diversifying risks with hedge fundshedge-fund-analysis.net/media/docs/fmb_riskdiversify_1006.pdf ·...

1

Diversifying Risks with Hedge Funds

presented to the Graduate School of Business of the

University of Stellenbosch

in partial fulfilment of the requirements for the degree of

Master of Business Administration

by

FLORIAN BÖHLANDT

Supervisor: Prof. Niel Krige Date: 31 July 2006

2

Diversifying Risks with Hedge Funds Assignment for Portfolio Management

STUDENT NUMBER : 14959747

SURNAME: BOEHLANDT INITIALS : FMB

TELEPHONE NUMBER: 072 270 9058

SUBJECT: Portfolio Management

NUMBER OF PAGES (INCLUDING THIS PAGE) 21

LECTURER: Prof. Niel Kriege

COURSE: MBA FULL-TIME 2006

DUE DATE : 23/10/2006

CERTIFICATION

I certify the content of the assignment to be my own and original work and that all sources have been accurately reported and acknowledged, and that this document has not previously been submitted in its entirety or in part at any educational establishment.

Florian Böhlandt

VIR KANTOORGEBRUIK / FOR OFFICE USE

DATUM ONTVANG:

DATE RECEIVED :

Table of Contents

1 Hedge Funds – An introduction .................................................................................4

2 Investment Styles ........................................................................................................5

2.1 Global Macro ...........................................................................................................6

2.2 Long-Short Equity ....................................................................................................6

2.3 Managed Futures ......................................................................................................7

2.4 Event Driven ............................................................................................................8

2.5 Distressed Securities .................................................................................................8

2.6 Merger Arbitrage ......................................................................................................8

2.7 Equity Market Neutral ..............................................................................................9

2.8 Convertible Bond Arbitrage ......................................................................................9

2.9 Fixed Income Arbitrage ............................................................................................9

3 Diversification of Market Risks ............................................................................... 10

3.1 Interest Rate Risks .................................................................................................. 10

3.2 Pricing Risks .......................................................................................................... 11

3.3 The Theory of Portfolio Diversification .................................................................. 11

4 Portfolio Diversification with Hedge Funds .......................................................... 13

4.1 Diversifying Equity Portfolios ................................................................................ 13

4.2 Diversifying Bond Portfolios .................................................................................. 16

4.3 Exchange rate related Risks .................................................................................... 19

5 Measuring the Risks of Hedge Funds ...................................................................... 19

5.1 Non-normal probability distribution ....................................................................... 19

5.2 Disrupting effects of time series analysis ................................................................ 20

5.3 Changing market correlations ................................................................................. 20

5.4 Performance history and statistical inference .......................................................... 21

6 Concluding Remarks ................................................................................................. 21

7 List of Sources ............................................................................................................ 23

Diversifying Risks with Hedge Funds University of Stellenbosch

4

1 Hedge Funds – An introduction

Hedge Funds are generally regarded as high risk investment opportunities that can yield

exceptional returns on investment. Hedge Funds offer absolute positive returns even in

bearish markets. The name ‘Hedge’ Funds, however, is somewhat of a misnomer. In fact,

rather than hedging the investor’s risk exposure, Hedge Funds use derivatives and

leverage to enhance their performance. Historically, alternative investment funds

(Hedge Funds, Private Equity, and Venture Capital) displayed a low or negative

correlation with traditional investment opportunities. This report tries to show that

Hedge Funds can be used, in accordance with Sharpe’s Capital Asset Pricing Model, to

limit the overall risk exposure of a combined portfolio whilst increasing the return on

investment (Schneeweis, 1998).

Hedge Funds differ substantially from non-alternative investments. Funds managers use

derivatives to hedge their position and generate additional returns, borrow money to

leverage the performance, and usually avoid disclosing information about asset

allocation and performance (most Hedge Funds are located in countries such as the

Cayman islands with favourable legislation concerning auditing and reporting standards

of funds). The unique structure of alternative investment funds has led to the perception

of many private and corporate investors that hedge and private equity funds are high-

risk profile investments, utterly unsuited to be combined with conservative portfolios.

The demise of the Long-term Capital Management Fund (LTCM) in 1998 has made

investors suspicious about Hedge Funds and their alleged superior performance. A

number of professional investment banks such as Union de la Banque de Suisse (UBS)

and Dresdner Kleinwort Wasserstein lost millions of their investment in LTCM. Private

investors have become more reluctant to invest directly into Hedge Funds due to feeble

reporting standards and a generally low understanding about the inner workings of

alternative investments. In addition, private and corporate investors may not be allowed

to allocate money to Hedge Funds due to local legislation (a number of European

countries require extensive reporting standards to allow pension funds and insurance

companies to invest into these funds). High initial investments and lock-down periods

pose an additional hurdle for private investors.


5

Whilst little doubt exists about the relatively high volatility of Hedge Funds returns, one

should not assume that alternative investments offer unfavourable risk-return profiles.

In fact, the unique structure of hedge funds allows them to achieve better risk adjusted

returns as traditional investment funds (as measured by Sharpe’s ratio). Because of

manager’s high degree of flexibility in allocating the fund’s money, Hedge Funds were

able to accomplish exceptional returns in downward markets. Traditional funds

measure their performance against a benchmark (usually equity or bond indices such as

the Dow Jones Industrial Average or Eurostoxx 50). Their within lies the problem with

traditional investment funds. In downward markets, managers are able to outperform

their benchmark by realizing a negative fund performance. Hedge Funds aim at

producing absolute positive performance, regardless of the current market situation.

Hedge Funds managers are usually rewarded with a variable performance bonus

depending on the absolute positive performance of the managed fund compared to the

previous year’s performance. High-water marks guarantee that fund managers

compensate for losses realized in a given year before receiving the performance-related

component of their fees. It has been argued that Hedge and Venture Capital funds

increase market efficiency and improve the functioning of international bond and equity

markets.

As this introduction shows, Hedge and Private Equity Funds differ significantly from

traditional investments (hence the name ‘alternative’ investments). Statistical evidence

suggests that alternative investments can offset the risks associated with investing into

traditional equity and bond portfolios, whilst increasing the overall performance. We

will try to demonstrate this relationship empirically during the course of this report. In

order to improve the understanding of Hedge Funds, the subsequent sections explain 9

unique investment styles (strategies) managers employ to generate exceptional returns.

2 Investment Styles

One can distinguish between 9 different styles of hedge funds. Although the investment

strategies are not exclusive, most managers choose to follow only one or two styles.

Generally speaking, Hedge Funds follow one of two basic strategies: Directional or Non-

Directional. Directional funds (Global Macro, Long-Short Equity, and Managed Futures)

are dependant on the development of the overall equity and bond markets. Non-

directional funds (Event Driven, Distressed Securities, Merger Arbitrage, Equity Market


6

Neutral, Convertible and Fixed Income Arbitrage) generally follow a market neutral

approach (Lavinio, 2000). The fund’s investment focus on equity, fixed interest

securities, derivatives, commodities or currencies allow for a further differentiation.

2.1 Global Macro

Along with Long-Short Equity strategies, Global Macro strategies were amongst the first

Hedge Funds styles that emerged. Global Macro funds invest in all kinds of financial

instruments. In addition to long investments into equities, Global Macro funds use

derivatives such as options and futures on currencies, interest rates and equity indices

to limit their risk exposure. In addition, these funds invest into distressed securities, try

to realize profit from merger arbitrage, or allocate money into Private Equity Funds.

Hence, Global Macro funds represent the most holistic form of Hedge Funds.

Global Macro managers try to predict macroeconomic developments and to assess their

influences on international equity and bond markets (‘top-down’ strategy). Thanks to

their substantial size, Global Macro funds can utilize market inefficiencies quicker than

other market participants. In many cases, Global Macro funds reach a critical size (such

as George Soros Quantum Fund) to allow them to directly influence and manipulate

different markets. Emerging Market funds are a special category of Global Macro funds.

Their investment focus lies with emerging and developing countries. Managers of

Emerging Market funds try to identify and invest into equities that have been

historically undervalued. When macroeconomic developments in emerging markets (e.g.

a more favourable legislative and economic policy) cause these investments to

appreciate, the strategy was successful. Currency funds, on the other hand, invest

exclusively into foreign exchange (interest options, currency futures, carry trades and

currency swaps).

2.2 Long-Short Equity

Long-Short Equity managers try to identify and buy undervalued shares whilst short-

selling overvalued shares within the same industry (‘pair trade’). Managers utilize a

historical performance analysis to identify shares that have outperformed their

benchmark index in the past (‘bottom-up’ strategy). When managers choose to

distribute their funds equally amongst long- and short strategies, the Hedge Fund can be

seen as factor neutral. In theory, managers can diversify away the entire market risk. In

reality, however, most Long-Short Equity funds are ‘Equity-Non-Hedge’ Funds that


7

employ a hedge ratio of below 100%. Conversely, the smaller proportion of managers

follows a short or short-only strategy. ‘Equity-Hedge’ managers invest the larger part of

their funds in hedging derivatives such as futures and options (‘hedge overlay’). In

downward markets, gains form short-positions overcompensate for the funds exposure

to long equities. Hence, Equity Hedge funds are able to achieve a smoother return on

investment compared to traditional investments. Dedicated Short Bias strategies focus

exclusively on equity options, short-selling and forward contracts. During the bullish

equity markets of the 1990’s, however, this form of short-only investment has almost

disappeared. Similar to Global Macro funds, Long-Short strategies can be further

subdivided into their geographic focus (e.g. emerging markets). Successful managers of

Long-Short Equity Funds usually have exceptional experience and skills in the market

they operate in. Long-Short Equity Funds are, on average, highly correlated with

international equity markets.

2.3 Managed Futures

Managed Futures developed independently from Hedge Funds and are thus not a

subcategory of Hedge Funds. Commodity Trading Advisors (CTAs) were originally

developed as an alternative of investing directly into forward markets. Professionals

actively manage CTAs for their clients by investing into Foreign Exchange forwards and

other financial forward contracts. Similar to Hedge Funds, CTA managers use derivatives

and leverage to enhance the fund’s performance.

CTAs invest exclusively into listed and publicly traded forward contracts. With analytical

methods and electronic trading models, CTA managers try to predict movements on

futures markets and seek exceptional return on investments by employing a mix of long

and short positions. Futures are standardized and publicly traded. Future markets are

generally more liquid than other forward markets. Managers can clear their positions

quickly and leverage their investments substantially (traders on future markets are

required to deposit only an initial margin as a percentage of their overall investment).

Since managers of CTAs trade with futures, they are subject to the requirements and

regulations of the exchange supervisory authorities. Hence, CTAs are more transparent

than other forms of alternative investment funds.


8

2.4 Event Driven

Managers of Event Driven Funds either try to react quickly to changing market

circumstances or occurrences, or induce changes in the markets themselves to be able to

profit from rapid market movements. Managers try to identify and predict special

market occurrences that will alter the performance of specific equities or bonds. One can

differ between three different kinds of disruptive events: Insolvency of an existing

company, mergers or acquisitions, and restructuring of a company. Whether an Event

Driven strategy proves to be successful or not depends mainly on the speed and

efficiency with which managers can react to these events. In addition, managers must be

able to accurately predict events (or assess their probability) to estimate future

movements in the price of an equity stock or bond. Under- or overvalued securities are

another investment focus of Event Driven funds managers.

2.5 Distressed Securities

This special form of Event driven funds tries to identify companies that are in financial

or operational distress. The fund invests into undervalued securities and speculates on

management’s ability to restructure the distressed company. Besides directly investing

into equities or bonds, a number of funds issue credits to troubled companies or take

over liabilities and credits. Due to the exceptionally high default risks, Distressed

Securities funds managers hedge their positions with short-positions and equity options

and do not leverage their exposure with borrowed capital. The purchase and sale of

‘orphan’ securities and ‘junk’ bonds is another dimension of distressed securities

trading. ‘Vulture’ investors utilize the current situation of the company to purchase a

controlling stake in the company at an undervalued price. Distressed Securities

managers may opt to actively assist management in the restructuring process and thus

increase the possibility for recovery.

2.6 Merger Arbitrage

Companies that are faced with merger, take-over or restructuring decisions are the

target for Merger Arbitrage funds. It depends on the skills and experience in the industry

of the fund manager to accurately predict the outcome of these transactions. Other than

financial and operational influences, decisions of local antitrust authorities determine

the success or failure of merger and take-over transactions. In order to limit the funds

risk exposure, managers generally speculate exclusively on publicly announced

transactions. In the case of a (hostile) take-over attempt, fund managers buy stocks of


9

the target company whilst short-selling stocks of the bidding company. Fund managers

use stock borrowing to leverage their performance to react more effectively to changing

circumstances and hedge their position with derivatives. The success of the investment

depends on the ‘standstill return’ (the expected return on investment in case of a

successful transaction) and the probability of the transaction itself.

2.7 Equity Market Neutral

Market Neutral funds try to realize arbitrage gains with bonds, convertible bonds, rights

issues and equity stocks. Long Short Equity funds achieve arbitrage by simultaneously

purchasing and short-selling similar stocks of companies in the same industry, whilst

hedging the inherent systematic risk. When arbitrage profits exceed the costs of hedging,

the transaction was beneficial. Generally speaking, Market Neutral funds try to diversify

away any specific risk whilst generating the highest possible return on investment.

Hence, Market Neutral strategies use the highest degree of leverage compared to other

Hedge Funds investment styles. Traditionally, Long Short Equity funds belonged to the

Market Neutral funds (today most Long Short Equity fund managers do not manage

factor neutral portfolios).

2.8 Convertible Bond Arbitrage

Managers of Convertible Bond Arbitrage funds identify and purchase undervalued

convertible bonds whilst simultaneously short-selling the underlying stock, thus

realizing arbitrage gains. Arbitrage gains can only be realized, when pricing of

convertible bonds display a different degree of volatility compared to the underlying

stock (e.g. when increases in stock prices lead to only marginal increases in convertible

bond prices). Gains from the convertible bonds should overcompensate losses from the

short-position in the event of rising stock prices and vice versa in the even to falling

prices. However, hedging through short-selling may not be sufficient to compensate for

unexpected expansions of the premium on convertible bonds. Leverage can be used to

enhance the performance of this strategy.

2.9 Fixed Income Arbitrage

Arbitrage funds that speculate on fixed income securities try to play the pricing

differences between fixed interest securities and their derivatives. One strategy involves

buying under-rated securities and hedging the position with short-selling and

derivatives against changes in prime rates, increases in spreads, or market risks.


10

Substantial leverage is necessary to generate sufficient return on investment. Yield

Curve Arbitrage generates gains from disparities in the yield curve by purchasing

securities with different maturities. The portfolio is automatically hedged against

horizontal movements of the yield curve. Treasury/Eurobond (TED) strategies play

differences in interest rates between government bonds and Eurodollars. Mortgage

Backed Securities strategy funds purchase mortgages with the option of early retirement

and speculate on increases in interest rates (whilst hedging themselves against falling

interest rates). Credit Spreads allow funds to purchase and short-sell securities with

similar spreads above the risk-free rate and realize arbitrage gains with over-/under-

rated securities. Capital structure arbitrage speculates on the difference between junior

and senior bonds of the same issuer.

3 Diversification of Market Risks

Bonds and equities have an exposure to unfavourable or unexpected pricing and interest

rate movements. In the subsequent section, we will first identify the different risks

bonds and equities can be exposed to and try to analyze how modern portfolio theory

can be a basis for diversifying away the inherent risks of investments into single

securities.

3.1 Interest Rate Risks

Fixed Interest Securities are subject to unfavourable changes in market interest rates.

Increasing interest rates can make a bond appear less attractive, falling interest rates

can make a loan relatively more expensive. Interest rate risks can be defined as the risks

resulting from realizing a lower expected interest gain in a given period due to changes

in the market rate. The effects of changing market rates can be twofold. Increases in

interest rates lower the par value of bonds. Conversely, falling interest rates increase the

value of the bond. Changes in the interest rate premiums over the risk-free rate can limit

interest gains and nullify earnings from fixed income arbitrage oriented strategies.

Variable Interest Securities may respond differently to interest rate changes (inelasticity

of interest rates) and pose an additional risk to the expected return of a portfolio.

In close relation to interest rate changes are risks resulting from unfavourable

movements of exchange rates (as local interest rates are a determinant of the cross-rates

between two currencies). Currency related risks derive from the possibility of exchange


11

rate related losses when changing money from one currency into another. Future gains

from fixed interest securities and equities can be offset by the effects of exchange rate

movements. Exchange rate related risks depend on the exposure of an investor to

different currencies. Investors may choose to construct portfolios in which all future

currency movements cancel each other out. Swap risks result from future contracts that

do not match each other in terms of maturity. Whilst positions in different currencies

may cancel each other out in terms of value, investors have to account for roll-over risks.

Roll-over risks can be associated with risks deriving from the necessity to roll-over

shorter term contracts and the possibility of changing terms and rates.

3.2 Pricing Risks

Pricing risks can be described as risks that result from unfavourable or unexpected

movements in the pricing of bonds or equities. Investors need to differentiate systematic

risks and unsystematic risks. Systematic risks (market risks), in the context of market-

dependent pricing risks, can be seen as differences in actual and expected prices of

bonds, equities, or a portfolio that derive from deviations in the overall markets. All

securities are influenced by systematic risks. Diversified portfolios do not eliminate

systematic risks. Unsystematic risks are risks that result from specific circumstances

that influence the pricing of a single security. These specific risks can be diversified

away in efficient portfolios.

Changing interest rates influence the pricing of securities, and hence, the pricing risks.

Higher interest rates make Fixed Interest Securities relatively more attractive compared

to equity stocks, and thus exert pressure on equity markets. Currency related risks can

leverage the pricing risks of securities.

3.3 The Theory of Portfolio Diversification

Markowitz developed the basis principles of the modern portfolio theory. According to

Markowitz, risks can be fully diversified by combining weakly or negatively correlated

securities in a portfolio. Modern portfolio theory measures the risk of a portfolio with

the variation (standard deviation) of its overall returns. With the exception of strictly

positively correlated securities, the risk of a portfolio of securities will be lower

compared to the risk of a single investment. Markowitz postulated that, for any risk

level, we are only interested in that portfolio with the highest expected return.

Alternatively, managers should only be interested in portfolios with the lowest


12

variability in returns for any targeted expected return (hypothesis of efficient market

frontier). All minimum-variance portfolios can be plotted on a graph to create the

efficient market line. The efficient market line is the representation of all possible

portfolio combinations with superior risk-return profiles compared to all other potential

portfolios (Markowitz assumed that correlations between securities remain stable in the

short and medium term). According to the personal risk preference, investors then

choose a portfolio on the efficient market line (assuming the efficient market hypothesis

is true). The expected return of any portfolio can be described by the capital market line

(Bodie, 2005):

( )*

CML

Pf

Pf rf

CML rf r

r

E r rr r σ

σ

− = +

Equation 3.1

With rrf = risk-free rate; σ = Standard deviation; rPf = portfolio return; E = Expected Value

Sharpe expanded on Markeowitz’s original theories and developed the Capital Asset

Pricing Model (CAPM). Contrary to Markowitz, Sharpe does not compare correlations

between different assets, but rather determines the correlation of a single security to the

market portfolio. Beta determines the relationship between a single asset and the

overall market. Market Beta is used to describe the additional risk an individual security

adds to a diversified portfolio. Beta describes the relationship of stocks and bonds with

the overall market. A Beta of greater than one signifies a higher degree of sensitivity to

changes in the market place. A Beta of lower than one indicates a lower risk of the

respective security (the bond or stock responds less to changes in overall markets). It

has been argued that Beta is not an ideal measure of risk because of changing market

correlations and negatively/positively skewed return distributions (an argument that

holds particularly true with alternative investments). Beta represents the proportion of

a stock’s or bond’s performance standard deviation that can not be diversified away. A

regression analysis of individual stock returns versus the returns of a stock index

returns the security market line, which can be described with the following formula:

( ) i i mtE r rα β ε= + + Equation 3.2

With α = alpha coefficient; β = beta coefficient; ε = error term


13

According to the CAPM, managers that achieve return on investments that exceed the

return of the stock index by 100% can be expected to have constructed a portfolio with a

Beta of two. A Beta of less than two signifies managerial skill. Portfolios with higher Beta

in bullish markets and a lower Beta in falling markets can be seen as attractive

investment opportunities. The error term ε stands for a stock’s unsystematic risk and

can be diversified away in efficient portfolios. Beta factors hold true in the event of high

correlations with the market index and the long term stability of these correlations.

For the purpose of assessing the risks of a combined portfolio of traditional and non-

traditional investments, we can us the variance formula for two asset portfolios as

described below:

2 2 2 2 22 ( ; )Pf T T A A T A T Aw w w w Cov r rσ σ σ= + + Equation 3.3

With wT = Weighting traditional investment; wA = Weighting alternative investment; Cov = Covariance of the portfolio returns

We expect traditional portfolios to be lowly correlated with alternative investment

portfolios. Hence, managers should be able to decrease the variability of an overall

portfolio by combining hedge funds with traditional equity/bond portfolios. Whether

variability is an appropriate risk measure for alternative investments will be briefly

discussed in a later section of the report.

4 Portfolio Diversification with Hedge Funds

In the following sections we take a look at how Hedge Funds investments influence the

performance and risks of existing traditional equity and bond portfolios. Different style

indices for hedge funds were combined with equity/bond portfolios to analyze the

benefits of diversified portfolios.

4.1 Diversifying Equity Portfolios

Two style indices were used to simulate the performance of Hedge Funds portfolios. We

chose the S&P 500 index as an internationally diversified equity portfolio representing

the traditional investment. Market neutral strategies (Event Driven) as well as market

dependent strategies (Global Macro) were included in the analysis to assess the


14

diversification potential of both strategic sub-categories. For the purpose of the report,

we focussed on static portfolios (weightings do not change between traditional and non-

traditional investments, regardless of the individual performance or changes in

volatility). It must be noted that style indices may not necessarily be representative of

individual Hedge Funds. However, with fund certificates and the increasing number of

fund of funds private and corporate investors can limit their risks by investing into

multiple hedge funds at the same time. The expected diversification benefits of

certificates and fund of funds should be somewhat lower compared to investments in

Single funds (as fund of funds include the performance of many different hedge funds).

The following analysis refers to an investment into the S&P 500 index between June

1995 and June 2005 (the data was received from the Reuters server on October 16th

2006). During the same period, we assumed an investment into three different style

indices. It is the purpose of the analysis to assess how hedge funds reduce the

variability/volatility of portfolio returns during the ten year period. It must be noted

that the two Hedge Funds indices are non-investable indices. The performance of

investable indices varies slightly from the here displayed performance. The findings in

Table 1 and 2 can be transferred to a limited extent to other style indices as well (taking

into account differences in degree of leverage, the use of derivatives and short-selling).

In tables 1 and 2, we can observe the results for a combined portfolio of investments

into the S&P 500 and the Global Macro and Event Driven style index (Weightings from

0% to 50%). In addition, the tables show the minimum variance portfolio (the portfolio

for which the variability of returns would have been the lowest over a ten year period)

for each strategy. Due to the different development of the S&P 500 and the two Hedge

Funds indices, the weighting changes over time. In reality, it can make sense to shift

weightings to keep a portfolio balanced (dynamic portfolios).


15

Table 4.1: Global Macro Strategy (Data: Reuters, 2006) % Global Macro Return p.a. Stdev Semi-variance Sharpe Ratio Max. Drawdown

0% 9,00% 15,49% 9,04% 0,324 -46,28%

5% 9,26% 14,64% 8,61% 0,368 -42,61%

10% 9,71% 13,87% 8,23% 0,414 -38,86%

15% 10,06% 13,16% 7,92% 0,462 -35,03%

20% 10,40% 12,53% 7,65% 0,513 -31,13%

25% 10,74% 11,97% 7,45% 0,565 -27,15%

30% 11,07% 11,47% 7,31% 0,619 -23,08%

35% 11,40% 11,05% 7,22% 0,672 -18,93%

40% 11,73% 10,69% 7,14% 0,725 -14,69%

45% 12,05% 10,41% 7,10% 0,776 -11,14%

50% 12,36% 10,19% 7,09% 0,823 -12,05%

MinVar 13,53% 9,99% 7,35% 0,956 -15,79%

Table 4.2: Event Driven Strategy (Data: Reuters, 2006) % Event Driven Return p.a. Stdev Semi-variance Sharpe Ratio Max. Drawdown

0% 9,00% 15,49% 9,04% 0,324 -46,28%

5% 9,13% 14,89% 8,70% 0,346 -44,29%

10% 9,27% 14,29% 8,35% 0,370 -42,25%

15% 9,40% 13,70% 8,02% 0,396 -40,14%

20% 9,53% 13,12% 7,69% 0,424 -37,98%

25% 9,67% 12,45% 7,36% 0,454 -35,74%

30% 9,80% 11,97% 7,04% 0,486 -33,44%

35% 9,93% 11,42% 6,73% 0,522 -31,07%

40% 10,07% 10,86% 6,42% 0,561 -28,62%

45% 10,20% 10,32% 6,11% 0,603 -26,09%

50% 10,34% 9,79% 5,81% 0,650 -23,48%

MinVar 11,74% 5,85% 3,33% 1,328 -16,05%

With an increasing share of Hedge Funds as part of a combined portfolio, the annual

variability decreases (The optimal combination of Hedge Funds and traditional funds

has been found to be as high as 68%). At the same time, the average return on

investment improves. The lowered volatility of the combined portfolio can be explained

with the anti-cyclical return profile of Hedge Funds. In bearish markets, Hedge Funds

compensate for the losses realized with the traditional portfolio. In bullish markets,

Hedge Funds were able to outperform the traditional portfolio most of the time (hence

the improvement in profitability). Because Hedge Funds try to realize absolute positive

returns in any market, they are traditionally low correlated with equity indices. In

addition, Hedge Funds can react more quickly and flexible to changes in the market

place (since they are not bound by regulatory limitations). As could be expected, the

minimum variance portfolio (in accordance with Markowitz’s theorem) shows the best

risk-return profile of all possible portfolios (Sharpe Ratio). In addition, the maximum

variance portfolio was able to limit the maximum continuous drawdown significantly

(Maximum drawdown is the maximum continuous loss an investor has to realize when

investing into the combined portfolio). Hence, the minimum variance portfolio proves to

be superior to any other possible combination of traditional funds with Hedge Funds.


16

It should be mentioned that not all style indices were able to produce the same

exceptional returns as Global Macro and Event Driven strategies. Dedicated Short Bias

strategies realized continuous losses throughout the 1990’s and are only slowly

recovering since 2001. In addition, the performance of Single Hedge Funds can differ

significantly from the here displayed performance of style indices (the LTCM fund lost

80% of its value in 1998). Also, Hedge Funds have been found to have negatively skewed

performance distributions (which is indicative to the higher default risks of alternative

investments). Hence, Hedge Funds influence the skewness and excess kurtosis of

combined portfolios (defying the assumptions of normally distributed returns).

Statistical evidence suggests that ‘fat tails’ of Hedge Funds have a significant influence on

default risks when using Market Neutral strategies to diversify equity portfolios. The

unique risk dimensions of hedge funds will be discussed briefly in a later section of the

report.

Table 4.3: Beta Values (Data: Reuters, 2006) Weighting Global Macro Event Driven

5% 0,935 0,935

10% 0,883 0,914

15% 0,832 0,875

20% 0,784 0,837

25% 0,737 0,798

30% 0,691 0,760

35% 0,647 0,722

40% 0,605 0,683

45% 0,563 0,645

50% 0,523 0,606

MinVar 0,379 0,209

Table 3 refers to the changes in market beta when combining Hedge Funds with

traditional investment funds. Because of the low correlation of Hedge Funds with

market indices, they add less additional Beta to the combined portfolio. Table 3

emphasizes the low dependability of alternative investments on general market

movements. The decreasing values of Beta (for higher proportion of Hedge Funds in the

combined portfolio) explain why diversified portfolios do better in downward markets.

In addition, Hedge Funds have been found to adjust their betas more quickly to upward

markets (in order to benefit from higher market correlations).

4.2 Diversifying Bond Portfolios

The performance of Corporate and Government Bonds is highly dependent on changes

in interest rates. Arbitrage oriented Hedge Funds managers try to identify and to benefit

from over-/under-evaluations of Fixed Interest Securities. Hence, Hedge Funds are


17

generally independent from interest movements (Hedge Funds react less sensitive to

horizontal movements of the yield curve). Only when interest rates at the long end

develop differently from interest rates at the short end, Hedge Funds share the same or a

higher exposure to interest rate related risks as traditional bond investments. When the

yield curve shifts horizontally, Hedge Funds can limit changes in par value by purchasing

relatively cheaper bonds and short-selling more expensive ones with different

maturities.

Hedge Funds managers speculate on the difference between government bonds and

Eurodollar exchanges. Hence, these managers can benefit from changes in the spreads

between corporate and government bonds. The TED-spread can be seen as an interest

premium on Eurodollar deposits versus risk-free Treasury Bills (to account for higher

default risks). Eurodollar-futures are generally regarded as counter-image of Credit

Ratings for bank and corporate bonds (Eurodollars are direct obligations of private

banks). Arbitrage oriented investors expect the three-months rates of Eurodollars and

Treasury bills to develop differently. Falling interest rates can be compensated with long

and corresponding short positions in Eurodollars and Treasury bills (as long as the

short-term rates of the two investments develop differently). When managers anticipate

the widening or narrowing of the spread correctly, they can create interest rate neutral

portfolios. It seems logical that the combination of traditional bond portfolios with

interest rate arbitrage oriented Hedge Funds should limit the exposure of the overall

portfolio to changes in the interest rate.

To simulate a traditional investment in bonds, we combined the Merrill Lynch Corporate

Bond Industrial Index with JP Morgan’s Government Bond Index (both investments

were weighted 50%). The resulting index basket was combined with Fixed Income

Arbitrage strategies (Fixed Income Arbitrage style index) to assess the diversifying

effects of Hedge Funds. The resulting combined portfolio was not dynamically re-

weighted to maintain the initial weighting.


18

Table 4.4: Fixed Income Strategy (Data: Reuters, 2006) % Fixed Income Return p.a. Stdev Semi-variance Sharpe Ratio Max. Drawdown

0% 6,35% 2,95% 2,11% 0,807 -2,89%

10% 6,36% 2,68% 1,93% 0,890 -2,63%

20% 6,38% 2,47% 1,80% 0,971 -2,38%

30% 6,39% 2,34% 1,72% 1,033 -2,12%

40% 6,41% 2,29% 1,70% 1,060 -2,58%

50% 6,42% 2,34% 1,68% 1,045 -3,75%

MinVar 6,40% 2,30% 1,70% 1,057 -2,40%

Similar to the results for diversified equity portfolios, it can be concluded that Hedge

Funds can be used to diversify interest rate related risks of bond investments. It should

be noted that returns on Fixed Income Arbitrage strategies are limited. Thus, the

expected annual return when increasing the proportion of Hedge Funds in the overall

portfolio might actually drop (depending on the Benchmark index utilized). Annual

volatility of returns and maximum continuous drawdown were decreased in the

combined portfolios. As with equity oriented funds, the Minimum Variance portfolio

delivered the best results. Losses in par value could be partially compensated with

additional arbitrage gains from allocating more funds into Fixed Income Arbitrage funds.

Surprisingly, investments in Hedge Funds can actually decrease the risks associated with

investments into low-risk fixed income bonds.

0%

10%

20%

30%

40%

50%

60%

2,00% 2,10% 2,20% 2,30% 2,40% 2,50% 2,60% 2,70% 2,80% 2,90% 3,00%

Volatility

Weig

hting

Figure 4.1: Volatility at different HF Weightings

The above chart emphasizes the relationship between different weightings of Hedge

Funds in the overall portfolio and varying degrees of volatility. As could be expected

from the assumptions of the CAPM, there is a portfolio at which the overall variability is

the lowest. The remaining volatility of returns of 2.30% cannot be diversified away

(systematic risk). No other combination of alternative and traditional funds will produce

better results.


19

4.3 Exchange rate related Risks

Similar to the hedging of interest rate related risks, Hedge Funds can address the risks of

exchange rate fluctuations in the overall portfolio. By speculating on widening or

narrowing spreads, TED arbitrage oriented strategies can benefit from changing spreads

in Eurodollar/Treasury bills interest rates. Depending on the geographical market, the

Eurodollar can be played against different regional treasury bills (e.g. 3-month-Euribor

in the euro-area). Changes in exchange rates can have detrimental effects. Between June

2002 and 2005, the Dow Jones Industrial Average appreciated by 17.61% in total.

During the same period, the US Dollar lost 20% versus the Euro (resulting into an actual

loss of -4.76%). Single Funds focussing on spreads between two distinctive currency

regions (in this case USA and Europe) can effectively hedge part of the exposure by

employing Fixed Income Arbitrage Strategies.

5 Measuring the Risks of Hedge Funds

In the course of the analysis we assumed that, for the sake of simplicity, Hedge Funds

can be analyzed in the very same fashion as traditional investments. We postulated that

Hedge Funds earnings were normally distributed and that volatility and market Beta

was a good measure of the combined portfolio risk. In reality, however, there is

significant statistical evidence to infer that Hedge Funds returns are non-normally

distributed. Additionally, empirical research suggests that Beta factors of alternative

investments change frequently. The subsequent sections briefly address the unique risk

features of Hedge Funds. Managers must be aware of the short-comings of existing risk

measures when trying to evaluate the risks of Hedge Funds (the risks of combined

portfolios).

5.1 Non-normal probability distribution

Most alternative funds managers claim that, contrary to general believe, performance

variation of hedge and private equity funds can be limited with the use of derivatives

and financial leverage. Indeed, some alternative investment funds display a lower

degree of overall variation in their performance history. However, there is statistical

evidence that the distribution of hedge funds is significantly different from a normal

distribution (Fung, 1999). More specifically, the distributions of hedge funds returns

display excess and kurtosis and are negatively skewed. Whilst hedge funds returns are

less likely to deviate largely from their expected mean, there is a disproportionately


20

higher risk for returns to fall significantly below the mean. This risk represents the

higher default risk of alternative investments. Historically, Hedge Funds showed a

higher weighting of short positions. Hence, these funds were actually not completely

hedged from negative performance deviations (with the exception of arbitrage only

funds). The use of borrowed capital emphasized this problem. As a result, any risk

measures that derive from the assumption of a normal return distribution may not

adequately assess the risks of alternative investments.

5.2 Disrupting effects of time series analysis

Performance history of hedge and private equity funds fail to acknowledge the effects of

managerial and survivorship bias (Kritzmann, 2002). The former refers to performance

smoothing of fund returns by their managers. Most alternative funds grant managers a

fixed and a variable compensation. The variable component of a manager’s

remuneration is tied to the yearly performance of the funds they manage. Usually, high-

water marks are implemented to guarantee that managers only receive compensation

when the fund exceeds the previous year’s performance. It has been argued that

managers tend to avoid extreme performance movements by realizing gains a year

earlier or carrying over losses to the follow-period. Thus, the distribution of funds

returns appear to be smoother than they actually are. This effect is more commonly

referred to as autocorrelation. Autocorrelation describes the entire width of effects that

result in correlation between time series. The latter refers to a practical problem of

analyzing funds through industry indices. Sunk and defaulted funds, as well as closed

funds, are excluded from alternative investment indices. Naturally, the performance of

the overall industry appears better than it actually is.

5.3 Changing market correlations

Beta is widely used to describe the relationship between an investment and the overall

market. However, historic evidence suggests that disruptive market events can

significantly change that interrelation between market and single investment (Spurgin,

2000). Alternative investment funds tend to be more susceptible to disruptive market

events than traditional investment funds. Although Beta rarely reflects the risks of

certain investments accurately, it is being used extensively throughout the financial

industry as an accepted measurement of risk. Alternative funds managers, as well as

analyst, have tried in the past to adapt Beta to different investment vehicles and


21

industries. Adapted Beta measures can improve the assumptions that can be derived

from the CAPM in terms of estimating the inherent risks of alternative investments.

5.4 Performance history and statistical inference

Both private equity and hedge funds are relatively new forms of capital investments.

When analyzing alternative investments, statisticians have to work with a relative short

performance history. Whilst their findings hold some merit, they are only true with a

certain degree of confidence (Liang, 2003).

A second and more considerable influence on statistical analysis has the availability of

data. It is the declared policy of many alternative investment funds to publish and

distribute as little data on performance as possible (hence we used Hedge Funds style

indices in our analysis). In consequence, the analysis of Single funds is difficult to

conduct. Many statisticians prefer to analyze fund of funds or industry indices to draw

inferences from industry performance on the performance of single funds. Fund of funds

incorporate a limited number of alternative investment funds and thus do not accurately

reflect the industry’s performance. In addition, fund of funds prefer to invest into

successful funds. Single funds with a similar strategy exposure to different asset classes

may still display a significantly different performance from fund of funds. Consequently,

statistical inference from fund of funds holds limited benefit. Shortcomings of inferences

from industry indices refer to the above mentioned problem of survivorship bias.

6 Concluding Remarks

We were able to prove in the course of the analysis that Hedge Funds can be used to

diversify the risks in traditional investment portfolios. Hedge Funds are able to address

three risk dimensions: pricing risks, interest rate related risks, and exchange rate

related risks. Not only were Hedge Funds able to lower the risks associated with

traditional investment funds, but they were able to maintain or improve the

performance of the combined portfolio (depending on the weighting of alternative

investments). Minimum Variance portfolios proved to be the most efficient ones.

The above mentioned shortcomings of existing risk measures must be taken into

consideration when combining traditional and non-traditional investment portfolios.

Adapted beta measures accounting for the effects of autocorrelation in conjunction with


22

different assumptions about the distribution of Hedge Funds returns can produce better

results when assessing the overall risk exposure of combined portfolios. Whilst the

limitations of our analysis do not nullify the findings, Hedge Funds investments tend to

display higher default risks than traditional investments. When investing into Fund of

Funds or style indices (via certificates), an investor may be able to spread default risks

over many different Single funds. Direct investment into Single Hedge Funds remains

risky for private investors and should be left to professional/corporate investors.


23

7 List of Sources

Bodie, Z.; Kane, A.; Marcus, A.J.: “Investments“, Sixth Edition; McGraw Hill; New York,

2005

Fung, William; Hsieh, David A.: “Is mean-variance analysis applicable to hedge funds?”;

Economic Letters; vol. 62; 1999

Download: http://www.duke.edu/~dah7/m-v.pdf

Kritzman, Mark; Rich, Don: “The Mismeasurement of Risk“; Financial Analysts Journal;

May/June 2002

Lavino, Stefano: “The Hedge Fund Handbook”; McGraw-Hill; New York, 2000

Liang, Bing: “On the performance of Hedge Funds“; Financial Analysts Journal;

July/August 1999

Schneeweis, Thomas; Spurgin, Richard: “Alternative Investments in the Institutional

Portfolio“;CISDM Working Papers; 1998

Download: http://cisdm.som.umass.edu/research/pdffiles/almaassetalloc031902.pdf

Spurgin, Richard; Martin, George; Schneeweis, Thomas: “A method of Estimating

Changes in Correlation Between Assets and its Applications to Hedge Fund

Investments“; CISDM Working Papers; 2000

Download: http://www. umass.edu/som/cisdm/files/papers/hedgeFundPaper.pdf

diversifying risks with hedge fundshedge-fund-analysis.net/media/docs/fmb_riskdiversify_1006.pdf ·...

Documents