similar bond but with a coupon set at zero. What is the equity participation that you could offer?

Consider the guaranteed note on the Nikkei described in the text:

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Solution Question 1.

• The present value of the straight bond is

• Because the bond is issued at 100 percent, the implicit value of 50 percent of a call option on the Nikkei is therefore equal to

• And the implicit value of 100 percent of one call option on the Nikkei index is equal to

84.1708.911002

( )2

3 10391 08

1 08 1 08P .

. .= + = ,

92.808.91100

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Solution Question 2.• There is clearly a negative relation between the amount of

the guaranteed coupon and the participation rate that can be offered in the option. A structured note with a zero coupon will leave more money to invest in the call option:

• The difference between the redemption value and the current market value of the zero-coupon bond (14.27% = 100 85.73) can be invested by the issuer in call options. The number of call options that can be purchased is equal to the participation rate that is set in the structured note. In the example, one call option on the Nikkei index is worth 17.84, and 14.27 is available to invest in options. Hence, this allows a participation rate of:

instead of 50 percent, as above.

( )2

0 10085 73

1 08 1 08P .

. .= + = ,

14 27 17 84 80. / . = ,

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Illustrative Example Customer takes a bullish view on EUR and believes EUR/USD will increase from 1.2800 to 1.3350 or above after 6 months.

• Type of Investment: European Bullish (EUR /USD)

• Principal Guarantee %: 100%

• Deposit Currency: HKD

• Principal: HKD 100,000

• Deposit Period: 6 months

• Trigger Level: EUR/USD 1.3350

• Potential Return Rate (if any): 2.50% (around 5.0%p.a.)

• Minimum Return Rate: 1.25%(around 2.5%p.a.)

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In the above example, total return at maturity is calculated as follows:

Scenario at Maturity Total Return at Maturity

Scenario 1 - Movement of EUR is the same as customer’s anticipation On the Final Exchange Rate Determination Date, the Final Exchange Rate of EUR/USD is 1.3510 (i.e. above or equal to the Trigger Level)

Guaranteed Principal x (1 + Potential Return Rate) = HKD100,000 x (1+ 2.50%) = HKD102,500.00

Scenario 2 - Movement of EUR is different from customer’s anticipation On the Final Exchange Rate Determination Date, the Final Exchange Rate of EUR/USD is 1.3250 (i.e. below the Trigger Level)

Guaranteed Principal x (1 + Minimum Return Rate) = HKD100,000 x (1+ 1.25%) = HKD101,250.00

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CPI: Bullish on EUR

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How can we Offer (Construct) such a CPI?

298


Bearish on EUR

299


Modest bullish/bearish AUD

300


Key Takeaways: Insuring with Options

• Options on an index can be used to speculate, up or down, with limited risk.

• Options on an index can be used to insure a portfolio against market risk.

• To insure you always need to BUY an option, not sell (write) an option. Writing options is reserved to specialist traders.

• Insuring with an expensive (in the money) option provides good protection against adverse movements but with a cost, hence reduces profit potential.

• Insuring with a cheap (out of the money) option provides less protection against adverse movements but with a lower cost, hence better profit potential.

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Key Takeaways: Currency Options

• The difficulty with currency option is to pick the correct option as an exchange rate implies two currencies.

• To find the exchange rate that will be relevant when insurance is needed (option exercised) you compute the “all-in-cost/revenue”:

1. If the direction of quotation requires to buy a put, the relevant exchange rate (‘you receive’) is:

Strike price – put premium

2. If the direction of quotation requires to buy a call the relevant exchange rate (‘you pay’) is:

Strike price + call premium

302


Key Takeaways: Structured products

• Options are extensively used in large “deals”.

• Structured products using optional features are (still)

extensively used for retail and institutional clients.

• They can be decomposed as a mixture of zero-coupon

bonds and options.

303

CLASS 5ALTERNATIVE INVESTMENTS

- Alternative Investments- Private Equity, Hedge Funds

- LTCM

304

Alternative Investments

• Many kinds, have in common relative illiquidity:

– Real Estate– Venture Capital, Private Equity– Distressed securities– Commodities– Anything

305

Private Equity(very brief,

see other Modules)

306

Private Equity

• Private equity investing has grown rapidly in the 2000s.

• Private equity investments are equity investments that are not traded on exchanges.

• The limited partnership is called the “Fund”.

• General partners are sometimes designated as the “Management Company”.

307

Private Equity

• There are three main categories of private equity:

– Venture capital– Leverage buyout– Distressed investing

308

Private equity – Leveraged buyout investing

• The largest category of private equity

• Investors put up an equity stake (20-40%) and borrow the rest.

• Company is then taken private. Private equity firm then gets involved in the management of the acquired company and takes steps to increase its value.

• The objective is to resell the company a few years later at a higher price.

309

Hedge Funds

310

• Definition• Legal structure• Type of strategy• Fee structure• Funds of funds• The pros and cons • Index / performance

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Hedge Funds: Definition

• Huge Industry:

– The 1990s witnessed rapid growth in hedge funds.

– In 2007, assets under management surpassed $2 trillion.

– In 2007, the number of hedge funds exceeded 13,000.

– In 2008, AUM peaked to $2.5 trillion, then dropped sharply late 2008/mid 2009. Recovered a bit late 2009.

– As of End-2014, AUM $2.85 trillion for Hedge funds (including 0.45 for FoFs).

312

Hedge Funds: Definition

• Today, funds using the “hedge fund” appellation follow all kinds of strategies and cannot be considered a homogeneous asset class.

• Hedge funds can be defined as:

– Funds that seek absolute returns– Having a legal structure that avoids

some government regulations– Have option-like fees, including a base

management fee and an incentive fee proportional to realized profits.

313

Hedge Funds

• Hedge fund managers can create leverage in trading by:

1) Borrowing external funds to invest more or sell short more than the equity capital that they put in.

2) Borrowing through a brokerage margin account

3) Use of financial instruments and derivatives.

314

Legal Structure in US

• The legal structure of a hedge fund largely depends on who its investors will be. For example, a private investment vehicle formed for the benefit of persons who reside outside of the United States will be organized differently than an investment vehicle formed for the benefit of United States residents.

315


• Domestic US: A Limited partnership (LP) where investors are limited partners and the manager is General partner. Under Investment Act, no more than 100 investors, and no public solicitation

316


• International: For the purpose of managing the assets of persons residing outside of the US, and also tax-exempt US investors, an offshore fund is ordinarily structured as a corporation and organized in a tax haven jurisdiction (e.g. Bermuda, British Virgin Islands, Cayman Islands, Ireland).

317


Often, the manager of an offshore fund forms a corporate entity to provide advisory services to the fund. This entity serves as the investment manager of the fund. If the hedge fund manager already manages the assets of a domestic partnership through a single corporate entity, the general partner of the partnership may also serve as the investment manager of the offshore fund.

318

Prof Bruno Solnik

Master Feeder Structure (“hub and spoke”)

- “Feeder” refers to the legal structure used.

- The master fund is generally an offshore fund

319

Types of Investment Strategies

• Classifications are arbitrary and vary across data providers.

• Hedge funds can be classified as:– Long/short– Market neutral– Fixed income– Global macro

• Emerging market funds• Managed futures funds

– Event driven• Distressed securities funds• Risk arbitrage in M&A

320

Long / Short

Long/short funds are the traditional type of hedge funds, taking short and long bets in common stocks. They vary their short and long exposure according to forecasts, use leverage, and now play on numerous markets throughout the world.

321

Long / Short

These funds often maintain net positive or negative market exposures; so they are not necessarily market-neutral. In fact, a subgroup within this category is funds that have a systematic short bias, known as dedicated-short funds, or short-seller funds.

The distinction with traditional funds is getting blurred, as some mutual funds offer a 130/30 strategy (or 120/20 etc..). And some hedge funds started to compete with similar products.

322

Example: Long / Short

A hedge fund has a capital of 10 million and invests in a market neutral long/short strategy on the British equity market.

323


Shares can be borrowed from a primary broker with a cash margin deposit equal to 18% of the value of the shares. Given the high level of cash margin, no additional costs are charged to borrow the shares. The hedge fund has drawn up a list of shares regarded as undervalued (list A) and a list of shares regarded as overvalued (list B). The hedge fund expects that shares in list A will outperform the British index by 5% over the year, while shares in list B will underperform the British index by 5% over the year.

324


The hedge fund wishes to retain a cash cushion of 1 million for unforeseen events. What strategy would you suggest?

325

Answer

The hedge fund would sell short shares from list B and use the proceed to buy shares from list A for an equal amount. Some capital needs to be invested in the margin deposit. The hedge funds could take long/short positions for 50 millions:

326

Answer

• Keep 1 million in cash

• Borrow 50 million of shares B from a broker,

• Deposit 9 million in margin (18%50 million),

• Sell shares B for 50 million in cash,

• Use the sale proceeds to buy 50 million worth of shares AThe positions in shares A & B are established so that the portfolio’s beta is close to zero. The ratio of invested assets to equity capital is roughly 5:1.

327

Answer (2)

If expectations materialize, the long/short portfolio of shares should have a gain over the year of 10% on 50 million whatever the movement in the general market index. To be market neutral, the fund would aim for a beta of zero.

This 5 million gain will translate into an annual return before fees of 50% over the invested capital of 10 million.

328

Answer (2)

This calculation does not take into account the return on invested cash (1 million) and assumes that the dividends on longs will offset dividends on shorts.

329

Market Neutral hedge funds

• Market-neutral funds are a form of long / short funds that attempt to be hedged against a general market movement. They take bets on valuation differences of individual securities within some market segment.

330

Market Neutral hedge funds

• Long / Short equity funds are a form of market neutral funds. But there are all kinds of market neutral strategies, mostly based on some form of arbitrage:

– equity long/short – fixed-income hedging,– pairs trading,– warrant arbitrage,– mortgage arbitrage,– convertible bond arbitrage, – closed-end fund arbitrage, and– statistical arbitrage.

331

Example : Merger Risk Arbitrage

A merger has been announced between a French company A and a German company B. A will acquire B by offering one share of A for two shares of B.

332

Example : Merger Risk Arbitrage

Shares of B were trading in a €15 to €20 range prior to any merger discussion. Shares of B currently trade at €24, while shares of A trade at €50. The merger has been approved by both boards of directors but is awaiting ratification by all shareholders (that is extremely likely) and approval by the EU commission (there is a slight risk because the combined company has a large European market share in some products). How could a hedge fund take advantage of the situation? What are the risks?

333

Answer

• The hedge fund should construct a hedged position where it buys two shares of B for every share of A that it sells short. As the proceeds of the short sale of one share of A (€50) can be used to buy two shares of B (€48), the position can be highly leveraged. Of course the cost of securities lending and margin deposit should also be taken into account. When the merger is completed, the hedge fund will make a profit of approximately 2 euros for each share of A.

334

Answer

• The risk is that the merger will be cancelled. It is hard to tell what will be the stock price reaction to this announcement, but it is clear that the stock price of B will drop more, because it was to be acquired at a price well above its pre-merger market value. That would mean a sizable loss for the hedge fund.

335

Fee Structure

• Total fee = Base (fixed) fee + Incentive (performance) fee

• Typically 2% (fixed) plus 20% (performance).

• The calculation of performance fee varies and is somewhat complicated because of “high watermark”.

336

Funds of Funds

• Definition: Funds of funds (FOF) have been created to allow easier access to small investors, but also to institutional investors. A FOF is open to investors and, in turn, invests in a selection of hedge funds.

• Additional fee: typically 1% and 10%, on top of the hedge funds fees (typically 2% and 20%).

337

Fund of Funds – Advantages

• Retailing• Diversification• Managerial expertise• Due diligence process (but is it really

done?)

338

Fund of Funds – Disadvantages

• Potentially high fees• Little evidence of persistence performance• Absolute return loss through diversification

339

The Pros and Cons of Hedge Funds

• Major Pro: – Hedge Funds attract talent.

• Major Con: – Hedge Funds can be more risky than

they claim.

340

Hedge Funds – Pros

• Hedge funds mostly search for absolute returns, not alphas.

• Much more flexible than traditional asset management.

• You invest in “strategies” not “asset classes”.• Correlation with traditional asset classes likely

to be low.• In bull markets, hedge funds are likely to do not

as great; but would fare better in down markets.

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Performance of Hedge Funds

342

Hedge Funds – Cons (Risks)

• The unique risks of hedge funds include:– Liquidity risk– Pricing risk– Counterparty credit risk– Settlement risk– Short squeeze risk– Financing squeeze risk

343

Impact of the financial Tsunami• Many hedge funds use highly-leveraged strategies. The credit

market closed in 2008. Given the high volatility, prime brokers dramatically increased the amount of required collateral. It is improving.

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Hedge Fund Index/database

• There are a number of indexes that track the hedge fund industry. The list of hedge fund index providers is long:

- Specialized hedge fund firms (such as HFR, Van Hedge, Hennessee, Greenwich)

- Banks such as Barclays or Dow Jones Crédit Suisse

345


• Index providers (such as MSCI, S&P, FTSE), and even universities (CISDM, EDHEC) offering dedicated hedge fund indexes.

These indexes are also broken down in subindexes for various classifications of hedge funds according to the investment strategy they follow. But the classifications vary across providers.

346


The launching date of these indexes differs markedly. Some were launched in the 1990s, others in the 2000s. In some cases, the historical value of the index was back-calculated to an earlier date, with the risk of only including surviving hedge funds and biasing the performance upward.

347

Biases in Reported Performance

• Investors should exercise caution when using historical track record of hedge funds in reaching asset allocation decisions.

• The biases present in performance reporting:– Self selection bias– Instant backfilling bias– Survivorship bias on return and risk– Smoothed pricing on infrequently traded assets– Option-like investment strategies– Fee structure-induced gaming

348

51

Key Takeaways: Alternative Investments

• Alternative Investments are characterized by illiquidity.• Funds using the “hedge fund” appellation follow all

kinds of strategies and cannot be considered a homogeneous asset class.

• They have an option-like fee structure with a fixed fee plus a performance fee with some high-water mark.

• Hedge funds are characterized by the strategy they follow.

• Many hedge funds resort to leverage, sometimes high leveraging.

• Risks are not easy to assess because of illiquidity (stale pricing) and “non-normal” strategies followed.

349

Value at Risk (VaR)

Module 4 − Prof Bruno Solnik 350

Value at Risk

• Motivation and Definition• Measurement of VaR• Some important assumptions• Too good to be true!


Motivation

• A single, summary, statistical measure of possible portfolio losses resulting from “normal” market movements.

• Losses greater than VaR are suffered only with a specified small probability

• Once one crosses the hurdle of using a statistical measure, the concept of VaR is straightforward to understand.


Definition

• VaR is the loss that is expected to be exceeded with a probability x percent and a holding period of t days.

• x is typically 1%, 2 ½% or 5%

• t is typically one day, one week or one month.


Definition

• If x = 1 percent, one assumes that only 1% of market fluctuations are “abnormal”. The maximum loss in “normal” market conditions is therefore equal to VaR.

• hence there is a 99% chance of losing less than VaR.

• Note however, that there is a 1% chance of losing more, even much more, than VaR.


Measurement of VaR

• Delta-Normal• Historic• Monte Carlo Simulation

While the degree of sophistication varies (modeling complex securities/arbitrage,..), all methods basically rely on some assumptions about sigmas and correlations.


Simple Relations under Normality

• VaR(5%) = 1.645 - E(R)

• VaR(1%) = 2.326 - E(R)

• VaR(1%) 1.414 VaR (5%)

• VaR(T days) T VaR(1 day)However, note that the expected value is multiplied by T while the standard deviation only by T .



-6 -4 -2 0 2 4 6-1,645

Beyond VaR:Tails and Stress-Testing


VaR is grossly misunderstood

• VaR only deals with normal risks• VaR is not the maximum loss that can be incurred. It

is the maximum loss under “normal” market conditions.

• A major risk is what happens in “abnormal” market conditions.


Stress Testing

• What is it?• What scenario to use?• We always fight the last war.


Daily VaR (1%) and Trading Revenue of BNP Paribas

(annual report 2007, in 000€)


Daily VaR and Trading Revenue of BNP Paribas (annual report 2007, in 000€)

• The green line reports daily trading revenue. The grey line reports daily VaR estimated at 1%.

• If the model is good we expect that daily losses exceed VaR in 1%250days = 2.5 days.

• Actual number is 3 days, so model looks good.• But with the financial tsunami, market conditions became

“abnormal” in 2008.



Lessons from the Crisis and new Research in Risk Management

• Academic research is often presented as one of the guilty party of the current crisis.

• Financial economics is primarily about concepts. One major conclusion is that excess return cannot be generated without taking systematic risk, risks that CANNOT be diversified away.

• Financial mathematics is another branch of modern finance originating in option pricing and dynamic hedging. It developed powerful models. In particular they assume that markets are liquid with continuous prices. Parameters of the processes must be estimated using past and present data. Even if future volatility can be inferred from current option prices, the assumption is that this volatility estimates are good estimates of future volatility. In turn, these models are used to implement sophisticated risk management systems.


Lessons from the Crisis and new Research in Risk Management

• Over time finance has become more mathematics and less economics. In itself such a trend is not bad, but increased model sophistication gives a false sense of security and makes models appear as infallible black boxes. It is sad to see that many concepts such as VaR and risk management are poorly understood by board of directors and top management of financial institutions, rating agencies or regulators.

Lessons from Crises• Market crash of 1987

– Illiquidity can fail models badly– estimated parameters such as delta/hedge ratio can be very wrong ex_post,

especially with disruptions in market volatility.

• Demise of LTCM in 1998– Illiquidity can fail models badly– All models are primarily based on past data (possibly adjusted); estimated

parameters can be very wrong ex-post especially with disruptions in market volatility.

– Correlation is extremely important in risk management. Market crashes can lead to extreme rise in correlation across all markets.

• Financial Tsunami of 2007/2008– Illiquidity can fail models badly– All models are primarily based on past data (possibly adjusted); estimated

parameters can be very wrong ex-post especially with disruptions in market volatility.

– Correlation is extremely important in risk management. Market crashes can lead to extreme rise in correlation across all markets.


Implication of Recent Market Situation• Illiquidity: implies serial correlation (big losses

followed by big losses)• Periods of high volatility: amplitude of

Profit/Losses increases because higher sigma.• Return distributions are not unconditionally

normal: Fat tails, etc…• High correlation across assets: amplitude of

Profit/Losses increases, because no diversification of risks


Daily VaR and Daily Realized Profit & Loss


The Case of SocGen 2008 (Annual Report)

• Daily VaR at 99% implies that in a year, the daily loss should exceed VaR around 2 or 3 days per year (1% of 250 trading days). In 2008, it happened 26 days.– Periods of high volatility– Illiquidity induced serial correlation– Dramatic increase in correlation across markets/asset

classes (loss of diversification benefits) has an huge impact on P&L


Example of the Impact of Correlation Rise

• One trade of 100, with daily of return 1%, VaR at 99% is 2.326 (Investment × × 2.326)

• Ten uncorrelated trades (r = 0): then daily of return 0.316%, VaR at 99% is 7.35 (Investment × × 2.326 = 1000 × 0.316% × 2.326 = 7.35, not ten times 2.326)

• Assume that Correlation is actually One between the ten trades. Then daily of return 1% (no diversification benefits), VaR at 99% is 23.26 (ten times 2.326, the VaR of each project).

• Further assume that markets volatility has doubled to a daily 2%. VaR at 99% is 46.52 (1000 × 2% × 2.326).– VaR rise from 7.35 to 46.52.


Recent Academic Research (very partial)• I believe that we focused too much on modeling individual

asset prices/risks, and not enough on modeling correlation (except on CDOs).

• “Extreme Value Theory” brings useful contribution.• A seminal paper: "Extreme Correlation of International Equity

Returns ", F. Longin and B. Solnik, Journal of Finance, April 2001.

• Yes, extreme events are rare, but there are techniques that allow to get better estimations and models of correlation during crises. That is a very fruitful area of research.

• Risk managers live in the « fat tails » and they also need quantitative tools in those fat tails. Common sense is needed to « fly » the starship in this space, but that is not enough, you also need instruments.


Final Words

• I also believe that education has badly failed.• Risk management models are based on assumptions

and estimated parameters. When these assumptions (illiquidity) and parameters (past data not good estimates of future) fail, one needs to adapt very quickly.

• Institutions where risk management was a “culture” and top management was well “educated” fared much better than others.

• The mission of researchers is not only to build further black boxes, but also, and maybe more importantly , educate the whole institutions (from traders/asset managers to top management) in terms that they can understand.

• There is no alternative to quantitative techniques.


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risk optimization

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