any any assistance on on this this examination.

Transcription

1 I I ledge on on my honor that I have not given or received any any assistance on on this this examination. Signed: Name: Perm #: TA: This quiz consists of 11 questions and has a total of 6 ages, including the cover age. Please show your work clearly. You have 80 minutes. Good Luck! 1

2 1. Which of the following statements are correct concerning the variance of the annual returns on an investment? I. The larger the variance, the more the actual returns tend to differ from the average return. II. The larger the variance, the larger the standard deviation. III. The larger the variance, the greater the risk of the investment. IV. The larger the variance, the higher the exected return. A. I and III only. II, III, and IV only C. I, III, and IV only D. I, II, and III only E. I, II, III, and IV 2. One year ago, you urchased a stock at a rice of $32 a share. Today, you sold the stock and realized a total return of 25%. Your caital gain was $6 a share. What was your dividend yield on this stock? A. 1.25%. 3.75% C. 6.25% D % E % 3. A stock had returns of 8%, -2%, 4%, and 16% over the ast four years. What is the standard deviation of this stock for the ast four years? A. 6.3%. 6.6% C. 7.1% D. 7.5% E. 7.9% 4. What are the arithmetic and geometric average returns for a stock with annual returns of 21%, 8%, -32%, 41%, and 5%? A. 5.6%; 8.6%. 5.6%; 6.3% C. 8.6%; 5.6% D. 8.6%; 8.6% E. 8.6%; 6.3% 2

3 5. You would like to combine a risky stock with a beta of 1.5 with U.S. Treasury bills in such a way that the risk level of the ortfolio is equivalent to the risk level of the overall market. What ercentage of the ortfolio should be invested in Treasury bills? A. 25%. 33% C. 50% D. 67% E. 75% 6. The market has an exected rate of return of 9.8%. The long-term government bond is exected to yield 4.5% and the U.S. Treasury bill is exected to yield 3.4%. The inflation rate is 3.1%. What is the market risk remium? A. 2.2%. 3.3% C. 5.3% D. 6.4% E. 6.7% 7. What is the ortfolio variance if 30% is invested in stock S and 70% is invested in stock T? A C D E The beta of a security rovides an: A. estimate of the market risk remium.. estimate of the sloe of the Caital Market Line. C. estimate of the sloe of the Security Market Line. D. estimate of the systematic risk of the security. E. None of the above. 3

4 9. You have $1 million currently invested entirely in mutual fund A. You are considering switching into a combination of T-bills and mutual fund for the next year. Mutual fund is invested 50% in stock 1 and 50% in stock 2. A one year T-bill (zero couon) with face value $10,000 is currently selling for $9523. You have come u with the following assessments of the return to mutual fund A along with the returns to stock 1 and 2 for the next year. A ) = 0.1, σ A = 0.2; 1) = 0.1, σ1 = 0.2; Using just the T-bill and mutual fund show how you 2) = 0.18, σ 2 = 0.3; ρ = 0.5 1,2 can construct an investment of your $1 million such that the ortfolio is better than your current investment in mutual fund A. You must show clearly why the new ortfolio is better and indicate the dollar investment in T-bills and mutual fund. (6 oints) Mutual fund, ) = 0.5(0.1) + (0.5)(0.18) = Var( R ) = (0.5) (0.2) + (0.5) (0.3) + 2(0.5)(0.5)(0.5)(0.2)(0.3) = σ ( R ) = = , 000 From T-bill, we can find risk-free rate, 9523 =, rf = 0.05 (1oint), if we can 1+ rf construct a ortfolio of T-bills and mutual fund, that has same exected return as mutual fund A, but smaller standard deviation, then the ortfolio is better investment than mutual fund A. Set ) = w(0.14) + (1 w)(0.05) = 0.1, w = 0.56 Thus σ( R) = wσ = (0.56)(0.22) = 0.12 < σ A (1 oint) 4

5 10. You are analyzing two stocks, let s call them Stock A and Stock. ased on current dividend yields and exected growth rates, the stocks are currently roviding a return of 11% and 14% resectively. Also, the standard deviation on the returns of the two stocks is 10% and 11%. Your statistical analysis of both stocks revealed the betas to be 0.8 and 1.5 resectively. In addition to this information, you know that the return on the T-bill is currently 6% and the exected return of the S&P 500 Index is 12% (a) What s your advice on stock A and, to buy or to sell, why? (3 oints) (b) Stock A is currently selling at $75 and stock is selling at $60. Given that, at the current rice, the dividend yield for both stocks is 5%, what would you exect the rice of these stocks to be, one year from now, if the exected growth rate of dividends does not change?(4 oints) (art b is a challenging question) (a) y CAPM, (1 oint) A) = Rf + β A( Rm Rf ) = 6% + 0.8(12% 6%) = 10.8% < 11% ) = Rf + β( Rm Rf ) = 6% + 1.5(12% 6%) = 15% > 14% uy A, sell. 2 (b) The formula you use to calculate rice is = 1 r g, because you are asked the exected rice of stock, you should use exected rate of return as your discount rate, which comes from art (a). Next, you need to find the growth rate of dividends (assuming it doesn t change). The total return on stock has two arts, current yield lus caital gain, and caital gain rate is equal to growth rate of dividends. r= + gg, = r g g A current yield = 11% 5% = 6%, notice we are using the realized return here. (1 oint) = 14% 5% = 9% 1A 1 = $75(5%) = 3.75 = $60(5%) = 3, (1 oint) (1 + g ) 3.75( ) 1A A 1A = = = A) ga (1 + g ) 3( ) 2 A 2 A = = = ) g $82.81 $54.5 5

6 11. Jack's Construction Co. has 80,000 bonds outstanding that are selling at ar value. onds with similar characteristics are yielding 8.5%. The comany also has 4 million shares of common stock outstanding. The stock has a beta of 1.1 and sells for $40 a share. The U.S. Treasury bill is yielding 4% and the market risk remium is 8%. Jack's tax rate is 35%. What is Jack's weighted average cost of caital? (5 oints) Re =.04 + (1.1.08) =.128 (1 oint) Debt: 80,000 $1,000 = $80m (1 oint) Common: 4m $40 = $160m (1 oint) Total = $80m + $160m = $240m 6

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