Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 1 Chapter 13 Equity Valuation

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 2 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 3 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 4 Dividend Discount Models: General Model V 0 = Value of Stock D t = Dividend k = required return

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 5 No Growth Model Stocks that have earnings and dividends that are expected to remain constant Preferred Stock

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 6 No Growth Model: Example E 1 = D 1 = $5.00 k =.15 V 0 = $5.00 /.15 = $33.33

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 7 Constant Growth Model g = constant perpetual growth rate

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 8 Constant Growth Model: Example E 1 = $5.00b = 40% k = 15% (1-b) = 60%D 1 = $3.00 g = 8% V 0 = 3.00 / ( ) = $42.86

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 9 Estimating Dividend Growth Rates g = growth rate in dividends ROE = Return on Equity for the firm b = plowback or retention percentage rate – (1- dividend payout percentage rate)

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 10 Shifting Growth Rate Model g 1 = first growth rate g 2 = second growth rate T = number of periods of growth at g 1

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 11 Shifting Growth Rate Model: Example D 0 = $2.00 g 1 = 20% g 2 = 5% k = 15% T = 3 D 1 = 2.40 D 2 = 2.88 D 3 = 3.46 D 4 = 3.63 V 0 = D 1 /(1.15) + D 2 /(1.15) 2 + D 3 /(1.15) 3 + D 4 / ( ) ( (1.15) 3 V 0 = = $30.40

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 12 Specified Holding Period Model P N = the expected sales price for the stock at time N N = the specified number of years the stock is expected to be held

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 13 Partitioning Value: Growth and No Growth Components PVGO = Present Value of Growth Opportunities E 1 = Earnings Per Share for period 1

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 14 Partitioning Value: Example ROE = 20% d = 60% b = 40% E 1 = $5.00 D 1 = $3.00 k = 15% g =.20 x.40 =.08 or 8%

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 15 Partitioning Value: Example V o = value with growth NGV o = no growth component value PVGO = Present Value of Growth Opportunities

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 16 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 17 P/E Ratio: No expected growth E 1 - expected earnings for next year –E 1 is equal to D 1 under no growth k - required rate of return

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 18 P/E Ratio with Constant Growth b = retention ration ROE = Return on Equity

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 19 Numerical Example: No Growth E 0 = $2.50 g = 0 k = 12.5% P 0 = D/k = $2.50/.125 = $20.00 PE = 1/k = 1/.125 = 8

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 20 Numerical Example with Growth b = 60% ROE = 15% (1-b) = 40% E 1 = $2.50 (1 + (.6)(.15)) = $2.73 D 1 = $2.73 (1-.6) = $1.09 k = 12.5% g = 9% P 0 = 1.09/( ) = $31.14 PE = 31.14/2.73 = 11.4 PE = (1 -.60) / ( ) = 11.4

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 21 Chapter 10 Bond Prices and Yields

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 22 Bond Characteristics Face or par value Coupon rate –Zero coupon bond Compounding and payments –Accrued Interest Indenture

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 23 Provisions of Bonds Secured or unsecured Call provision Convertible provision Put provision (putable bonds) Floating rate bonds Sinking funds

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 24 Default Risk and Ratings Rating companies –Moody’s Investor Service –Standard & Poor’s –Duff and Phelps –Fitch Rating Categories –Investment grade –Speculative grade

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 25 Factors Used by Rating Companies Coverage ratios Leverage ratios Liquidity ratios Profitability ratios Cash flow to debt

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 26 Bond Pricing P B =Price of the bond C t = interest or coupon payments T = number of periods to maturity r = semi-annual discount rate or the semi-annual yield to maturity

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 27 C t = 40 (SA) P= 1000 T= 20 periods r= 3% (SA) P B = $1, Solving for Price: 10-yr, 8% Coupon Bond, Face = $1,000 t=1 + 20= P B 40 1 ) ( 1+.03) t ( ) 20

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 28 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 29 Prices and Coupon Rates Price Yield

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 30 Approximate Yield to Maturity YTM = (Avg. Income) / (Avg. Price) Avg. Income = Int. +(Par-Price) / Yrs to maturity Avg. Price = (Price + Par) / 2 Using the earlier example Avg. Income = 80 + ( )/10 = Avg. Price = ( )/2 = Approx. YTM = 65.10/ =.0606 or 6.06% Actual YTM = 6.00%

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 31 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 32 Yield Curves Yields Maturity Upward Sloping Downward Sloping

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 33 Theories of Term Structure Expectations Liquidity Preference –Upward bias over expectations Market Segmentation –Preferred Habitat

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 34 Chapter 11 Managing Fixed- Income Investments

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 35 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 36 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 37 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 38 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 39 Duration: Calculation

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 40 Duration Calculation

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 41 Duration/Price Relationship Price change is proportional to duration and not to maturity  P/P = -D x [  (1+y) / (1+y) D * = modified duration D * = D / (1+y)  P/P = - D * x  y

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 42 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 43 Chapter 16 Options Markets

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 44 Option Terminology Buy - Long Sell - Short Call Put Key Elements –Exercise or Strike Price –Premium or Price –Maturity or Expiration

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 45 Market and Exercise Price Relationships In the Money - exercise of the option would be profitable Call: market price>exercise price Put: exercise price>market price Out of the Money - exercise of the option would not be profitable Call: market price>exercise price Put: exercise price>market price At the Money - exercise price and asset price are equal

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 46 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 47 Different Types of Options Stock Options Index Options Futures Options Foreign Currency Options Interest Rate Options

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 48 Payoffs and Profits on Options at Expiration - Calls Notation Stock Price = S T Exercise Price = X Payoff to Call Holder ( S T - X) if S T >X 0if S T < X Profit to Call Holder Payoff - Purchase Price

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 49 Payoffs and Profits on Options at Expiration - Calls Payoff to Call Writer - ( S T - X) if S T >X 0if S T < X Profit to Call Writer Payoff + Premium

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 50 Profit Stock Price 0 Call Writer Call Holder Profit Profiles for Calls

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 51 Payoffs and Profits at Expiration - Puts Payoffs to Put Holder 0if S T > X (X - S T ) if S T < X Profit to Put Holder Payoff - Premium

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 52 Payoffs and Profits at Expiration - Puts Payoffs to Put Writer 0if S T > X -(X - S T )if S T < X Profits to Put Writer Payoff + Premium

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 53 Profit Profiles for Puts 0 Profits Stock Price Put Writer Put Holder

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 54 Equity, Options & Leveraged Equity - Text Example InvestmentStrategyInvestment Equity onlyBuy shares$8,000 Options onlyBuy options$8,000 LeveragedBuy options $1,000 equityBuy 2% $7,000 Yield

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 55 Equity, Options & Leveraged Equity - Payoffs Microsoft Stock Price $75$80$100 All Stock$7,500$8,000$10,000 All Options$0$0$16,000 Lev Equity $7,140$7,140 $9,140

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 56 Equity, Options & Leveraged Equity - Rates of Return Microsoft Stock Price $75 $80$100 $75 $80$100 All Stock-6.25% 0% 25% All Options-100% -100%100% Lev Equity % %14.25%

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 57 Put-Call Parity Relationship S T X Payoff for Call Owned 0S T - X Payoff for Put Written-( X -S T ) 0 Total Payoff S T - X S T - X

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 58 Payoff of Long Call & Short Put Long Call Short Put Payoff Stock Price Combined = Leveraged Equity

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 59 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 = S 0 - X / (1 + r f ) T If the prices are not equal arbitrage will be possible

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 60 Put Call Parity - Disequilibrium Example Stock Price = 110 Call Price = 17 Put Price = 5 Risk Free = 10.25% Maturity =.5 yr X = 105 C - P > S 0 - X / (1 + r f ) T > (105/1.05) 12 > 10 Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 61 Put-Call Parity Arbitrage ImmediateCashflow in Six Months PositionCashflowS T 105 Buy Stock-110 S T S T Borrow X/(1+r) T = Sell Call+17 0-(S T -105) Buy Put S T 0 Total 2 0 0

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 62 Option Strategies Protective Put Long Stock Long Put Covered Call Long Stock Short Call Straddle (Same Exercise Price) Long Call Long Put

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 63 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 expiration Vertical or money spread Same maturity Different exercise price Horizontal or time spread Different maturity dates

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 64 Chapter 17 Option Valuation

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 65 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 66 Time Value of Options: Call Option value X Stock Price Value of Call Intrinsic Value Time value

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 67 Factors Influencing Option Values: Calls FactorEffect on value Stock price increases Exercise price decreases Volatility of stock price increases Time to expirationincreases Interest rate increases Dividend Ratedecreases

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 68 Black-Scholes Option Valuation C o = S o e -  T N(d 1 ) - Xe -rT N(d 2 ) d 1 = [ln(S o /X) + (r –  +  2 /2)T] / (  T 1/2 ) d 2 = d 1 - (  T 1/2 ) where C o = Current call option value. S o = Current stock price N(d) = probability that a random draw from a normal dist. will be less than d.

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 69 Black-Scholes Option Valuation X = Exercise price.  = Annual dividend yield of underlying stock e = , 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 function  Standard deviation of annualized cont. compounded rate of return on the stock

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 70 Call Option Example S o = 100X = 95 r =.10T =.25 (quarter)  =.50  = 0 d 1 = [ln(100/95)+(.10-0+(  5 2 /2))]/(  5 .25 1/2 ) =.43 d 2 =.43 - ((  5 .25 1/2 ) =.18

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 71 Probabilities from Normal Dist. N (.43) =.6664 Table 17.2 d N(d) Interpolation

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 72 Probabilities from Normal Dist. N (.18) =.5714 Table 17.2 d N(d)

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 73 Call Option Value C o = S o e -  T N(d 1 ) - Xe -rT N(d 2 ) C o = 100 X e -.10 X.25 X.5714 C o = Implied Volatility Using Black-Scholes and the actual price of the option, solve for volatility. Is the implied volatility consistent with the stock?

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 74 Put Option Value: Black-Scholes P=Xe -rT [1-N(d 2 )] - S 0 e -  T [1-N(d 1 )] Using the sample data P = $95e (-.10X.25) ( ) - $100 ( ) P = $6.35

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 75 Put Option Valuation: Using Put-Call Parity P = C + PV (X) - S o = C + Xe -rT - S o Using the example data C = 13.70X = 95S = 100 r =.10T =.25 P = e -.10 X P = 6.35

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 76 Using the Black-Scholes Formula Hedging: Hedge ratio or delta The number of stocks required to hedge against the price risk of holding one option Call = N (d 1 ) Put = N (d 1 ) - 1 Option Elasticity Percentage change in the option’s value given a 1% change in the value of the underlying stock

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 77 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 78 Chapter 18 Futures Markets

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 79 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 80 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 price Short = original futures price minus spot

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 81 Types of Contracts Agricultural commodities Metals and minerals (including energy contracts) Foreign currencies Financial futures Interest rate futures Stock index futures

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 82 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 83 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.

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 84 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 85 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 86 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 87 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 88 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 89 Parity Example Outcomes Strategy A: ActionInitial flowsFlows at T Buy stock-S o S T Strategy B:ActionInitial flowsFlows at T Long futures0S T - F O Invest in Bill F O (1+r f ) T - F O (1+r f ) T F O Total for B - F O (1+r f ) T S T

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 90 Price of Futures with Parity Since the strategies have the same flows at time T F O / (1 + r f ) T = S O F O = S O (1 + r f ) T The futures price has to equal the carrying cost of the stock

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 91 Chapter 9 The Efficient Market Hypothesis

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 92 Efficient Market Hypothesis (EMH) Do security prices reflect information ? Why look at market efficiency –Implications for business and corporate finance –Implications for investment

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 93 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 94 SecurityPrices Time Random Walk with Positive Trend

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 95 Why are price changes random? –Prices react to information –Flow of information is random –Therefore, price changes are random Random Price Changes

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 96 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 97 Forms of the EMH Weak Semi-strong Strong

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 98 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 99 Active Management –Security analysis –Timing Passive Management –Buy and Hold –Index Funds Implications of Efficiency for Active or Passive Management

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 100 Even if the market is efficient a role exists for portfolio management Appropriate risk level Tax considerations Other considerations Market Efficiency and Portfolio Management