Finance 100: Corporate Finance Professor Michael R. Roberts Quiz 3 November 8, 006 Name: Solutions Section ( Points...no joke!): Question Maximum Student Score 1 30 5 3 5 4 0 Total 100 Instructions: Please read each question carefully Formula sheets are attached to the back of the quiz You must show all work to receive credit & all numbers must be precise to the second decimal place. Good luck 1
1. (30 points) Please clearly circle the appropriate answer. (No explanation is necessary.) (a) (3 points) The relevant measure of risk for the Capital Market Line is standard deviation. (b) (3 points) The minimum variance portfolio on the Capital Market Line contains only the risk-free security. (c) (3 points) All equal-weighted portfolios of risky securities lie on the Security Market Line (d) (3 points) Under the assumptions of the CAPM, every security will, in general, be off of the Capital Market Line and on the Security Market Line. (e) (3 points) If a security s expected return does not lie on the Security Market Line, then there is an arbitrage opportunity. (the security still contains idiosyncratic risk)
(f) (3 points) By diversifying an equal-weighted portfolio among a large number of risky assets, it is possible to reduce the standard deviation of the portfolio return to (almost) zero if the asset returns are uncorrelated. (portfolio variance will tend towards average covariance) (g) (3 points) The standard deviation of a portfolio of securities is a weighted sum of the individual security s standard deviations. (standard deviation is a nonlinear function) (h) (3 points) The Sharpe Ratio measures the expected excess return on an asset relative to its standard deviation. (i) (3 points) A risky security cannot have an expected return less than the risk-free rate because no risk-averse investor would be willing to hold this asset in equilibrium. (think negative beta securities) (j) (3 points) The internal rate of return rule and NPV rule yield the same result as long as the cash flows alternate sign (e.g., negative, positive, negative, etc.) 3
. (5 points) Assume that there are n securities, each having expected returns (E(r i )) equal to 10%, variances (σ i ) equal to 10%, and pair wise covariances (σ i,j for i j) equal to 0.5%. (a) (5 points) What is the expected return of an equally-weighted portfolio containing all n securities? E(r p ) = n i=1 1 n E(r i) = 0.10 (1) (b) (10 points) What is the variance of an equally-weighted portfolio containing all n securities? σ (r p ) = = = n n 1 1 n n σ(r i, r j ) i=1 j=1 n ( ) 1 n σ 1 1 (r i ) + n n n σ(r i, r j ) i=1 i=1 j i ( ) 1 n 0.1 + 1 n(n 1)(0.005) n n = 0.10 n + ( 1 1 ) (0.005) n (c) (5 points) What value will the variance approach as you continue to add securities with the same characteristics as mentioned above? (i.e., as n gets big) σ (r p ) 0.005 as n (d) (5 points) What characteristics of securities are most important in the determination of the variance of a well diversified portfolio? The average covariance dominates simply because the number of covariance terms increases more quickly than the number of variance terms as the number of securities in the portfolio gets larger. 4
3. (5 points) You are given the following cash flow information for two potential projects. Project Year 0 Year 1 Year C -9,000 9,000,000 D -9,000 1,000 11,000 The appropriate discount rate for the projects is 10%. (a) (5 points) Calculate the payback period for both projects. Payback period (C) = 1. Payback period (D) =. (b) (5 points) Calculate the internal rate of return (IRR) for project C. 0 = 9, 000 + 9, 000 1 + IRR +, 000 = IRR = 18.7% (1 + IRR) (c) (5 points) Calculate the internal rate of return (IRR) for project D. 0 = 9, 000 + 1, 000 11, 000 + = IRR = 16.% 1 + IRR (1 + IRR) (d) (10 points) Suppose that the two projects are mutually exclusive so that you can only choose one. Using only the IRR, determine which of these projects you should invest in, if either. We can use the incremental cash flows (D - C) since both projects have IRRs that are greater than the discount rate. 0 = 0 + 8, 000 1 + IRR + 9, 000 = IRR = 1.5% (1 + IRR) Since 1.5% is greater than 10% we should take project D. 5
4. (0 points) The following questions pertain to the picture below from our class discussions. B C A (a) (4 points) What does point A represent? Point A is the minimum variance portfolio among the set of risky assets. (b) (4 points) What portfolio does point B represent? Point B is the market portfolio. (c) (4 points) What portfolio does point C represent? Point C is the risk-free asset (d) (4 points) What are the y-axis and x-axis units? The y-axis is expected returns. The x-axis is standard deviation. (e) (4 points) If you were forced to borrow at a higher rate than what you could lend at, how would the picture change? The CML would kink downward to the right of the market portfolio. 6