review prof. ian giddy new york university stern school of business

Review

Prof. Ian GiddyNew York University

New York UniversityStern School of Business

Copyright ©2001 Ian H. Giddy Investing and Trading 2

Topics

The Financial Markets Time Value of Money and Yields Money and Bond Markets Risk and Return Risk and Diversification Valuation and Asset Pricing (CAPM) Arbitrage and Market Efficiency


Topics (continued)

International Financial Markets Equity Valuation Cash, Futures, FRAs and Swaps Options Portfolio Management and Performance

Evaluation


R isk-F ree A sset

B onds R eal E s tate

C onE d V iacom C hase S iemens

Security Selection

S tocks C om m odities FX

A sset A llocation

R isky A ssets

C apital A llocation

Managing a Portfolio


Performance Benchmarking:Buy Kellogg?

Conclusion: Benchmarks are needed because performance is

relative


The Players, such as Institutional Investors and Money Managers

Institutional Investors Money Managers

Mutual Funds

Insurance Companies

Pension Funds

Hedge funds, Central banks, etc.

Stocksand

bonds

Money managers


The Instruments

What Investments?

Treasury Bills?(risk-free)

Stocks and Bonds?(risky)


M unicipa l Bonds M ortgage-Backed Securities

Foreign Bonds Private P lacem ents

Euroyen Bonds, etc.

Euro$bonds

C orporate Bonds

U S T reasury Bonds

Fixed-Income Securities


Maturity(years)

Yield toMaturity

12345678910

5.426.026.426.696.826.927.077.167.247.23

Fixed-Income Securities


Future Value

20%

15%

5%0%

Future Valueof One Dollar ($)

Periods

1.00


Future Values: Summary

Single amount:the amount times the future value of interest factor, or

FVIFk,n :

Annuity:the periodic payment times the future value of annuity

factor, or FVIFAr,n :

FVA PMTxFVIFA PMTx rrr n r n

n

, ,( )

1 1

FV PVxFVIF PVx rr n r nn

, , ( ) 1


If J&J’s new pharmaceuticals facility in Mexico can produce the following dollar profits for the next four years, at a discount rate of 6%, what is the present value of the cash flow stream?Year 1 2 3 4Cash Flow $100 $400 $1000 $300

$100 $400 $1,000 $300

1 2 3 4

$ 94.30 (PVIF6%,1) = .943 356.00 (PVIF6%,2) = .890 840.00 (PVIF6%,3) = .840 237.60 (PVIF6%,4) = .792

$1,527.90 = Present Value of cash flow stream (HP:1,519.24)

Present Value(Example: J&J Mexico)


Present Values: Summary

Single amount:

the amount times the present value of interest factor, or

PVIFr,n :

Annuity:

the periodic payment times the present value of annuity

factor, or PVIFAr,n :

PVA PMTxPVIFA PMTx rrr n r n

n

, ,/( )

1 1 1

PV FVxPVIF FVxrr n r n n, , ( )

1

1


J&J leases $12,000 of computer equipment from Hewlett-Packard. How much would its annual end-of-year payments have to be at a 15% interest rate if the cost must be fully repaid in 3 years?

PVA3 = $12,000; r = 15%; n = 3PVA3 = PMT x PVIFA15%,3

PMT = PVA3/PVIFA15%,3 = $12,000/2.283= $5,256.24

Loan Amortization Schedule - A schedule of equal payments to repay a loan. It shows the allocation of each loan payment to interest and principal.

Loan Amortization Example


Basic Bond Valuation

WHERE: Bo = value of the bond at time zero

I = annual bond interest in dollars (interest payment) M = par value of the bond rt = required rate of return n = number of years to maturity

B Ix PVIFA Mx PVIF

B Ir

Mr

r n n

t nt

n

0

01 1 1

( ) ( )

( ) ( )

,


The Zero Approach

Use zero-coupon rates to value each cash flow - then add them!

Where can we get the z’s? One place is from the Treasury strip market.

B Cz

Cz

Mzn

n01

12

21 1 1

( ) ( )...

( )


Bond Lego

To value this bond, break it up into its component cash flows - e.g. 1st coupon of (5 3/4)/2 in Feb 1996, and so on...

Then use zero’s to see what each is worth, and add the total.

In general, breaking up a security into its component parts is an excellent path to valuation.

Rate6

M aturity, M o/Y rD ec 97

B id Asked99:29 99:31

Ask Y ld.6.01

A Treasury Noteas quoted in the W all Street Journal Monday, July 24, 1995


Forward Interest Rates

4

55.5 5.7

6 6.25

0

1

2

3

4

5

6

7

3 mo 6 mo 9 mo 1 yr 15 mo 18 mo

EURODOLLAR INTEREST RATES

The rate that can be locked in is the implied forward rate that equateslong term rates with short term rates


I can buy a 2-year note or buy a 1-year note and reinvest it at some "forward" rate f:

(1+y2)2=(1+y1)(1+f)

Find f!

Calculating Implied Forward Rates


Theories of Term Structure

Expectations Liquidity Preference

Upward bias over expectations Market Segmentation

Preferred Habitat


Identifying Undervalued Securities

BondsSpotRates

“Correct”pricing

Comparewith actual


A $1 Investment in Different Types of Portfolios: 1926-1996

0.1

1

10

100

1000

10000

1925 1935 1945 1955 1965 1975 1985 1995

Index ($)

$4,495.99

$33.73$13.54$8.85

$1,370.95

Small Company Stocks

Large Company StocksLong-Term

Government Bonds

Treasury BillsInflation Year-End


The Price-Yield Relationship

Selling at a discount is when a bond sells for less than its par value (i.e., the quote is <100)

Selling at premium is when a bond sells for more than its par value (i.e., the quote is >100)

100

9%

Price of a 9% bond


Bond Price Changes:Actual vs. Duration-Based

There’s an error in duration-based estimation, because duration is linear.

PRICE

YIELD9%

100Actual

Duration

Error


Calculating Duration:MacCauley and Modified

D

tCFr

P

D P dPP

Dr

MAC

tt

t

n

MOD

( )

%( )

1

1

1


Assets (each $10m):1-year E$ deposit5-year, 6% T-note

Duration=4.39-year Strip

Fixed liabilities:$10m 3 years$15m 5 years$5m 7 years

Asset Duration = .33(1)+.33(4.3)+.33(9) Liab Duration = .33(3)+.50(5)+.17(7)

Net duration is 4.77-4.67 = 0.10

Portfolio Duration


Lostyur Trust

Item Cash LoansTreas note IBM bond 6-mo CD 5-yr bond EquityFace value 2 13 20 6 3 33Settle date 1/1/97 1/1/97 1/1/97 1/1/97 1/1/97 1/1/97Mat date 1/1/97 4/1/97 1/1/01 1/1/04 7/1/97 1/1/02Rate - 10.25% 6.00% 7.90% 4.00% 9.00%Yield - 10.25% 6.35% 8.23% 4.00% 9.00%Frequency - 2 2 2 2 2

Price 100 100.00 98.78 98.27 100.00 100.00 46.52Value 2 13.00 19.76 5.90 3.00 33.00 4.65Modified duration 0 0.2 3.5 5.3 0.5 4.0

Assets Liab.+Eq. NetValue 40.65 40.65Modified duration 2.54 3.25 -0.71


International

Exchange Rate Risk is the risk arising from fluctuating exchange rates between two currencies


Foreign Exchange Quotations

Spot Forward points


Exchange Rates

CurrencyHowquoted

Spot(2 businessdays)

Forward(90 days)

Britishpounds(GBP)

US$perGBP

1.632 1.617

Japaneseyen (JPY)

Yen perUS$

117.5 116.3


A Typical Forward Contract

We agree today to pay a certain price for a currency in the future

Sony B of A

JPY


Interest-Rate Parity

$1 (1 + / E$) = ($1/ S t )(1 + /EBP) Fnt

where St is the spot exchange rate (dollars per British

Pound) and Fnt is the forward rate.

to a close approximation,(/E$ - /EBP) = [(Ft n - St)/St] (365/n) 100

Interest-rate differential = forward premium or discount


Returns with FX

(1 + rUS) = (1 + rFM) (1 + rFX)

rUS = return on the foreign investment in US Dollars

rFM = return on the foreign market in local currency

rFX = return on the foreign exchange


Hedging International Equity Investments

Buy foreign equity and hedge the anticipated future value, P+E(r)?

Use short-term, value-adjusted, roll-over hedges?

Do nothing, because equities bear no currency sign?

AnticipatedActualInitial


Categories of Financial Ratios

Short-Term Solvency or Liquidity Ability to pay bills in the short-run

Long-Term Solvency/Leverage Ability to meet long-term obligations

Asset Management Intensity and efficiency of asset use

Profitability Market Value

Going beyond financial statements


Returns, Standard Deviations, and Frequency Distributions: 1926-1996

Source: © Stocks, Bonds, Bills, and Inflation 1997 Yearbook™, Ibbotson Associates, Inc., Chicago (annually updates work by Roger G. Ibbotson and Rex A. Sinquefield). All rights reserved.

– 90% + 90%0%

Average Standard Series Annual Return Deviation Distribution

Large Company Stocks 12.7% 20.3%

Small Company Stocks 17.7 34.1

Long-Term Corporate Bonds 6.0 8.7

Long-Term Government Bonds 5.4 9.2

U.S. Treasury Bills 3.8 3.3

Inflation 3.2 4.5


The Normal Distribution

Probability

Return onlarge companystocks

68%

95%

> 99%

– 3 – 48.2%

– 2 – 27.9%

– 1 – 7.6%

012.7%

+ 1 33.0%

+ 2 53.3%

+ 3 73.6%


Credit Risk versus Market Risk


Portfolio Optimization

“Efficient frontier”

Individual assets

Global minimum-variance portfolio

E(r)


Portfolio Return...

To compute the return of a portfolio: use the weighted average of the returns of all assets in the portfolio, with the weight given each asset calculated as

(value of asset)/(value of portfolio).

The portfolio return E(Rp) is:

E(Rp) = (w1k1)+(w2k2)+ ... (wnkn) = wj kj where wj = weight of asset j, kj = return on asset j


Measuring Portfolio Risk

The variance of a 2-asset portfolio is:

where wA and wB are the weights of A and B in the portfolio.

P2

A2

A2

B2

B2

A B A B A B = w + w + 2 w w


Case Study: A Portfolio

Weight E(R) Std DevGPU 0 0.1267 0.1715Teledyne 0.25 0.1396 0.2893Kodak 0.25 0.1402 0.3082Thai Fund 0 0.2075 0.3278Merck 0 0.1781 0.341ATT 0.5 0.1126 0.1606TOTAL 1


Portfolio Risk Computation

CORRELATION MATRIXPRODUCT STD DEV GPU TeledyneKodakThai FundMerck ATT

GPU 0.1715 1Teledyne 0.2893 0.44 1Kodak 0.3082 0.17 0.65 1Thai Fund 0.3278 0.22 0.44 0.24 1Merck 0.341 0.35 0.15 0.13 0.03 1ATT 0.1606 0.68 0.4 0.43 0.23 0.6327 1

Portfolio Variance 3.48%Portfolio Std Deviation 18.66%


Plotting the Efficient Frontier

0

0.05

0.1

0.15

0.2

0.25

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

ORIGINAL

ATT

THAI FUND


Finding the Optimal Portfolio:Computations

Given the Risk-Free rate is: 5.00%

OPTIMAL PORTFOLIOSRisk Ratio

Return Std. Dev. Premium RP/SDGPU 11.26% 0.1606 6.26% 0.390

11.50% 0.1548 6.50% 0.42012.00% 0.1494 7.00% 0.46912.50% 0.1475 7.50% 0.508

MIN RISK 12.83% 0.1471 7.83% 0.53213.00% 0.1472 8.00% 0.54314.00% 0.1509 9.00% 0.59615.00% 0.1572 10.00% 0.63616.00% 0.168 11.00% 0.65517.00% 0.184 12.00% 0.65218.00% 0.2045 13.00% 0.63619.00% 0.2282 14.00% 0.613

THAI 20.75% 0.3278 15.75% 0.4800

0.05

0.1

0.15

0.2

0.25

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

That's the one!


Equity Risk and Return

Investors diversify, because you get a better return for a given risk.

There is a fully-diversified “market portfolio” that we should all choose

The risk of an individual asset can be measured by how much risk it adds to the “market portfolio.”


Types of Risk

PortfolioRisk

kp

Number of Securities (Assets) in Portfolio1 5 10 15 20 25

}}{

TOTAL RISK

NONDIVERSIFIABLE RISK

DIVERSIFIABLE RISK


Optimal Overall Portfolio

Indifference curve

Opportunity set

CALE(r)

P

Optimal complete portfolio (one example)

OPTIMAL RISKY PORTFOLIO


Security Market Line

Nondiversifiable Risk, 0 .50 1.0 1.5 2.0 . . .

SML

}Market RiskPremium: 4%} Asset Z’s Risk

Premium: 6%

1716151413121110987654321

kz =

km =

RF =

RequiredReturn, k(%)

RF m z


The Equation for the CAPM

kj = RF + j (km - RF)where:kj = Required return on asset j;RF = Risk-free rate of return

j = Beta Coefficient for asset j;km = Market return

The term [j(km - RF)] is called the risk premium and (km-RF) is called the market risk premium


Diversification and Asset Pricing: Summary

Investors diversify, because you get a better return for a given risk.

There is a fully-diversified “market portfolio” that we should all choose

The risk of an individual asset can be measured by how much risk it adds to the “market portfolio”

The CAPM tells us how the required return relates to the relevant risk.


Value is Not Price

What is Intrinsic Value?Self assigned ValueVariety of models are used for estimation

Market PriceWhat stock can be sold for or bought at

Trading Signal IV > MP Buy IV < MP Sell or Short Sell IV = MP Hold or Fairly Priced

More, less, or same as market portfolio?


Equity Valuation: From the Balance Sheet

Value of Assets Book Liquidation Replacement

Value of Liabilities

Book Market

Value of Equity

Book ValueLiquidation

ValueReplacement

ValueTobin’s Q:

Market/Replacement tends to 1?


The Balance SheetTotal Value of Liabilities

and Shareholders’ EquityTotal Value of Assets

NetWorkingCapitalCurrent

Assets

Fixed Assets

1. Tangible fixed assets

2. Intangible fixed assets

Current Liabilities

Long-Term Debt

Shareholders’Equity


Valuing a Firm with DCF: An IllustrationHistorical financial results

Adjust for nonrecurring aspects

Gauge future growth

Adjust for noncash items

Projected sales and operating profits

Projected free cash flows to the firm (FCFF)

Year 1 FCFF

Year 2 FCFF

Year 3 FCFF

Year 4 FCFF

Terminal year FCFF

Stable growth model or P/E comparable

Present value of free cash flows

+ cash, securities & excess assets

- Market value of debt

Value of shareholders equity

…

Discount to present using weighted average cost of capital (WACC)


Specified Holding Period Model

01

12

21 1 1V Dk

Dk

D Pk

N NN

( ) ( ) ( )...

PN = the expected sales price for the stock at time N

N = the specified number of years the stock is expected to be held


No Growth Model: Example

E1 = D1 = $5.00

k = .15V0 = $5.00 / .15 = $33.33

V Dk

o


Constant Growth Model: Example

Vo D gk go

( )1

E1 = $5.00b = 40% k = 15%

(1-b) = 60% D1 = $3.00 g = 8%

V0 = 3.00 / (.15 - .08) = $42.86


Shifting Growth Rate Model: Example

D0 = $2.00 g1 = 20% g2 = 5%

k = 15% T = 3 D1 = 2.40

D2 = 2.88 D3 = 3.46 D4 = 3.63

V0 = D1/(1.15) + D2/(1.15)2 + D3/(1.15)3 +

D4 / (.15 - .05) ( (1.15)3

V0 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40


The Gains From an Acquisition

Gains from merger

Synergies Control

Top line Financialrestructuring

BusinessRestructuring

(M&A)

Bottom line


Using The Restructuring Framework($ Millions of Value)

RestructuringFramework

1

2

CurrentMarketPrice

3

Optimalrestructuredvalue

Potentialvalue withinternaland externalimprovements

Potentialvalue withinternalimprovements

Companyvalue as is

Maximumrestructuringopportunity

Financialengineeringopportunities

4

Disposal/Acquisitionopportunities

Strategicand operatingopportunities

CurrentperceptionsGap: “Premium”

5

$ 25

$ 975

$ 300

$ 1,275$ 350

$ 1,625

$ 10

$ 1,635

$ 635

$1,000

Eg Increase D/E


Optika OptikaGrowth 5%Tax rate 35%Initial Revenues 3125COGS 89%WC 10%Equity Market Value 1300Debt Market Value 250Beta 1Treasury bond rate 7%Debt spread 1.5%Market risk premium 5.50%

T+1Revenues 3281-COGS 2920-Depreciation 74=EBIT 287EBIT(1-Tax) 187-Change in WC 16=Free Cash Flow to Firm 171Cost of Equity (from CAPM) 12.50%Cost of Debt (after tax) 5.53%WACC 11.38%

Firm Value 2278

CAPM:7%+1(5.50%)

Debt cost(7%+1.5%)(1-.35)

WACC:ReE/(D+E)+RdD/(D+E)

Value:FCFF/(WACC-growth rate)

Equity Value:Firm Value - Debt Value = 2680-250 = 2430

2680


Optika-Schirnding with SynergySchirnding-Optika

Optika Schirnding Combined SynergyGrowth 5% 5% 5% 5%Tax rate 35% 35% 35% 35%Initial Revenues 3125 4400 7525 7525COGS 89% 87.50% 86.00%WC 10% 10% 10% 10%Equity Market Value 1300 2000 3300 3300Debt Market Value 250 160 410 410Beta 1 1 1 1Treasury bond rate 7% 7% 7% 7%Debt spread 1.5% 1.5% 1.5% 1.5%Market risk premium 5.50% 5.50% 5.50% 5.50%

T+1 T+1 T+1Revenues 3281 4620 7901 7901-COGS 2920 4043 6963 6795-Depreciation 74 200 274 274=EBIT 287 378 664 832EBIT(1-Tax) 187 245 432 541-Change in WC 16 22 38 38=Free Cash Flow to Firm 171 223 394 503Cost of Equity (from CAPM) 12.50% 12.50% 12.50% 12.50%Cost of Debt (after tax) 5.53% 5.53% 5.53% 5.53%WACC 11.38% 11.98% 11.73% 11.73%

Firm Value 2278 3199 5859 7479Increase 1620

2680


What’s a Company Worth?Alternative Models

The options approachOption to expandOption to abandon

Creation of key resources that another company would pay forPatents or trademarksTeams of employeesCustomers

Examples?

Lycos

Messageclick.com


Commodities: Spot and Forward

$1584.5

$1607.0

ALUMINUM PRICEper tonne

3 MONTHS 6 MONTHSSPOT

How can Coke’s canners cap their can costs?


I can buy a 2-year note or buy a 1-year note and reinvest it at some "forward" rate f:

(1+y2)2=(1+y1)(1+f)

Find f!

Calculating Implied Forward Rates


Swaps

GE Chase

8% Fixed

3-mo Libor,floating

Ongoingshort-term

funding


Cost-of-Carry Theory Applied to Stock Futures

Stock that pays no cash dividendno storage costsno seasonal patterns in prices

Strategy 1: Buy the stock now and hold it until time T

Strategy 2: Put funds aside today to perform on a futures contract for delivery at time T that is acquired today


PayoffPayoff

Stock PriceStock Price

0

Call OptionCall Option

Options


PayoffPayoff

Stock PriceStock Price

0

Call WriterCall Writer

Call HolderCall Holder

Payoff Profiles for Calls


Put-Call Parity Relationship

ST < X ST > X

Payoff for

Call Owned 0 ST - X

Payoff for

Put Written -( X -ST) 0

Total Payoff ST - X ST - X


Arbitrage & Put Call Parity

Since the payoff on a combination of a long call and a short put are equivalent to leveraged equity, the prices must be equal.

C - P = S0 - X / (1 + rf)T

If the prices are not equal arbitrage will be possible


Option Pricing

94.5

Option Price= Intrinsic value + Time value

Option Price

UnderlyingPrice

94.75

Time value depends on Time Volatility Distance from the strike price


Market priceof instrument

Profit(gain or loss)

+

0

_

K F

K F

Time Value

F-K

Time Value

E(FJ *FJ >K)

How a Change in the Futures Price Changes the Option’s Price


Trading Options: Delta Hedging

Delta

We’ve written a put option

Hedged with 40% short

futures


Goal: Understand Options’ Sensitivity

An option trader has a portfolio of options with different deltas, gammas, etc. The goal is to discover the sensitivities of the portfolio to changes in rates, time, volatility, etc, and to neutralize them.

Greek Measures Delta Sensitivity of portfolio value to change in

price of the underlying asset Gamma Sensitivity of delta to change in price of

underlying asset Theta Sensitivity of portfolio value to change in

time Lambda

(Vega)Sensitivity of portfolio value to change involatility

Rho Sensitivity of portfolio to change in interestrate


Capital Allocation

R isk -F ree A sse t

B on d s R ea l E s ta te

C on E d V iacom C h ase S iem en s

S ecu rity S e lec tion

S tocks C om m od ities F X

A sse t A lloca tion

R isky A ssets

C ap ita l A lloca tion


Portfolio Performance Evaluation

How well did the portfolio do? How do we adjust for risk, to compare

different managers? Why?

RiskTimingAsset allocationSecurity selection


Performance Evaluation Measures

Sharpe’s measureThe portfolio’s average excess return per unit of total risk Treynor’s measureThe portfolio’s average excess return per unit of systematic risk Jensen’s measureThe excess of the portfolio’s return over that predicted by the

CAPM Appraisal ratioPortfolio’s abnormal return per unit of risk that could be

diversified by holding a market index portfolio


Performance Attribution

Asset allocation choicesBroad market allocations: equity, bonds, etc.Industry choicesSecurity selection

Evaluation: compare the portfolio returns at each level with returns on the appropriate index (benchmark portfolio or passive strategy)


Active Portfolio Management

Stock-picking and active portfolio management must pay, else the market would not be efficient!

The optimal risky portfolio maximizes the reward-to-variability ratio; the slope of the CAL:

PASSIVECAPITAL ALLOCATON LINE

ACTIVECAPITAL ALLOCATON LINEE(rp)


Conclusion: Hold Three Things

Risk-free asset Passive portfolio Active portfolio


Topics

The Financial Markets Time Value of Money and

Yields Money and Bond

Markets Risk and Return Risk and Diversification Valuation and Asset

Pricing (CAPM)

International Financial Markets

Equity Valuation Cash, Futures, FRAs

and Swaps Options Portfolio Management

and Performance Evaluation


Ian Giddy

Ian H. GiddyNYU Stern School of BusinessTel 212-998-0332; Fax [email protected]://giddy.org

review prof. ian giddy new york university stern school of business

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