Final 2001 - FINANCE 100: Corporate Finance Solutions to...

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FINANCE 100: Corporate Finance Solutions to Sample Final Exam Professor Roberts NAME: SECTION: LOCKER #: Question Maximum Student Score Q u e s t i o n 1 B o n d s 1 5 Question 2 Portfolio Analysis 10 Question 3 CAPM 15 Question 4 Futures, Forwards & Options 25 Question 5 Options 20 Question 6 Leverage 15 TOTAL 100 1
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Question 1: (Bonds, 15 points) a) Find the price of a 10% Government coupon bond that pays annual coupons, matures in exactly 2 years, and has a face value of $1,000. The yield to maturity is 4.09% p.a. compounded annually. The bond has just paid its annual coupon, hence you need to price it assuming that the first coupon that you will receive is due in exactly one year. (5 points) Answer: The value of this bond is: = + ⎡ − = 2 2 0 ) 0409 . 1 ( 000 , 1 0409 . ) 0409 . 1 ( 1 100 P $1,111.3 b) You have the following data on spot and forward rates on US treasury securities: Time horizon Rates r 0 , 1 4.12% f 1,2 4.06% f 2,3 4.36% f 3,5 4.18% For example, the one-year spot interest rate, r 0 , 1, is 4.12%. The one-year forward rate starting in one year for one year, f 1,2 , is 4.06%. All rates compound annually. Construct the term structure of interest rates from the data above. That is, calculate the implied yields on a 1, 2, 3, and 5-year zero coupon bonds using the information about the forward rates. (6 points) Answer: the yield on a one-year zero coupon bond is given as 4.12%. The yield on the 2- year zero coupon bond is obtained by noting that: (1+ r 0,2 ) 2 = (1+ r 0,1 )*(1+ f 1,2 ) so r 0,2 = 4.09%. The rest of the yields are calculated similarly and given in the next table: Time horizon Rates r 0,1 4.12% 4.12% f 1,2 4.06% r 0,2 = 4.09% f 2,3 4.36% r 0,3 = 4.18% f 3,5 4.18% r 0,5 = 4.18% 2
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c) What is the forward rate f 1,5 ; that is, the forward rate on a four-year loan starting in one year? (4 points) Answer: We know that the following relationship holds: (1+ r 0,5 ) 5 = (1+ r 0,1 )*(1+ f 1,5 ) 4 , so (1.0418) 5 = (1.0412)*(1+ f 1,5 ) 4 , therefore f 1,5 = 4.195% Question 2: (Portfolio Analysis, 10 points) Asset A has an expected return of 18% and a standard deviation of 38%. Asset B has an expected return of 14% and a standard deviation of 21%. The correlation between asset A and B is –0.4. a) How much should you invest in asset A and asset B in order to obtain an expected return of 17%? (3 points) Answer: We need to invest 25% of our wealth in asset B and 75% in asset A. % 25 % 18 * ) 1 ( % 14 * % 17 = + = w w w b) Assuming you can borrow and lend at the risk-free rate of 8%, which asset (A or B) offers a better investment opportunity? Explain why. (3 points) Answer: We can compare the Sharpe ratio for each asset as: Since asset B has a greater Sharpe ratio, it offers a better investment opportunity. ( ) () 286 . 0 21 . 0 08 . 0 14 . 0 ) ( 263 . 0 38 . 0 08 . 0 18 . 0 ) ( = = = = = = B f B A f A r r E B Sharpe r r E A Sharpe σ 3
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c) Can you construct a risk-free portfolio using only assets A and B, assuming you may short-sell either asset? If so, what are the weights of your portfolio. In not, explain. (4 points) Answer: Without perfect correlation, or inclusion of the risk-free asset, it is not possible to eliminate all uncertainty (SD = 0) in a portfolio of just assets A and B.
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Final 2001 - FINANCE 100: Corporate Finance Solutions to...

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