3. You have been given this probability distribution for the holding period return for XYZ stock:

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1 Fin 85 Sample Final Solution Name: Date: Part I ultiple Choice 1. Which of the following is true of the Dow Jones Industrial Average? A) It is a value-weighted average of 30 large industrial stocks. ) It is a price-weighted average of 30 large industrial stocks. C) he divisor must be adjusted for stock splits. D) A and C. E) and C.. Assume that you purchased 00 shares of Super Performing mutual fund at a net asset value of $1 per share. During the year you received dividend income distributions of $1.50 per share and capital gains distributions of $.85 per share. At the end of the year the shares had a net asset value of $3 per share. What was your rate of return on this investment? A) 30.4% ) 5.37% C) 7.19% D).44% E) 9.18% 3. You have been given this probability distribution for the holding period return for XYZ stock: State of the Economy Probability HPR oom.30 18% Normal growth.50 1% Recession.0-5% What is the standard deviation for XYZ stock? A).07% ) 9.96% C) 7.04% D) 1.44% E) 8.13%

2 Use the following to answer question 4: Investment Expected Return E(r) Standard Deviation U E(r) - (A/)s, where A ased on the utility function above, which investment would you select? A) 1 ) C) 3 D) 4 E) cannot tell from the information given 5. he Capital arket Line I) is a special case of the Capital Allocation Line. II) represents the opportunity set of a passive investment strategy. III) has the one-month -ill rate as its intercept. IV) uses a broad index of common stocks as its risky portfolio. A) I, III, and IV ) II, III, and IV C) III and IV D) I, II, and III E) I, II, III, and IV 6. Security X has expected return of 1% and standard deviation of 0%. Security Y has expected return of 15% and standard deviation of 7%. If the two securities have a correlation coefficient of 0.7, what is their covariance? A) ) C) D) E) 0.054

3 7. Given the following two stocks A and Security Expected rate of return eta A If the expected market rate of return is 0.09 and the risk-free rate is 0.05, which security would be considered the better buy and why? A) A because it offers an expected excess return of 1.%. ) because it offers an expected excess return of 1.8%. C) A because it offers an expected excess return of.%. D) because it offers an expected return of 14%. E) because it has a higher beta. 8. In the single-index model represented by the equation r i E(r i ) + β i F + e i, the term e i represents A) the impact of unanticipated macroeconomic events on security i's return. ) the impact of unanticipated firm-specific events on security i's return. C) the impact of anticipated macroeconomic events on security i's return. D) the impact of anticipated firm-specific events on security i's return. E) the impact of changes in the market on security i's return. 9. A bond with a 1% coupon, 10 years to maturity and selling at 88 has a yield to maturity of. A) over 14% ) between 13% and 14% C) between 1% and 13% D) between 10% and 1% E) less than 1% 10. he duration of a par value bond with a coupon rate of 8% and a remaining time to maturity of 5 years is A) 5 years. ) 5.4 years. C) 4.17 years. D) 4.31 years. E) none of the above.

4 11. he maximum loss a buyer of a stock call option can suffer is equal to A) the striking price minus the stock price. ) the stock price minus the value of the call. C) the call premium. D) the stock price. E) none of the above. 1. Relative to non-dividend-paying European calls, otherwise identical American call options A) are less valuable. ) are more valuable. C) are equal in value. D) will always be exercised earlier. E) none of the above.

5 Answer Key 1. E. A 3. E 4. C 5. E 6. A 7. C A 10. D 11. C 1. C Part II Problem Solving: 1. Consider a stock market with two stocks X and Y only. P represents prices and Q represents shares outstanding. wo periods: 0 and 1. Stock P 0 Q 0 P 1 Q 1 X $100/share 00 $108/share 00 Y $80/share 300 $4/share 600 Immediately after time 0, company Y announced a two-for-one split. (1) Compute the price-weighted indexes at time 0 and 1 respectively. Index 0 (100+80)/90 Divisor(100+40)/ Index 1 ((108+4)/ () Compute the rate of return using the market-value-weighted index. Index0(100*00+80*300)44,000 Index1(108*00+4*600) ,800 Rate( )/ %

6 . (CAP and Single-index odel) In a two-stock capital market, information of stocks A and is given in the following table. Stock Capitalization Expected Return Standard Deviation A 500 7% 15% 300 9% 5% he coefficient of correlation between the two stocks is ρ0.5. he risk-free rate is r f 4%. (1) What is the arket Portfolio? Answer: (w A 0.65, w 0.375) () Compute the expected return and standard deviation of the market portfolio? Answer: r w r A A + wr E( r ) wae( ra ) + w E( r ) % + Var( wara + wr ) wa A + w + waw A ρ ( 0.65) ( 0.15) + ( 0.375) ( 0.5) + ( 0.65)( 0.375)( 0.15)( 0.5)( 0.5) % % 7.75% (3) Assume that the CAP is holding and the capital market is in equilibrium. As an investor in the capital market, what is your optimal risky portfolio? Answer: Same as the arket Portfolio (w A 0.65, w 0.375). (4) Write down the equation for Security arket Line. E r i β β Answer: ( ) i ( ) i (5) Compute the etas for stock A and separately.

7 Cov β A wa A + w A ρ Answer: wa A ( r, r ) Cov( r, w r + w r ) ( 0.65)( 0.15) + ( 0.375)( 0.15)( 0.5)( 0.5) 0.8 Cov β A A A A ( r, r ) Cov( r, w r + w r ) ( 0.65)( 0.15)( 0.5)( 0.5) + ( 0.375)( 0.5) 1.33 ρ + w A A (6) According to the Single-index odel, calculate the covariance between A and using their betas. cov r, β β Answer: ( ) ( )( )( ) 081 A r A 3. An insurance company must make payments to a customer of $10 million in years and $0 million in 5 years. he yield to maturity is flat at 10%. If it wants fully fund and immunize its obligation to this customer with a single issue of a zero-coupon bond, what maturity bond must it purchase? D 1 and D 5, 10 p p 1 p p w w ( ) 0 ( ) 1 D D w 1 + p p p D w p p (0.4) + 5(0.6) 3.8

8 4. A butterfly spread can be created by put options and used to profit from low volatility in stock prices. For example, the investor will buy a put with strike price of X 1 $100; buy a put with strike price of X 3 $140; sell two puts with strike price of X $10. Derive the payoffs on the expiration day and plot the payoff profile for this utterfly spread. Solution: Payoff max{ 100 S,0} + max{ 140 S,0} max{ 10 S,0} If S 100, then payoff 100 S S ( 10 S ) 0 If ( 100,10) S 10 S S If S ( 10,140), then payoff S S If S 140, the payoff0 S, then payoff ( ) 100 In summary, we have Payoff 0 S S 0 [ 0,100] ( 100,10) ( 10,140) S S S S [140, ) Payoff to utterfly Spread S 5. Stock price of XYZ Company follows following pattern in six months. Every period is three months. here is no dividend payment during the six months. Risk-free rate is 4%.

9 $14 $11 oday, State 1,1 $1 State,1 $11 State, $11 $1 $10 Value a call option on XYZ stock with an exercise price X$11 and six months to expiration. Solution: Risk neutral probabilities: p S 0 ( 1+ r) S u S S d d

10 p p p C C ( + 4% ) ( + 4% ) ( + 4% ) (0.377)3 (0.554)1 (0.1084) C 3 / / / ( ) /1 ( 1+ 4% ) + ( ) /1 ( 1+ 4% ) ( 1.107) + ( )( ) 3 /1 ( 1+ 4% ) p $ State 1,1 p $1.107 State,1 p $ State, $3 0 1 $0