Answers Learning Objectives Questions

Answers to the questions/problems recommended in the Learning Objectives Chapter 2 1. Return relative = (39 + 1.50)/34 = 1.191 HPR = 1.191 - 1 = 0.191 or 19% 2. Return relative = (61 + 3)/65 = 0.985 HPR = 0.985 - 1 = -0.015 or –1.5% 3. $4,000 used to purchase 80 shares at $50 per share Return relative = (4720 + 400)/4000 = 1.28 HPR = 1.280 - 1 = 0.28 or 28% HPR due to price increase alone = (4720/4000) –1 = 1.180 –1 = 0.18 HPR due to dividend income = 0.28 – 0.18 = 0.10 4. (1 + Nominal HPR) = (1 + Real HPR)(1 + Inflation Rate) For Problem # 1: (1 + HPR) = 1.191 at 4% inflation: (1 + Real HPR) = 1.191/1.04 = 1.145. Real HPR = 0.145 at 8% inflation: (1 + Real HPR) = 1.191/1.08 = 1.103. Real HPR For Problem # 2: = 0.103 (1 + HPR) = 0.985 at 4% inflation:(1 + Real HPR) = 0.985/1.04 = 0.947. Real HPR = -0.053 at 8% inflation: For Problem # 3: 5. (1 + Real HPR) = 0.985/1.08 = 0.912. Real HPR = -0.088 (1 + HPR) = 1.280 at 4% inflation: (1 + Real HPR) = 1.280/1.04 = 1.231. Real HPR at 8% inflation: (1 + Real HPR) = 1.28/1.08 = 1.185. Real HPR = 0.185 Asset A. Annualized HPR = 1.101/(8/12) – 1 = 0.1537 Asset B. Annualized HPR = 0.941/(15/12) – 1 = -0.0483 Asset C. Annualized HPR = 1.081/2 – 1 = 0.0392 Asset D. Annualized HPR = 1.151/3 – 1 = 0.0477 Asset E. Annualized HPR = 1.051/(18/52) – 1 = 0.1513 = 0.231 6. The table below shows the calculation of arithmetic mean (AM) and standard deviation (SD) using formulas provided in the text. Year Return 2 0.081 1 0.063 3 U.S. T-Bills (Return - AM)2 Return Return - AM (Return - AM)2 0.002 4E-06 -0.043 -0.1564 0.02446096 0.000121 0.192 0.0786 -0.016 0.076 -0.003 5 0.085 0.006 AM 0.079 4 0.09 SUM 0.395 σ2 U.K. Stock Return - AM 0.011 0.000256 9E-06 3.6E-05 0.000426 0.0001065 0.15 0.374 -0.106 0.567 0.0366 0.2606 -0.2194 0.1134 a. For U.S. T-Bills AM = 7.9% and the standard deviation (σ) = 1.03% For U.K. stock AM = 11.34% and the standard deviation (σ) = 19.24% b. For U.S T-bills the CV = 1.03/7.9 = 0.1304 For U.K stock the CV = 19.24/11.34 = 1.697 0.00133956 0.06791236 0.00617796 0.04813636 0.1480272 0.0370068 The average return of U.S. Government T-Bills is lower than the average return of United Kingdom Common Stocks because U.S. Government T-Bills are riskless, therefore their risk premium would equal 0. The U.K. Common Stocks are subject to the following types of risk: business risk, financial risk, liquidity risk, exchange rate risk, (and to a limited extent) country risk. c. For U.S. T-Bills GM= [(1.063)(1.081)(1.076)(1.090)(1.085)]1/5 -1 = 0.079 For U.K. Common stock GM = [(1.150)(.957)(1.374)(1.192)(.894)] 1/5 -1 = 0.10 In the case of the U.S. Government T-Bills, the arithmetic and geometric means are approximately equal (.079), therefore the standard deviations (using E(Ri) = .079) would be equal. The geometric mean (.10) of the U.K. Common Stocks is lower than the arithmetic mean (.113), and therefore the standard deviations will also differ. 7. a. AM(T) =[ (.19) + (.08) + (-.12) + (-.03) + (.15)]/5 = 0.054 AM(B) = [(.08) + (.03) + (-.09) + (.02) + (.04)]/5 = 0.016 Stock T is more desirable because the arithmetic mean annual rate of return is higher. b. σ2 (T) = [(.19 -.054)2 + (.08 -.054)2 + (-.12 - .054)2 + (-.03 -.054)2 + (.15 - .054)2]/5 = .01315 σ (T) = [0.0135]1/2 = 0.1147 σ2 (B) = [(.08 -.016)2 + (.03 -.016)2 + (-.09 - .016)2 + (.02 -.016)2 + (.04 .016)2]/5 = 0.00323 σ(B) = [0.00323] 1/2 = 0.05681 By this measure, B would be preferable. c. CV(T) = 0.1147/0.054 = 2.1233. CV(B) = 0.05681/0.016 = 3.5513 By this measure, T would be preferable. d. GM(T) = [(1.19)(1.08)(.88)(.97)(1.15)]1/5 – 1 = 0.0457 GM(B) = [(1.08)(1.03)(.91)(1.02)(1.04)]1/5 – 1 = 0.1435 Stock T has more variability than Stock B. The greater the variability of returns, the greater the difference between the arithmetic and geometric mean returns. 8. Returns to a U.S. investor from investment in: Russsia. U.K. Gemany. Japan. 9. HPR HPR HPR HPR = = = = (1 (1 (1 (1 + + – – 0.105)(1 0.051)(1 0.125)(1 0.128)(1 – + + – 0.186) 0.123) 0.143) 0.045) – – – – 1 1 1 1 = = = = -0.1005 0.1803 0.0001 -0.1672 The worksheet below provides calculations for mean, variance, and standard deviation. Year Return 1991 0.0538 1990 1992 1993 0.075 U.S. T-Bills Return - AM (Return - AM)2 -0.0252 0.00063504 0.0343 0.03 -0.004 -0.0447 -0.049 1.6E-05 0.00199809 0.002401 1994 0.0425 -0.0365 0.00133225 1996 0.0501 -0.0289 0.00083521 1995 1997 1998 1999 2000 2001 SUM AM σ2 0.0549 0.0506 0.0495 0.0429 0.0566 0.0387 0.5789 0.0482417 σ Average T-Bill rate = 0.0482 -0.0241 -0.0284 -0.0295 -0.0361 -0.0224 -0.0403 0.00058081 0.00080656 0.00087025 0.00130321 0.00050176 0.00162409 0.01290427 0.001173115 0.034250773 Standard deviation for T-Bills = 0.0342 10. E(R) = (.30)(-.10) + (.10)(0.00) + (.30)(.10) + (.30)(.25) = (-.03) + .000 + .03 + .075 = .075 11.E(R) = (.05)(-.60) + (.20)(-.30) + (.10)(-.10) + (.30)(.20) + (.20)(.40) + (.15)(.80) = (-.03) + (-.06) + (-.01) + .06 + .08 + .12 = .16 Chapter 4 1. Net asset value (NAV) is equal to the total market value of all the assets (number of shares times current price) divided by the number of shares of the fund outstanding. 2. After the initial public sale of the investment company the open-end fund will continue to sell new shares to the public at the NAV with or without a sales charge and will redeem (buy back) shares of the fund at the NAV. In contrast, the closedend fund does not buy or sell shares once the original issue is sold. Therefore, the purchase price or sales price for a closed-end fund is determined in the secondary market. 3. Two prices are provided for closed-end investment companies: (1) the NAV which is computed the same as any open-end fund, and (2) the current market price of the shares as determined in the secondary market (e.g., the NYSE). In the majority of cases the shares are selling at a discount to NAV of about 5-20 percent--i.e., the current market price is 5-20 percent below the NAV. 4. The load fund charges a sales commission of about 7.5 -8 percent when you buy the fund shares. Therefore, when you buy the shares you only get securities worth about 92- 92.5 percent of what you invest. In contrast, with a no-load fund you pay only the NAV (i.e., there is no sales commission). Notably, in order to purchase a noload fund it is necessary to directly contact the fund to buy or sell shares. 5. A common stock fund only invests in common stock and typically will not acquire any bonds with the possible exception of convertible bonds. A balanced fund will invest in stocks and in bonds in various proportions depending upon their outlook for the market. Because of the combination of stocks and bonds you would expect the balanced fund to have lower risk and return than a pure common stock fund. 6. An investor would acquire shares in a money market fund for the same reasons he would put money into a savings account or buy short-term government notes. Specifically, the investor is probably looking for a low risk, very liquid investment. The money market fund will almost certainly promise a higher rate of return than a savings account and typically a higher return than a government T-bill. Further, they are low risk because it is a diversified portfolio of high grade short-term investments like commercial paper, etc. Finally, there is typically no commission involved and they are very liquid and there is no charge or penalty for withdrawal (i.e., you receive interest daily until the money is withdrawn). 7. You definitely should care about how well a mutual fund is diversified. One of the major advantages of a mutual fund is instant diversification, so it truly is important. Given the CAPM, it is known that the market only pays for systematic risk so it is important to eliminate unsystematic risk, which is the purpose of diversification. A portfolio that is completely diversified will be perfectly correlated with the market portfolio (R2 = + 1.00). 8. Risk stability is important because an investor will often select a fund on the basis of his risk preference and it is important to know that the fund will remain in the same risk class over time. The empirical results are generally quite encouraging--funds typically have high correlation of their beta coefficients over time. Therefore, it is possible that historical risk classes can be used for future investment decisions. Also, there tends to be a relationship between the return and risk for alternative funds. 9. The performance of mutual funds should be judged on a risk-adjusted basis, because it is possible to get high return by simply investing in a portfolio of high beta stocks. Assuming investors are risk-averse, it is obviously necessary to consider return and risk. You can envision an example where two funds have a small difference in return that is more than compensated by risk differences: Fund A: Return = 11.5%; Beta = 1.5 and Fund B: Return 11.0%; Beta = 0.9. Fund A has a higher return but much higher risk. 10. The net return for a fund is the return after all research and management costs. The gross return is before these expenses. The net return is the return reported to the stockholder since all expenses have been allowed for in the NAV. To compute the gross return it is necessary to compute the expenses of the fund and add these back to the ending NAV and compute the returns with these expenses added back. Typically, the average difference in return is about one percent a year, but this varies by fund. 11. As an investor, it is the net return that is important because these are the returns that you derive. 12. In order to determine whether the manager is better than average in selecting stocks or at market timing, you should examine gross returns that do not include his expenses. Assuming the gross returns will indicate superior management ability, the net returns will indicate whether the managers are superior enough to cover the expenses involved. 13. Just because only half do better than buy-and-hold on the basis of risk-adjusted return does not mean you ignore them because there are other functions that investment companies perform that are important. These other functions include diversification, flexibility, and record keeping. To derive these other advantages it may be necessary to give up some of the return. 17. An individual investor may consider purchasing shares of a mutual funds rather than investing directly in the individual assets. Mutual funds provide the benefits of diversification, reinvestment, and recordkeeping. 18. In addition to the basic (diversification, reinvestment, and sell at a discount to NAV. benefits offered by investment record-keeping), closed-end funds companies generally 19. Numerous studies have shown that the majority of money managers have been unable to match the risk-return performance of stock or bond indexes. Therefore, including index funds in an investment portfolio is recommend. Index funds provide the investor with a diversified portfolio that does not require active management (and the associated costs). Chapter 6 1. A market is a means whereby buyers and sellers are brought together to aid in the transfer of goods and/or services. While it generally has a physical location it need not necessarily have one. Secondly, there is no requirement of ownership by those who establish and administer the market--they need only provide a cheap, smooth transfer of goods and/or services for a diverse clientele. A good market should provide accurate information on the price and volume of past transactions, and current supply and demand. Clearly, there should be rapid dissemination of this information. Adequate liquidity is desirable so that participants may buy and sell their goods and/or services rapidly, at a price reflecting the supply and demand. The costs of transferring ownership and middleman commissions should be low. Finally, the prevailing price should reflect all available information. 3. Liquidity is the ability to sell an asset quickly at a price not substantially different from the current market assuming no new information is available. A share of AT&T is very liquid, while an antique would be a fairly illiquid asset. A share of AT&T is highly liquid since an investor could convert it into cash within 1/8 of a point of the current market price. An antique is illiquid since it is relatively difficult to find a buyer and then you are uncertain as to what price the prospective buyer would offer. 4. The primary market in securities is where new issues are sold by corporations to acquire new capital via the sale of bonds, preferred stock or common stock. The sale typically takes place through an investment banker. The secondary market is simply trading in outstanding securities. It involves transactions between owners after the issue has been sold to the public by the company. Consequently, the proceeds from the sale do not go to the company as is the case with a primary offering. Thus, the price of the security is important to the buyer and seller. The functioning of the primary market would be seriously hampered in the absence of a good secondary market. A good secondary market provides liquidity to an investor if he or she wants to alter the composition of his or her portfolio from securities to other assets (i.e., house, etc.). Thus, investors would be reluctant to acquire securities in the primary market if they felt they would not subsequently have the ability to sell the securities quickly at a known price. 9. One reason for the existence of regional exchanges is that they provide trading facilities for geographically local companies that do not qualify for listing on a national exchange. Second, they list national firms thus providing small local brokerage firms that are not members of a national exchange the opportunity to trade in securities that are listed on a national exchange. The essential difference between the national and regional exchanges is that the regional exchanges have less stringent listing requirements, thus allowing small firms to obtain listing. 13. (a) A market order is an order to buy/sell a stock at the most profitable ask/bid prices prevailing at the time the order hits the exchange floor. A market order implies the investor wants the transaction completed quickly at the prevailing price. Example: I read good reports about AT&T and I'm certain the stock will go up in value. When I call my broker and submit a market buy order for 100 shares of AT&T, the prevailing asking price is 60. Total cost for my shares will be $6,000 + commission. (b) A limit order specifies a maximum price that the individual will pay to purchase the stock or the minimum he will accept to sell it. Example: AT&T is selling for $60--I would put in a limit buy order for one week to buy 100 shares at $59. (c). A short sale is the sale of stock that is not currently owned by the seller with the intent of purchasing it later at a lower price. This is done by borrowing the stock from another investor through a broker. Example: I expect AT&T to go to $48--I would sell it short at $60 and expect to replace it when it gets to $55. (d) A stop-loss order is a conditional order whereby the investor indicates that he wants to sell the stock if the price drops to a specified price, thus protecting himself from a large and rapid decline in price. Example: I buy AT&T at $60 and put in a stop loss at $57 that protects me from a major loss if it starts to decline. 2(a). Since the margin is 40 percent and Lauren currently has $50,000 on deposit in her margin account, if Lauren uses the maximum allowable margin her $50,000 deposit must represent 40% of her total investment. Thus, $50,000 = .4x then x = $125,000. Since the shares are priced at $35 each, Lauren can purchase $125,000 – $35 = 3,571 shares (rounded). 2(b). Total Profit = Total Return - Total Investment (1) If stock rises to $45/share, Lauren's total return is: 3,571 shares x $45 = $160,695. Total profit = $160,695 - $125,000 = $35,695 (2) If stock falls to $25/share, Lauren's total return is: 3,571 shares x $25 = $89,275. Total loss = $89,275 - $125,000 = -$35,725. 2(c). Market Value - Debit Balance Margin = ---------------------------Market Value where Market Value = Price per share x Number of shares. Initial Loan Value = Total Investment - Initial Margin. = $125,000 - $50,000 = $75,000 Therefore, if maintenance margin is 30 percent: (3,571 shares x Price) - $75,000 .30 = -------------------------------(3,571 shares x Price) .30 (3,571 x Price) = (3,571 x Price) - $75,000. 1,071.3 x Price = (3,571 x Price) - $75,000 -2,499.7 x Price = -$75,000 Price = $30.00 5(a). I am satisfied with the profit resulting from the sale of the 200 shares at $40. 5(b). With the stop loss: ($40 - $25)/$25 = 60% Without the stop loss: ($30 - $25)/$25 = 20%