irwin / mcgraw-hill

Essentials of Investments

© 2001 The McGraw-Hill Companies, Inc. All rights reserved.

Fourth Edition

Irwin / McGraw-Hill

Bodie • Kane • Marcus1

Chapter 13

Equity Valuation



Fourth Edition

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Fundamental Stock Analysis: Models of Equity Valuation

• Basic Types of Models– Balance Sheet Models– Dividend Discount Models– Price/Earning Ratios

• Estimating Growth Rates and Opportunities



Fourth Edition

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Intrinsic Value and Market Price

• Intrinsic Value– Self assigned Value– Variety of models are used for estimation

• Market Price– Consensus value of all potential traders

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



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Dividend Discount Models:General Model

V Dk

ot

tt

( )11

• V0 = Value of Stock• Dt = Dividend• k = required return



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No Growth Model

V Dk

o

• Stocks that have earnings and dividends that are expected to remain constant

• Preferred Stock



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No Growth Model: Example

E1 = D1 = $5.00

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

V Dk

o



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Constant Growth Model

Vo D gk go

( )1

• g = constant perpetual growth rate



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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



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Estimating Dividend Growth Rates

g ROE b

• g = growth rate in dividends• ROE = Return on Equity for the firm• b = plowback or retention percentage rate

– (1- dividend payout percentage rate)



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Shifting Growth Rate Model

V D gk

D gk g k

o o

t

tt

TT

T

( )

( )( )

( )( )11

11

1

1

2

2

• g1 = first growth rate

• g2 = second growth rate

• T = number of periods of growth at g1



Fourth Edition

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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



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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



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Partitioning Value: Growth and No Growth Components

V Ek

PVGO

PVGO D gk g

Ek

o

o

1

11( )( )

• PVGO = Present Value of Growth Opportunities

• E1 = Earnings Per Share for period 1



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Partitioning Value: Example

• ROE = 20% d = 60% b = 40%

• E1 = $5.00 D1 = $3.00 k = 15%

• g = .20 x .40 = .08 or 8%



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V

NGV

PVGO

o

o

315 08

86

515

33

86 33 52

(. . )$42.

.$33.

$42. $33. $9.

Partitioning Value: Example

VVoo = value with growth = value with growthNGVNGVoo = no growth component value = no growth component valuePVGO = Present Value of Growth OpportunitiesPVGO = Present Value of Growth Opportunities



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Price Earnings Ratios

• P/E Ratios are a function of two factors– Required Rates of Return (k)– Expected growth in Dividends

• Uses– Relative valuation– Extensive Use in industry



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P/E Ratio: No expected growth

P Ek

PE k

01

0

1

1

• E1 - expected earnings for next year– E1 is equal to D1 under no growth

• k - required rate of return



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P/E Ratio with Constant Growth

PD

k gE b

k b ROEPE

bk b ROE

01 1

0

1

1

1

( )( )

( )

• b = retention ration• ROE = Return on Equity



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Numerical Example: No Growth

E0 = $2.50 g = 0 k = 12.5%

P0 = D/k = $2.50/.125 = $20.00

PE = 1/k = 1/.125 = 8



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Numerical Example with Growth

b = 60% ROE = 15% (1-b) = 40%E1 = $2.50 (1 + (.6)(.15)) = $2.73

D1 = $2.73 (1-.6) = $1.09

k = 12.5% g = 9%P0 = 1.09/(.125-.09) = $31.14

PE = 31.14/2.73 = 11.4PE = (1 - .60) / (.125 - .09) = 11.4



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Chapter 10

Bond Prices and Yields



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Bond Characteristics

• Face or par value• Coupon rate

– Zero coupon bond• Compounding and payments

– Accrued Interest• Indenture



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Provisions of Bonds

• Secured or unsecured• Call provision• Convertible provision• Put provision (putable bonds)• Floating rate bonds• Sinking funds



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Default Risk and Ratings

• Rating companies– Moody’s Investor Service– Standard & Poor’s– Duff and Phelps– Fitch

• Rating Categories– Investment grade– Speculative grade



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Factors Used by Rating Companies

• Coverage ratios• Leverage ratios• Liquidity ratios• Profitability ratios• Cash flow to debt



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Bond Pricing

P Cr

ParValuer

B tT

t

TT

T

( ) ( )1 11

PB = Price of the bond

Ct = interest or coupon payments

T = number of periods to maturityr = semi-annual discount rate or the semi-annual

yield to maturity



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CCtt = 40 (SA)= 40 (SA)PP = 1000= 1000TT = 20 periods= 20 periodsrr = 3% (SA)= 3% (SA)

PB = $1,148.77

Solving for Price: 10-yr, 8% Coupon Bond, Face = $1,000

tt=1=1++

2020== PPBB 4040 11

(1+.03)) t 1000 1(1+.03) 20



Fourth Edition

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Bond Prices and Yields

Prices and Yields (required rates of return) have an inverse relationship

• When yields get very high the value of the bond will be very low

• When yields approach zero, the value of the bond approaches the sum of the cash flows



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Prices and Coupon Rates

Price

Yield



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Approximate Yield to Maturity

YTM = (Avg. Income) / (Avg. Price)Avg. Income = Int. +(Par-Price) / Yrs to maturityAvg. Price = (Price + Par) / 2

Using the earlier exampleAvg. Income = 80 + (1000-1149)/10 = 65.10Avg. Price = (1000 + 1149)/2 = 1074.50Approx. YTM = 65.10/1074.50 = .0606 or

6.06%Actual YTM = 6.00%



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Term Structure of Interest Rates

• Relationship between yields to maturity and maturity

• Yield curve - a graph of the yields on bonds relative to the number of years to maturity– Usually Treasury Bonds– Have to be similar risk or other factors

would be influencing yields



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Yield Curves

Yields

Maturity

Upward Upward SlopingSloping

Downward Downward SlopingSloping



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Theories of Term Structure

• Expectations• Liquidity Preference

– Upward bias over expectations• Market Segmentation

– Preferred Habitat



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Chapter 11

Managing Fixed-Income Investments



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Managing Fixed Income Securities: Basic Strategies

• Active strategy– Trade on interest rate predictions– Trade on market inefficiencies

• Passive strategy– Control risk– Balance risk and return



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Bond Pricing Relationships

• Inverse relationship between price and yield

• An increase in a bond’s yield to maturity results in a smaller price decline than the gain associated with a decrease in yield

• Long-term bonds tend to be more price sensitive than short-term bonds



Fourth Edition

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Bond Pricing Relationships (cont.)

• As maturity increases, price sensitivity increases at a decreasing rate

• Price sensitivity is inversely related to a bond’s coupon rate

• Price sensitivity is inversely related to the yield to maturity at which the bond is selling



Fourth Edition

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Duration• A measure of the effective maturity of a bond• The weighted average of the times until each payment is received,

with the weights proportional to the present value of the payment• Duration is shorter than maturity for all bonds except zero coupon

bonds• Duration is equal to maturity for zero coupon bonds



Fourth Edition

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Duration: Calculation

t ttw CF y ice ( )1 Pr

D t wt

T

t

1

CF Cash Flow for period tt



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Duration Calculation

8%Bond

Timeyears

Payment PV of CF(10%)

Weight C1 XC4

1 80 72.727 .0765 .0765

2 80 66.116 .0690 .1392

Sum3 1080 811.420

950.263

.8539

1.0000

2.5617

2.7774



Fourth Edition

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Duration/Price Relationship

Price change is proportional to duration and not to maturity

P/P = -D x [(1+y) / (1+y)D* = modified durationD* = D / (1+y)P/P = - D* x y



Fourth Edition

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Uses of Duration

• Summary measure of length or effective maturity for a portfolio

• Immunization of interest rate risk (passive management)– Net worth immunization– Target date immunization

• Measure of price sensitivity for changes in interest rate



Fourth Edition

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Chapter 16

Options Markets



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Option Terminology

• Buy - Long • Sell - Short• Call• Put • Key Elements

– Exercise or Strike Price– Premium or Price– Maturity or Expiration



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Market and Exercise Price Relationships

In the Money - exercise of the option would be profitableCall: market price>exercise pricePut: exercise price>market price

Out of the Money - exercise of the option would not be profitableCall: market price>exercise pricePut: exercise price>market price

At the Money - exercise price and asset price are equal



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American vs European Options

American - the option can be exercised at any time before expiration or maturity

European - the option can only be exercised on the expiration or maturity date



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Different Types of Options

• Stock Options• Index Options• Futures Options• Foreign Currency Options• Interest Rate Options



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Payoffs and Profits on Options at Expiration - Calls

Notation Stock Price = ST Exercise Price = XPayoff to Call Holder

(ST - X) if ST >X 0if ST < X

Profit to Call HolderPayoff - Purchase Price



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Payoffs and Profits on Options at Expiration - Calls

Payoff to Call Writer - (ST - X) if ST >X

0 if ST < XProfit to Call Writer

Payoff + Premium



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ProfitProfit

Stock PriceStock Price

0

Call WriterCall Writer

Call HolderCall Holder

Profit Profiles for CallsProfit Profiles for Calls



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Payoffs and Profits at Expiration - Puts

Payoffs to Put Holder0 if ST > X

(X - ST) if ST < X

Profit to Put Holder Payoff - Premium



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Payoffs and Profits at Expiration - Puts

Payoffs to Put Writer0 if ST > X

-(X - ST) if ST < X

Profits to Put WriterPayoff + Premium



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Profit Profiles for PutsProfit Profiles for Puts

0

Profits

Stock Price

Put Writer

Put Holder



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Equity, Options & Leveraged Equity - Text Example

Investment Strategy Investment

Equity only Buy stock @ 80 100 shares $8,000

Options only Buy calls @ 10 800 options $8,000

Leveraged Buy calls @ 10 100 options $1,000equity Buy T-bills @ 2% $7,000

Yield



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Equity, Options & Leveraged Equity - Payoffs

Microsoft Stock PriceMicrosoft Stock Price

$75$75 $80$80 $100$100

All StockAll Stock $7,500$7,500 $8,000$8,000 $10,000$10,000

All OptionsAll Options $0$0 $0$0 $16,000$16,000

Lev Equity Lev Equity $7,140$7,140 $7,140$7,140 $9,140 $9,140



Fourth Edition

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Equity, Options & Leveraged Equity - Rates of Return

Microsoft Stock PriceMicrosoft Stock Price

$75$75 $80 $80 $100$100

All StockAll Stock -6.25%-6.25% 0% 0% 25% 25%

All OptionsAll Options -100% -100%-100% -100% 100%100%

Lev Equity Lev Equity -10.75% -10.75%-10.75% -10.75% 14.25%14.25%



Fourth Edition

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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



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Payoff of Long Call & Short Put

Long Call

Short Put

Payoff

Stock Price

Combined =Leveraged Equity



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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



Fourth Edition

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Put Call Parity - Disequilibrium Example

Stock Price = 110 Call Price = 17Put Price = 5 Risk Free = 10.25%Maturity = .5 yr X = 105

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

17- 5 > 110 - (105/1.05) 12 > 10

Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative



Fourth Edition

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Put-Call Parity Arbitrage

ImmediateImmediate Cashflow in Six MonthsCashflow in Six MonthsPositionPosition CashflowCashflow SSTT<105<105 SSTT>> 105 105

Buy StockBuy Stock -110-110 S STT S STT

BorrowBorrowX/(1+r)X/(1+r)TT = 100 = 100 +100+100 -105-105 -105-105

Sell CallSell Call +17+17 0 0 -(S-(STT-105)-105)

Buy PutBuy Put -5 -5 105-S105-STT 0 0

TotalTotal 22 0 0 0 0



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Option Strategies

Protective PutLong Stock Long Put

Covered Call Long StockShort Call

Straddle (Same Exercise Price)Long Call Long Put



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Option Strategies

Spreads - A combination of two or more call options or put options on the same asset with differing exercise prices or times to expirationVertical or money spread

Same maturityDifferent exercise price

Horizontal or time spreadDifferent maturity dates



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Chapter 17

Option Valuation



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Option Values

• Intrinsic value - profit that could be made if the option was immediately exercised– Call: stock price - exercise price– Put: exercise price - stock price

• Time value - the difference between the option price and the intrinsic value



Fourth Edition

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Time Value of Options: Call

Option value

XStock Price

Value of Call Intrinsic Value

Time value



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Factors Influencing Option Values: Calls

Factor Effect on valueStock price increasesExercise price decreasesVolatility of stock price increasesTime to expiration increasesInterest rate increasesDividend Rate decreases



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Black-Scholes Option Valuation

Co = Soe-TN(d1) - Xe-rTN(d2)

d1 = [ln(So/X) + (r – + 2/2)T] / (T1/2)

d2 = d1 - (T1/2)

whereCo = Current call option value.

So = Current stock price

N(d) = probability that a random draw from a normal dist. will be less than d.



Fourth Edition

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Black-Scholes Option Valuation

X = Exercise price. = Annual dividend yield of underlying stocke = 2.71828, the base of the nat. log.r = Risk-free interest rate (annualizes

continuously compounded with the same maturity as the option.

T = time to maturity of the option in years.ln = Natural log functionStandard deviation of annualized cont.

compounded rate of return on the stock



Fourth Edition

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Call Option Example

So = 100 X = 95

r = .10 T = .25 (quarter)= .50 = 0d1 = [ln(100/95)+(.10-0+(5 2/2))]/(5.251/2)

= .43 d2 = .43 - ((5.251/2)

= .18



Fourth Edition

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Probabilities from Normal Dist.

N (.43) = .6664Table 17.2

d N(d) .42 .6628 .43 .6664 Interpolation .44 .6700



Fourth Edition

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Probabilities from Normal Dist.

N (.18) = .5714Table 17.2

d N(d) .16 .5636 .18 .5714 .20 .5793



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Call Option Value

Co = Soe-TN(d1) - Xe-rTN(d2)Co = 100 X .6664 - 95 e- .10 X .25 X .5714

Co = 13.70

Implied VolatilityUsing Black-Scholes and the actual price

of the option, solve for volatility.Is the implied volatility consistent with the

stock?



Fourth Edition

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Put Option Value: Black-Scholes

P=Xe-rT [1-N(d2)] - S0e-T [1-N(d1)]

Using the sample dataP = $95e(-.10X.25)(1-.5714) - $100 (1-.6664)P = $6.35



Fourth Edition

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Put Option Valuation: Using Put-Call Parity

P = C + PV (X) - So

= C + Xe-rT - So

Using the example dataC = 13.70 X = 95 S = 100r = .10 T = .25P = 13.70 + 95 e -.10 X .25 - 100P = 6.35



Fourth Edition

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Using the Black-Scholes Formula

Hedging: Hedge ratio or delta The number of stocks required to hedge against

the price risk of holding one optionCall = N (d1)

Put = N (d1) - 1

Option ElasticityPercentage change in the option’s value given a 1% change in the value of the underlying stock



Fourth Edition

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Portfolio Insurance - Protecting Against Declines in Stock Value

• Buying Puts - results in downside protection with unlimited upside potential

• Limitations – Tracking errors if indexes are used for the

puts– Maturity of puts may be too short– Hedge ratios or deltas change as stock

values change



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Chapter 18

Futures Markets



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Futures and Forwards

• Forward - an agreement calling for a future delivery of an asset at an agreed-upon price

• Futures - similar to forward but feature formalized and standardized characteristics

• Key difference in futures– Secondary trading - liquidity– Marked to market– Standardized contract units– Clearinghouse warrants performance



Fourth Edition

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Key Terms for Futures Contracts

• Futures price - agreed-upon price at maturity

• Long position - agree to purchase• Short position - agree to sell• Profits on positions at maturity

Long = spot minus original futures priceShort = original futures price minus spot



Fourth Edition

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Types of Contracts

• Agricultural commodities• Metals and minerals (including energy

contracts)• Foreign currencies• Financial futures

Interest rate futuresStock index futures



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Trading Mechanics

• Clearinghouse - acts as a party to all buyers and sellers.– Obligated to deliver or supply delivery

• Closing out positions– Reversing the trade– Take or make delivery– Most trades are reversed and do not

involve actual delivery



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Margin and Trading Arrangements

Initial Margin - funds deposited to provide capital to absorb losses

Marking to Market - each day the profits or losses from the new futures price and reflected in the account.

Maintenance or variance margin - an established value below which a trader’s margin may not fall.



Fourth Edition

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Margin and Trading Arrangements

Margin call - when the maintenance margin is reached, broker will ask for additional margin funds

Convergence of Price - as maturity approaches the spot and futures price converge

Delivery - Actual commodity of a certain grade with a delivery location or for some contracts cash settlement



Fourth Edition

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Trading Strategies

• Speculation - – short - believe price will fall– long - believe price will rise

• Hedging -– long hedge - protecting against a rise in

price– short hedge - protecting against a fall in

price



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Basis and Basis Risk

• Basis - the difference between the futures price and the spot price– over time the basis will likely change and

will eventually converge• Basis Risk - the variability in the basis

that will affect profits and/or hedging performance



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Futures Pricing

• Spot-futures parity theorem - two ways to acquire an asset for some date in the future– Purchase it now and store it– Take a long position in futures– These two strategies must have the same

market determined costs



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Parity Example

Stock that pays no cash dividend– no storage costs– no 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



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Parity Example OutcomesParity Example Outcomes

Strategy A: Strategy A: ActionAction Initial flowsInitial flows Flows at TFlows at T

Buy stockBuy stock -S-Soo SSTT

Strategy B:Strategy B: ActionAction Initial flowsInitial flows Flows at TFlows at T

Long futuresLong futures 00 SSTT - F - FOO

Invest in BillInvest in BillFFOO(1+r(1+rff))TT - F - FOO(1+r(1+rff))TT FFOO

Total for B Total for B - F - FOO(1+r(1+rff))TT SSTT



Fourth Edition

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Price of Futures with Parity

Since the strategies have the same flows at time T

FO / (1 + rf)T = SO

FO = SO (1 + rf)T

The futures price has to equal the carrying cost of the stock



Fourth Edition

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Chapter 9

The Efficient Market Hypothesis



Fourth Edition

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Efficient Market Hypothesis (EMH)

• Do security prices reflect information ?• Why look at market efficiency

– Implications for business and corporate finance

– Implications for investment



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• Random Walk - stock prices are random– Actually submartingale

• Expected price is positive over time• Positive trend and random about the trend

Random Walk and the EMH



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Security Security PricesPrices

TimeTime

Random Walk with Positive TrendRandom Walk with Positive Trend



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• Why are price changes random?– Prices react to information– Flow of information is random– Therefore, price changes are random

Random Price Changes



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EMH and Competition

• Stock prices fully and accurately reflect publicly available information

• Once information becomes available, market participants analyze it

• Competition assures prices reflect information



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Forms of the EMH

• Weak• Semi-strong• Strong



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Types of Stock Analysis

• Technical Analysis - using prices and volume information to predict future prices– Weak form efficiency & technical analysis

• Fundamental Analysis - using economic and accounting information to predict stock prices– Semi strong form efficiency & fundamental

analysis



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• Active Management– Security analysis– Timing

• Passive Management– Buy and Hold– Index Funds

Implications of Efficiency for Active or Passive Management



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Even if the market is efficient a role exists for portfolio management

• Appropriate risk level• Tax considerations• Other considerations

Market Efficiency and Portfolio Management

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