Fin 652 INVESTMENT ANALYSIS
1. (based on Problem 16 of chapter 8) During a particular time period, the riskfree rate was 8%, while the average return on the market portfolio was 20%, with a standard deviation of returns of 25%. Investor A's portfolio had a beta of 1.5, with an average return of 16%, while investor B's portfolio had a beta of 2.0, with an average return of 23%. Which of the two investors did a better job of picking stocks? Assuming that the investors picked portfolios with the betas that they wanted, what could they have done to improve their expected return? (Answer using the information that you have available to you in the question. I don't want general advice.)
2. (Similar to prob. 6, p. 223, chapter 7)You have available to you, two mutual funds, whose returns have a correlation of 0.2. Here is some information on their return probability distributions:
|Expected Return||Standard Deviation|
In addition, you can also invest in a riskfree 1-year T-bill yielding 12%
3. Bret Barakett has a margin account and deposits $50,000. Assuming the prevailing initial margin requirement is 40%, commissions are ignored, and Reebok is selling at $35 per share:
E(RA)=.08+1.5(.20-.08) = 0.26; Jensen's alpha = .26-.16 = -.10
E(RB)=.08+2(.20-.02) = 0.32; Jensen's alpha = .32-.23 = -.09
According to Jensen's measure, B is better.
Both of them could have done better by borrowing at 8% and investing in the market portfolio. Thus, A should have borrowed 50% of his original investment and invested all of it in the market portfolio, while B should have borrowed an amount equal to his original investment and invested it in the market portfolio.
2. a., b.The tangent portfolio is given by
wmp = 0.0521.
The variance of returns of this portfolio is .94782(30)2+.05212322+2(.0521)(.9478)(30)(32)(.2) = 830.2389, and a standard deviation of returns of 28.81. The expected return is 23(.9478) + (15)(.0521) = 22.5809.
The optimal amount to invest in this portfolio is (22.58-12)/(.01)(4)(830.2389) = 0.3186. Hence, we find that the final investment proportions are .3186(.9478) = .3020 in Ventura, .3186(.0521)=.0166 in Marco Polo and .6814 or the rest in the riskfree asset.
c. To get an expected return of 50% without shortselling the riskfree asset, the only way is to shortsell the Marco Polo fund. Solve 0.5 = .15wMP + .23(1- wMP) to get wMP = -3.375 and wv = 4.375
3. a. Brett can buy 50000/(.4)(35) or 3571.43 shares.
b.If the price falls to $25, the loss is (35-25)(3571.43) or 35714.30.
c. The price can fall up P, where P is given by
, or P = $30.
d. If the price falls to $25, he needs to have 0.4(25)(3571.43) or $35714.30; he originally had $50,000, of which he lost 35714.30. Hence he now needs an additional 35714.30 - (50000-35714.30) = $21428.
1. The following bonds are available at the present time (making annual coupon payments)
2. You have the following obligations and expected cash inflows for the next 5 years:
|Time||In 1 year||In 2 years||In 3 years||In 4 years|
3. Consider the following information regarding the performance of a fund manager in a recent month. The table represents the actual return of each sector of the managers portfolio in Column 1, the fraction of the portfolio allocated to each sector in Column 2, the benchmark or neutral sector allocations in Column 3, and the returns of sector indices in Column 4.
|Actual Return||Actual Weight||Benchmark Weight||Index Return|
1. It is easy to determine that the yield on all bonds is 10%; hence the term structure is flat at 10%.
2. a. The term structure is known to be flat at 10%. Using this information, the duration of the net obligations of the individual works out to 2.68. The present value of the net obligations equals $10,825.80.
|Inflow||$ 5,000.00||$ 12,000.00|
The durations of the bonds can be worked out more easily; for bonds A and D, the duration equals the maturity, for bond C, which is selling at par, rule 8 can be used; for bond B, rule 7 can be used.
b. We need to create portfolios with durations equal to 2.68. Since the yields of all the bonds are the same, the duration of any portfolio is equal to the value-weighted average of the individual bonds. Hence, if we invest y percent in bond B and (1-y) percent in bond C, where 1.95y + 2.74(1-y) = 2.68, wed be able to immunize the net obligations. Solving, we get y = 7.59%. That is, we would invest 7.59% of 10825.80, or $821.68 in Bond B and $10,004.12 in Bond C.
c. If it were possible to use bonds A and D, I would use them for two reasons: one, I would get better convexity properties, because the cashflows from the bond portfolio would be more dispersed. Secondly, it would be possible to shield against interest rate risk completely by constructing a portfolio using bonds A, B, C, and D so that the net flows in each period from the portfolio equal the net obligations in that period.
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