1 Bodie Kane Marcus Essentials of Investments Fourth

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

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

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

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

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

6 Bodie • Kane • Marcus Essentials of Investments Fourth Edition No Growth Model: Example E 1 = D 1 = $5. 00 k =. 15 V 0 = $5. 00 /. 15 = $33. 33 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

8 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Constant Growth Model: Example E 1 = $5. 00 b = 40% k = 15% (1 -b) = 60% D 1 = $3. 00 g = 8% V 0 = 3. 00 / (. 15 -. 08) = $42. 86 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

9 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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) Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

11 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 / (. 15 -. 05) ( (1. 15)3 V 0 = 2. 09 + 2. 18 + 2. 27 + 23. 86 = $30. 40 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

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

14 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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% Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

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

17 Essentials of Investments Bodie • Kane • Marcus Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

19 Essentials of Investments Bodie • Kane • Marcus Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

20 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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/(. 125 -. 09) = $31. 14 PE = 31. 14/2. 73 = 11. 4 PE = (1 -. 60) / (. 125 -. 09) = 11. 4 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

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

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

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

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

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

27 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Solving for Price: 10 -yr, 8% Coupon Bond, Face = $1, 000 20 P B = 40 S t =1 1 1 + 1000 (1+. 03) t (1+. 03) 20 PB = $1, 148. 77 Ct P T r Irwin / Mc. Graw-Hill = 40 (SA) = 1000 = 20 periods = 3% (SA) © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

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

30 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 + (1000 -1149)/10 = 65. 10 Avg. Price = (1000 + 1149)/2 = 1074. 50 Approx. YTM = 65. 10/1074. 50 =. 0606 or 6. 06% Actual YTM = 6. 00% Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

45 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

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

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

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

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

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

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

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

54 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Equity, Options & Leveraged Equity Text Example Investment Strategy Equity only Buy stock @ 80 100 shares $8, 000 Options only Buy calls @ 10 800 options $8, 000 Leveraged equity Buy calls @ 10 100 options Buy T-bills @ 2% Yield $1, 000 $7, 000 Irwin / Mc. Graw-Hill Investment © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

55 Essentials of Investments Bodie • Kane • Marcus Fourth Edition 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 $9, 140 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

56 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Equity, Options & Leveraged Equity Rates of Return Microsoft Stock Price $75 $80 $100 All Stock -6. 25% 0% 25% All Options -100% Lev Equity -10. 75% 14. 25% Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

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

59 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 + rf)T If the prices are not equal arbitrage will be possible Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

60 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 + 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

61 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Put-Call Parity Arbitrage Position Immediate Cashflow Buy Stock -110 ST ST Borrow X/(1+r)T = 100 +100 -105 Sell Call +17 0 Buy Put -5 Total 2 Irwin / Mc. Graw-Hill Cashflow in Six Months ST<105 ST> 105 -ST 0 -(ST-105) 0 0 © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

63 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

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

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

67 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Factors Influencing Option Values: Calls Factor Effect on value Stock price increases Exercise price decreases Volatility of stock price increases Time to expiration increases Interest rate increases Dividend Rate decreases Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

68 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Black-Scholes Option Valuation Co = Soe-d. TN(d 1) - Xe-r. TN(d 2) d 1 = [ln(So/X) + (r – d + s 2/2)T] / (s T 1/2) d 2 = d 1 - (s T 1/2) where Co = Current call option value. So = Current stock price N(d) = probability that a random draw from a normal dist. will be less than d. Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

70 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Call Option Example So = 100 X = 95 r =. 10 T =. 25 (quarter) s =. 50 d = 0 d 1 = [ln(100/95)+(. 10 -0+(. 5 2/2))]/(. 5. 251/2) =. 43 d 2 =. 43 - ((. 5)(. 251/2) =. 18 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

71 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Probabilities from Normal Dist. N (. 43) =. 6664 Table 17. 2 d N(d). 42. 6628. 43. 6664 Interpolation. 44. 6700 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

72 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Probabilities from Normal Dist. N (. 18) =. 5714 Table 17. 2 d N(d). 16. 5636. 18. 5714. 20. 5793 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

73 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Call Option Value Co = Soe-d. TN(d 1) - Xe-r. TN(d 2) Co = 100 X. 6664 - 95 e-. 10 X. 25 X. 5714 Co = 13. 70 Implied Volatility Using Black-Scholes and the actual price of the option, solve for volatility. Is the implied volatility consistent with the stock? Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

74 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Put Option Value: Black-Scholes P=Xe-r. T [1 -N(d 2)] - S 0 e-d. T [1 -N(d 1)] Using the sample data P = $95 e(-. 10 X. 25)(1 -. 5714) - $100 (1 -. 6664) P = $6. 35 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

75 Bodie • Kane • Marcus Essentials of Investments Fourth Edition Put Option Valuation: Using Put-Call Parity P = C + PV (X) - So = C + Xe-r. T - So Using the example data C = 13. 70 X = 95 S = 100 r =. 10 T =. 25 P = 13. 70 + 95 e -. 10 X. 25 - 100 P = 6. 35 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

76 Essentials of Investments Bodie • Kane • Marcus Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

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

79 Essentials of Investments Bodie • Kane • Marcus Fourth Edition 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 – – Irwin / Mc. Graw-Hill Secondary trading - liquidity Marked to market Standardized contract units Clearinghouse warrants performance © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

80 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

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

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

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

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

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

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

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

89 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Parity Example Outcomes Strategy A: Action Buy stock Strategy B: Action Long futures Irwin / Mc. Graw-Hill Initial flows Flows at T -So ST Initial flows Flows at T 0 ST - F O Invest in Bill FO(1+rf)T - FO(1+rf)T FO Total for B ST - FO(1+rf)T © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

90 Bodie • Kane • Marcus Essentials of Investments Fourth Edition 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 Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

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

93 Essentials of Investments Bodie • Kane • Marcus Fourth Edition Random Walk and the EMH • Random Walk - stock prices are random – Actually submartingale • Expected price is positive over time • Positive trend and random about the trend Irwin / Mc. Graw-Hill © 2001 The Mc. Graw-Hill Companies, Inc. All rights reserved.

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

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

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

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

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

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

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