MIDTERM EXAM 1BUS 431a: Investment and Portfolio Management
AUBG: Spring 2012
NAME____________________________________
Solution Guide (2)
INSTRUCTIONS:
1. You have 75 minutes to complete the exam.2. The exam is worth a total of 100 points.3. You may use a calculator and scratch paper sheets. You must hand in the sheets with
your exam (put your name on it). 4. Allocate your time wisely. Use the number of points assigned to each problem as
your guide.5. In order to get full credit on the problems, you must show ALL your work!6. You can get partial credits if you show your calculations or provide arguments to support your answer.7. No credits will be warded if you fail to state your assumptions or conclusions explicitly.
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A. Multiple choice questions (2.0 points each, 24 points in total): 1. The bid price of a T-bill in the secondary market is
A. the price at which the dealer in T-bills is willing to sell the bill.B. the price at which the dealer in T-bills is willing to buy the bill.C. greater than the asked price of the T-bill.D. the price at which the investor can buy the T-bill.E. never quoted in the financial press.
Answer: B. T-bills are sold in the secondary market via dealers; the bid price quoted in the financial press is the price at which the dealer is willing to buy the bill.
2. If the market prices of each of the 30 stocks in the Dow Jones Industrial Average (DJIA) all change by the same percentage amount during a given day, which stock will have the greatest impact on the DJIA?A. The stock trading at the highest dollar price per share.B. The stock with total equity has the higher market value.C. The stock having the greatest amount of equity in its capital structure.D. The stock having the lowest volatility.E. None of the above.
Answer: A. Higher priced stocks affect the DJIA more than lower priced stocks; other choices are not relevant.
3. You purchased JNJ stock at $50 per share. The stock is currently selling at $65. Your gains may be protected by placing a __________. A. stop-buy orderB. limit-buy orderC. market orderD. limit-sell orderE. none of the above.
Answer: D. With a limit-sell order, your stock will be sold only at a specified price, or better. Thus, such an order would protect your gains. None of the other orders are applicable to this situation.
4. Which one of the following statements regarding orders is false? A. A market order is simply an order to buy or sell a stock immediately at the prevailing market price.B. A limit sell order is where investors specify prices at which they are willing to sell a security.C. If stock ABC is selling at $50, a limit-buy order may instruct the broker to buy the stock if and when the share price falls below $45.D. A day order expires at the close of the trading day.E. None of the above.
Answer: E. All of the order descriptions above is correct.
5. Which of the following is not a characteristic of closed-end mutual fund?A. Bought and sold on a secondary market such as the NYSE B. The number of shares outstanding can change from day to dayC. Generally trade at a discount from Net Asset ValueD. All of the above are characteristics of closed-end funds
Answer: B. The number of shares outstanding can change for open-end mutual funds but not for closed-end funds which trade like a common stock
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6. Which of the following statements about Money Market Mutual Funds is true? A. They invest in commercial paper, CDs, and repurchase agreements.B. They usually offer check-writing privileges.C. They are highly leveraged and risky.D. All of the above are true.E. Both A and B are true.
Answer: E. Money Market Mutual Funds invest in commercial paper, CDs, repurchase agreements, and other money market securities. They usually offer check-writing privileges. Their NAV is fixed at $1 per share.
7. Differences between hedge funds and mutual funds are that A. hedge funds are only subject to minimal SEC regulation.B. hedge funds are typically open only to wealthy or institutional investors.C. hedge funds managers can pursue strategies not available to mutual funds such as short selling, heavy use of derivatives, and leverage.D. are commonly structured as private partnerships.E. all of the above
Answer: E. Hedge funds are typically open only to wealthy or institutional investors, are commonly structured as private partnerships, are only subject to minimal SEC regulation, and can pursue strategies not available to mutual funds such as short selling, heavy use of derivatives, and leverage.
8. When an investment advisor attempts to determine an investor's risk tolerance, which factor would they be least likely to assess? A. the investor's prior investing experienceB. the investor's degree of financial securityC. the investor's tendency to make risky or conservative choicesD. the level of return the investor prefersE. the investor's feeling about loss
Answer: D. Investment advisors would be least likely to assess the level of return the investor prefers. The investors investing experience, financial security, feelings about loss, and disposition toward risky or conservative choices will impact risk tolerance.
9. An investor who wishes to form a portfolio that lies to the right of the optimal risky portfolio on the Capital Allocation Line must: A. lend some of her money at the risk-free rate and invest the remainder in the optimal risky portfolio.B. borrow some money at the risk-free rate and invest in the optimal risky portfolio.C. invest only in risky securities.D. such a portfolio cannot be formed.E. B and C
Answer: E. The only way that an investor can create portfolios to the right of the Capital Allocation Line is to create a borrowing portfolio (buy stocks on margin). In this case, the investor will not hold any of the risk-free security, but will hold only risky securities.
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10. Which statement about portfolio diversification is correct?A. As more securities are added to the portfolio, total risk typically would be expected to fall at a decreasing rateB. Proper diversification can reduce or eliminate systematic riskC. Diversification reduces the portfolio’s expected return because it reduces the portfolio’s total riskD. The risk-reducing benefits of diversification do not occur meaningfully until at least 50 securities are included in the portfolio
Answer: A. Diversification does not reduce expected return.
11. Portfolio theory is most concern with:A. The effect of diversification on portfolio riskB. The elimination of systematic riskC. The identification of idiosyncratic (or unsystematic) riskD. Active portfolio management to enhance the return.
Answer: A. Portfolio theory is most concern with the effect of diversification on portfolio risk. Please note that diversification does not reduce systematic risk.
12. In a two-security minimum variance portfolio where the correlation between securities is greater than -1.0 A. the security with the higher standard deviation will be weighted more heavily.B. the security with the higher standard deviation will be weighted less heavily.C. the two securities will be equally weighted.D. the risk will be zero.E. the return will be zero.
Answer: B. The security with the higher standard deviation will be weighted less heavily to produce minimum variance. The return will not be zero; the risk will not be zero unless the correlation coefficient is exactly -1.
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B. Short answer (6 points each, 48 points in total):
1. Based on the information given, for a price-weighted index of the three stocks calculate: A. The rate of return for the first period (t =0 to t =1).B. The value of the divisor in the second period (t=2). Assume that Stock A had a 2-1 split during this period.
A. The price-weighted index at time 0 is (70 + 85 + 105)/3 = 86.67. The price-weighted index at time 1 is (72 + 81 + 98)/3 = 83.67. The return on the index is 83.67/86.67 - 1 = -3.46%.
B. The divisor must change to reflect the stock split. Because nothing else fundamentally changed, the value of the index should remain 83.67. So the new divisor is (36 + 81 + 98)/83.67 = 2.57. The index value is (36 + 81 + 98)/2.57 = 83.67.
2. You purchased 1000 shares of CSCO common stock on margin at $19 per share. Assume the initial margin is 50% and the maintenance margin is 30%. Below what stock price level would you get a margin call? Assume the stock pays no dividend; ignore interest on margin A. $12.86B. $15.75C. $19.67D. $13.57E. none of the above
Answer D. (1000 shares * $19) * .5 = $19,000 * 0.5 = $9,500 (loan amount); Solve for P:0.30 = (1000P - $9,500)/1000P; 300P = 1000P - $9,500; -700P = -$9,500; P = $13.57
3. Assume you sell short 100 shares of common stock at $30 per share, with initial margin at 50%. What would be your rate of return if you repurchase the stock at $35/share? The stock paid no dividends during the period, and you did not remove any money from the account before making the offsetting transaction. A. -33.33%B. -25.63%C. -57.14%D. -77.23%E. none of the above
Answer A. Profit on stock = ($30 - $35)(100) = -500; initial investment = ($30)(100)(.5) = $1,500; Return = $-500/$1,500 = -33.33%.
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4. You purchased shares of a mutual fund at a price of $12 per share at the beginning of the year and paid a front-end load of 4.75%. If the securities in which the fund invested increased in value by 9% during the year, and the funds expense ratio was 1.5%, your return if you sold the fund at the end of the year would be ____________. A. 4.75B. 3.54C. 2.65D. 2.39E. None of the above
Answer D. End value = {[$12 * (1 – 0.0475) * (1.09 - .015)] = $12.287Return = ($12.287 - $12) / $12 = 2.39%
For question 5: You invest $100 in a risky asset with an expected rate of return of 11% and a standard deviation of 21%, and in a T-bill with a rate of return of 4.5%.
5. A portfolio that has an expected outcome of $114 is formed by A. investing $100 in the risky asset.B. investing $80 in the risky asset and $20 in the risk-free asset.C. borrowing $46 at the risk-free rate and investing the total amount ($146) in the risky asset.D. investing $43 in the risky asset and $57 in the riskless asset.E. Such a portfolio cannot be formed.
Answer C. For $100, Return = (114-100)/100 = 14%; 0.14 = w1(0.11) + (1 - w1)(0.045); Solve for the weights 0.14 = 0.11w1 +0.045 -0 .045w1; 0.095 = 0.065w1; w1 = 1.461So, w1 = 1.46($100) = $146; and (1 - w1)$100 = -$46.
For question 6: You are considering investing $1,000 in a T-bill that pays 5% and a risky portfolio, P, constructed with 2 risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 14% and variance of 1.0%, and Y has an expected rate of return of 10% and a variance of 0.81%.
6. What would be the dollar value of your positions in X, Y, and the T-bills, respectively, if you decide to hold a complete portfolio that has an expected outcome of $1,100? A. Cannot be determinedB. $405; $270; $324C. $568; $54; $378D. $378; $54; $568E. $108; $514; $378
Answer B. Return ($1,100 - $1,000)/$1,000 = 10%; E(Rp) = (0.6)14% + (0.4)10% = 12.4%; E(Rc) = 10% = w5% + 12.4%(1 - w); Solve for w = .3243; 1 - w = .6757; Find w = 0.3243($1,000) = $324.43 (in T-bills); 1 - w = 0.6757($1,000) = $675.7 (in P); Then $675.7 x 0.6 = $405.42 in X; and $675.7 x 0.4 = $270.28 in Y.
For question 7: Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 13.2% and a standard deviation of 7.7%. B has an expected rate of return of 1.5% and a standard deviation of 1.1%. The coefficient of correlation between A and B is -1.0.
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7. Let G be the global minimum variance portfolio. The weights of A and B in G are __________ and __________, respectively (see the formula at the end of the exam). A. 0.40; 0.60B. 0.66; 0.34C. 0.34; 0.66D. 0.76; 0.24E. 0.12; 0.88
Answer E. Use the textbook formula: wA = [(1.1)2 - (7.7)(1.1)-1.0)]/[(7.7)2 + (1.1)2 - (2)(7.7)(1.1)(-1.0) = 0.125; wB = 1 - 0.125 = 0.875.
8. Consider a risky asset. Suppose the expected rate of return on the risky asset is 15%, the standard deviation of the asset return is 22%, and the risk-free rate is 6%. What is your optimal position in the risky asset if the degree of risk aversion is 5? What are the expected rate of return and the standard deviation of your complete portfolio? What is the risk premium of the complete portfolio in this case? (See the formula at the end of the exam).
Answer: The optimal position for an investor with a coefficient of risk aversion A = 5 in the risky asset is y*:
So, this particular investor will invest 37% of the investment budget in the risky asset, and 63% in the risk-free asset. This is the value of ‘y’ for which utility is maximized. With 37% invested in the risky asset, the complete portfolio will have an expected return and standard deviation as follows:
So, the risk premium of the complete portfolio is RP = 9.35% - 6% = 3.35%, which is obtained by taking on a portfolio with a standard deviation of 8.18%.
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C. Problem Solving (8 or 12 points each, 32 points in total)9. (8 points) Consider a simple economy with the following two risky securities (a stock
fund, and a long-term government bond fund). The probability distribution of the risky funds is as follows:
Stock fund (S): E(R) = 13% and standard deviation = 20%Bond fund (B): E(R) = 8% and standard deviation = 12%
The correlation between the two risky securities is ρ. Assume that ρ = 0.3, i.e., the two securities are positively correlated
a. Derive the weights in the two risky securities (i.e., w1 and w2) in the minimum variance portfolio. Show all the steps clearly.
b. Compute the expected return and the standard deviation of the minimum variance portfolio.
Solution: The parameters of the opportunity set are:E(rS) = 13%, E(rB) = 8%, σS = 20%, σB = 12%, ρ = 0.30
From the standard deviations and the correlation coefficient we generate the covariance matrix [note that ]:
Bonds StocksBonds 144 72Stocks 72 400
The minimum-variance portfolio is computed as follows:
wMin(S) =
wMin(B) = 1 – 0.18 = 0.82
The minimum variance portfolio mean and standard deviation are:
10. (12 points) Suppose that Intel currently is selling at $40 per share. You buy 500 shares using $15,000 of your own money, borrowing the remainder of the purchase price from your broker.
a. What is the percentage increase in the net worth of your brokerage account if the price of Intel immediately changes to: (i) $44; (ii) $40; (iii) $36?
b. If the maintenance margin is 25%, how low can Intel’s price fall before you get a margin call?
c. How would your answer to (b) change if you had financed the initial purchase with only $10,000 of your own money?
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d. What is the rate of return on your margined position (assuming again that you invest $15,000 of your own money) if Intel is selling after 1 year at: (i) $44; (ii) $40; (iii) $36? The rate on the margin loan is 6%.
e. (2 bonus points) Continue to assume that a year has passed. How low can Intel’s price fall before you get a margin call?
Solution:The total cost of the purchase is: $40 500 = $20,000. You borrow $5,000 from your broker, and invest $15,000 of your own funds. Your margin account starts out with equity of $15,000.
a. (i) Equity increases to: ($44 500) – $5,000 = $17,000
Percentage gain = $2,000/$15,000 = 0.1333 = 13.33%
(ii) With price unchanged, equity is unchanged.
Percentage gain = 0
(iii) Equity falls to ($36 500) – $5,000 = $13,000
Percentage gain = (–$2,000/$15,000) = –0.1333 = –13.33%
b. The value of the 500 shares is 500P. Equity is (500P – $5,000). You will receive a margin call when:
= 0.25 when P = $13.33 or lower
c. The value of the 500 shares is 500P. But now you have borrowed $10,000 instead of $5,000. Therefore, equity is (500P – $10,000). You will receive a margin call when:
= 0.25 when P = $26.67 or lower
With less equity in the account, you are far more vulnerable to a margin call.
d. By the end of the year, the amount of the loan owed to the broker grows to:$5,000 1.06 = $5,300
The equity in your account is (500P – $5,400). Initial equity was $15,000. Therefore, your rate of return after one year is as follows:
(i) = 0.1133 = 11.33%
(ii) = –0.0200 = –2.00%
(iii) = –0.1533 = –15.33%
e. The value of the 500 shares is 500P. Equity is (500P – $5,300). You will receive a margin call when:
= 0.25 when P = $14.13 or lower
11. (12 points) Suppose that you sell short 500 shares of Intel, currently selling for $40 per share, and give your broker $15,000 to establish your margin account.
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a. If you earn no interest on the funds in your margin account, what will be your rate of return after 1 year if Intel stock is selling at: (i) $44; (ii) $40; (iii) $36? Assume that Intel pays no dividends.
b. If the maintenance margin is 25%, how high can Intel’s price rise before you get a margin call?
c. Redo parts (a) but now assume that Intel also has paid a year-end dividend of $1.5 per share. The prices in part (a) should be interpreted as ex-dividend, that is, prices after the dividend has been paid.
d. Redo parts (b) but now assume that Intel also has paid a year-end dividend of $1.5 per share.
e. (2 bonus points) Explain why stop-buy orders often accompany short sales.
Solution:a. The gain or loss on the short position is: (–500 P). Invested funds = $15,000
Therefore Rate of return = (–500 P)/15,000
The rate of return in each of the three scenarios is:
(i) rate of return = (–500 $4)/$15,000 = –0.1333 = –13.33%
(ii) rate of return = (–500 $0)/$15,000 = 0%
(iii) rate of return = [–500 (–$4)]/$15,000 = +0.1333 = +13.33%
b. Total assets in the margin account equal:
$20,000 (from the sale of the stock) + $15,000 (the initial margin) = $35,000
Liabilities are 500P. You will receive a margin call when:
= 0.25 when P = $56 or higher
c. With a $1 dividend, the short position must now pay on the borrowed shares: ($1.5/share 500 shares) = $750. Rate of return is now:
[(–500 P) – 750]/15,000
(i) rate of return = [(–500 $4) – $750]/$15,000 = –0.1833 = –18.33%
(ii) rate of return = [(–500 $0) – $750]/$15,000 = –0.0500 = –5.00%
(iii) rate of return = [(–500) (–$4) – $750]/$15,000 = +0.0833 = +8.33%
d. Total assets are $35,000, and liabilities are (500P + 750). A margin call will be issued when:
= 0.25 when P = $54.80 or higher
e. Here I expect 1-2 sentences explaining the stop-buy orders.
Useful formulas:
1. Formula for the weights of minimum-variance portfolio is
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2. Optimal position for an investor with a coefficient of risk aversion A is:
3. Expected return and standard deviation of complete portfolio are:
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D. Bonus question (2 points each, 4 points in total):1. What is the German Stock Exchange index?
a. SOFIXb. Dow Jonesc. S & P 500d. DAX
Answer D.
2. The IPM students will visit in April 2012:a. American Stock Exchangeb. Armenian Stock Exchangec. Thessaloniki Stock Exchange Center d. Istanbul Stock Exchange
Answer D.
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