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CHAPTER 1 THE INVESTMENT SETTING TRUE/FALSE QUESTIONS (t) 1 The rate of exchange between certain future dollars and certain current dollars is known as the pure rate of interest. (t) 2 An investment is the current commitment of dollars over time to derive future payments to compensate the investor for the time funds are committed, the expected rate of inflation and the uncertainty of future payments. (f) 3 A dollar received to day is worth less than the same dollar received in the future. (f) 4 Expected Return = (1 + nominal risk-free rate)(1 + inflation rate)(1 + risk premium) - 1 (f) 5 The three components of the required rate of return are the nominal interest rate, an inflation premium, and a risk premium. (t) 6 Risk is the uncertainty that an investment will earn its expected rate of return. (f) 7 A manager with a passive asset allocation strategy will try to increase allocation of assets that he believes will outperform other classes in the next period. (t) 8 People invest with one or more of the following three basic needs in mind: income, capital preservation, capital appreciation. (t) 9 As the level of risk increases an investor will require an expected return that will compensate for this additional risk. (f) 10 An internally efficient market is one where stocks trade at low prices. (t) 11 The required rate of return is the minimum rate of return that will induce an investor to invest. (t) 12 Participants in primary capital markets that gather funds and channel them to borrowers are called financial intermediaries. (t) 13 A manager with an active security selection philosophy will try to identify securities that will do well over the coming period. 305 MULTIPLE CHOICE QUESTIONS (d) 1 An investment is the current commitment of resources for a period of time in the expectation that an investor will receive in the future a compensation for a) the time for which the resources are committed b) the expected rate of inflation c) the time for which the resources are committed and the expected rate of inflation d) the expected rate of inflation, the time for which the resources are committed, and the uncertainty of future payments. e) a) and b) (b) 2 The following is not a reason for investing a) b) c) d) e) (a) 3 to provide for retirement. to fund higher levels of current consumption. to fund higher levels of future consumption. to fund children’s education needs. to save up for a down payment on a house. The statement – ‘risk drives expected returns’ refers to the notion that a) an investor will require a higher rate of return the higher the perceived riskiness of an asset. b) an investor will require a lower rate of return the higher the perceived riskiness of an asset. c) markets over-react to news. d) markets under-react to news. e) none of the above. (a) 4 The basic trade-offs in the investment process are a) between the anticipated rate of return for a given investment instrumentand its degree of risk. b) between understanding the nature of a particular investment and havingthe opportunity to purchase it. c) between high returns available on single instruments and the d) diversification of instruments into a portfolio. e) between the desired level of investment and possessing the resources necessary to carry it out. (e) 5 The expected return is a function of a) The real risk-free rate plus the investment's variance. b) The prime rate and the rate of inflation. 306 c) The risk premium plus the inflation rate. d) The nominal risk free rate minus the rate of inflation. e) The nominal risk-free rate and the risk premium. (c) 6 An externally efficient market is one where a) b) c) d) e) (d) 7 An investor should diversify investment holdings across a) b) c) d) e) (a) 8 9 10 11 In cash, stocks and bonds Indirectly, in real assets and financial assets. In options, futures and through derivatives. Directly, indirectly and through derivatives. In stocks, directly and through derivatives. A direct investment occurs when an investor a) b) c) d) e) (d) Transaction costs of trading are low. Stocks of highly efficient companies trade. New information is quickly reflected into assets prices. There is no overreaction to news. Stock prices are low. An investor can invest in financial assets by investing: a) b) c) d) e) (a) Different asset classes. Different industries. Different countries. All of the above. None of the above. An internally efficient market is one where a) b) c) d) e) (d) Transaction costs of trading are low. Stocks of highly efficient companies trade. New information is quickly reflected into assets prices. There is no overreaction to news. None of the above. Buys shares of stocks or bonds. Buys shares of stocks or options and futures. Buys shares of stocks, bonds or mutual funds Deposits funds in a bank or buys mutual funds Deposits funds in a bank or buys derivatives. An indirect investment occurs when an investor a) b) c) d) Buys shares of stocks or bonds. Buys shares of stocks or options and futures. Buys shares of stocks, bonds or mutual funds Deposits funds in a bank or buys mutual funds 307 e) Deposits funds in a bank or buys derivatives. (c) 12 A portfolio manager with an active asset allocation decision philosophy will manage a portfolio by a) b) c) d) e) (b) 13 A portfolio manager with an active security selection decision philosophy will manage a portfolio by a) b) c) d) e) (d) 14 15 Tracking a well known market index Stock picking using a top-down or bottom-up approach Using market timing Maintaining predetermined allocation with periodic rebalancing None of the above A portfolio manager with a passive security selection decision philosophy will manage a portfolio by a) b) c) d) e) 308 Tracking a well known market index Stock picking using a top-down or bottom-up approach Using market timing Maintaining predetermined allocation with periodic rebalancing None of the above A portfolio manager with a passive asset allocation decision philosophy will manage a portfolio by a) b) c) d) e) (a) Tracking a well known market index Stock picking using a top-down or bottom-up approach Using market timing Maintaining predetermined allocation with periodic rebalancing None of the above Tracking a well known market index Stock picking using a top-down or bottom-up approach Using market timing Maintaining predetermined allocation with periodic rebalancing None of the above MULTIPLE CHOICE PROBLEMS (d) 1 If the nominal risk rate is 5% per year, the risk premium is 6% per year and the expected rate of inflation over the next year is 3%, an investment of $1000 today worth_____ one year from today. a) b) c) d) e) (c) 2 If the nominal risk free rate is 8%, the expected rate of inflation is 2.5%, and the risk premium is 5%, the required rate of return is a) b) c) d) e) (a) 3 $1000 $1081.50 $1091.80 $1113 $1146.39 10.5% 7.5% 13.4% 16.24% 10.7% Assume that nominal risk free interest rate is 6%, the expected rate of inflation is 2%, the risk premium is 3% and the required rate of return is 9.18%. What would be the value at the end of 25 years of $100 invested today at the required rate of return? a) b) c) d) e) $898.62 $343.51 $1474.28 $704.13 $918 USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS Consider the following information. The average annual return on a tax-deferred account over a 10-year period is 9%. The average annual return on a taxable account over the same 10-year period is 13%. The tax rate is 35%, and the amount invested at the beginning of the 10-year period is $2500. (b) 4 The before tax value of the tax deferred investment, assuming all savings are removed at the end of 10 years is a) b) c) d) e) $4414.17 $5918.41 $2943.42 $8663.71 $4987.26 309 (c) 5 The after tax value of the tax deferred investment, assuming all savings are removed at the end of 10 years is a) b) c) d) e) (e) 6 The value of the taxable investment, assuming all savings are removed at the end of 10 years is a) b) c) d) e) (c) 7 $4987.26 $5918.41 $3846.97 $2943.42 None of the above $8663.71 $6943.42 $3846.97 $5918.41 $5626.46 Consider an investment portfolio consisting of three asset classes. The allocations and returns for each asset class are as follows Asset Class 1 2 3 Allocation Percentage Annual Return 10% -10% 35% 35% 55% -5% The annual portfolio return is a) b) c) d) e) (d) 8 15.5% -10.0% 8.5% -7.75% 7.75% Consider an investment portfolio consisting of four asset classes. The allocations and returns for each asset class are as follows Asset Class 1 2 3 4 Allocation Percentage Annual Return 10% -10% 25% 15% 35% 10% 30% 5% The annual portfolio return is a) 15.5% b) 10.0% 310 c) 5.0% d) 7.75% e) None of the above CHAPTER 1 ANSWERS TO PROBLEMS 1 1000(1.05)(1.06) = 1113 2 (1.08)(1.05) – 1 = 11.34% 3 1.091825(100) = 898.62 4 1.0910(2500) = 5918.41 5 5918.41(1 – 0.35) = 3846.97 6 0.13(1 – 0.35) = 0.0845 1.084510(2500) = 5626.46 7 (0.1)(-0.1) + (0.35)(0.35) + (0.55)(-0.05)] = 0.085 8 [(0.1)(-0.1) + (0.25)(0.15) + (0.35)(0.10) + (0.30)(0.05)] = 0.0775 311 CHAPTER 2 RETURN AND RISK BASICS TRUE/FALSE QUESTIONS (f) 1 An investor should expect to receive higher returns from taking on lower risks (f) 2 The sources of investment returns are dividends and interest. (f) 3 The holding period return (HPR) is equal to the return relative stated as a percentage. (t) 4 The geometric mean is the nth root of the product of the annual holding period returns for N years minus one. (f) 5 The geometric mean of a series of returns is always larger than the arithmetic mean and the difference increases with the volatility of the series. (t) 6 When rates of return are the same for all years, the geometric mean and the arithmetic mean will be the same. (f) 7 The coefficient of variation is the expected return divided by the standard deviation of the return. (f) 8 Historically return relatives are used to measure the risk for a series of historical rates of return. (t) 9 Widening interest rate spreads indicate a flight to quality. (f) 10 The risk premium is a function of sales volatility, financial leverage, and inflation. MULTIPLE CHOICE QUESTIONS (b) 1 The return relative is calculated as a) b) c) d) e) (b) 2 (1 – HPR) (1 + HPR) (1 – HPR)n (1 + HPR)n (1 – (Income + Price Change)) When rates of return on a security have a high standard deviation then a) Arithmetic mean will equal geometric mean 312 b) The difference between arithmetic mean and geometric mean will be large. c) The difference between arithmetic mean and geometric mean will be small. d) Geometric mean will exceed arithmetic mean. e) None of the above. (d) 3 The coefficient of variation is a measure of a) b) c) d) e) (c) 4 The real risk free rate is influenced by the following factors: a) b) c) d) e) (c) 5 6 7 A downturn in the economy. A static economy. A change in the expected rate of inflation. A change in the real rate of interest. A change in risk aversion. The nominal risk free rate is influenced by the following factors: a) b) c) d) e) (a) Inflationary expectations and capital market conditions. Business risk and financial risk. Investment opportunities and time preference for consumption. All of the above. None of the above. If a significant change is noted in the yield of a T-bill, the change is most likely attributable to: a) b) c) d) e) (a) Central tendency. Absolute variability. Absolute dispersion. Relative variability. Relative return. Inflationary expectations and capital market conditions. Business risk and financial risk. Investment opportunities and time preference for consumption. All of the above. None of the above. The following would be an example of systematic risk: a) Changes in interest rates. b) Management decisions. 313 c) Stability of sales. d) The amount of debt financing. e) Liquidity. (b) 8 If U.S. firms increase their debt/total capital ratios, it will very likely cause required returns to a) Increase and change the slope of the capital market line (CML). b) Increase and cause a movement up along the capital market line (CML). c) Remain unchanged and cause a parallel shift of the capital market line (CML). d) Decrease and change the slope of the capital market line (CML). e) Decrease and cause a movement down along the capital market line (CML). (d) 9 An increase in the slope of the Capital Market Line (CML) is caused by a) b) c) d) e) (d) 10 Changes in business risk. Changes in financial risk. Changes in liquidity risk. Changes in systematic risk. Changes in unsystematic risk. A parallel shift in the capital market line (CML) is caused by changes in the following factors: a) b) c) d) e) Expected real growth in the economy. Capital market conditions. Expected rate of inflation. All of the above. None of the above. MULTIPLE CHOICE PROBLEMS (a) 1 The HPR on a security is 6.5%. If the holding period is 1 month, the annualized HPR is a) b) c) d) e) (c) 314 2 113% 78% 65% 6.5% 1.129% The HPR on a security is 3%. If the holding period is 4 weeks month, the annualized HPR is a) b) c) d) e) (d) 3 At the beginning of the year an investor purchased 100 shares of common stock from ABC Corporation at $10 per share. During the year, the firm paid dividends of $1 per share. At the end of the year, the investor sold the 100 shares at $11 per share. What is the HPR? a) b) c) d) e) (d) 4 5 1.20% 5.50% 12.00% 20.00% 30.00% Assume that you invest $1000 for 15 years in an account that pays an interest rate of 7% per year with annual compounding. Calculate the proportion of the total value of the account that can be attributed to intereston-interest, at the end of 15 years. a) b) c) d) e) (b) 39.15% 78.87% 46.87% 158.25% 52.25% 100% 38.06% 36.24% 25.70% 0% Given the following returns and return relatives over the past four years, compute the arithmetic mean (AM) and geometric mean (GM) rates of return. Period t1 t2 t3 t4 a) b) c) d) e) Returns 0.05 -0.10 0.11 -0.02 Return Relative 1.05 0.90 1.11 0.98 AM = 4.000%, GM = 1.010% AM = 1.000%, GM = 0.692% AM = 0.692%, GM = 4.000% AM = 1.000%, GM = 1.0692% AM = 4.000%, GM = 0.0692% 315 USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS Assume that you invest $5000 for 30 years in an account that pays an interest rate of 8.5% per year with annual compounding. (c) 6 The total value of your investment at the end of 30 years is? a) b) c) d) e) (b) 7 The amount of simple interest earned is? a) b) c) d) e) (d) 8 9 $67,750 $52,791 $57,791 $40,041 $60,000 Consider a stock that has an expected return of 10% and standard deviation of 14%. Assuming that future returns will resemble past returns, an investor can expect 95% of actual future returns to lie between a) b) c) d) e) 316 $67,750 $52,791 $57,791 $40,041 $60,000 The amount of interest-on-interest earned is? a) b) c) d) e) (e) $67,750 $52,791 $57,791 $40,041 $60,000 -10% and 24% 10% and 14% -32% and 52% -4% and 24% -18% and 38% CHAPTER 2 ANSWERS TO PROBLEMS 1 (1 + 0.065)1/(1/12) = 2.129. The HPR = 2.129 – 1 = 1.129 or 113% 2 (1 + 0.03)1/(4/52) = 1.4687. The HPR = 1.4687 – 1 = 0.4687 or 46.87% 3 HPR = 4 1000(1.07)15 = 2759.03 100 100 200 0.20 or 20% 1000 1000 Original principal Cumulative simple interest Cumulative interest-on-interest = 1000 = 1050 = 709.03 709.03/2759.03 = 0.257 or 25.7% 5 AM = [(.05) + (-.10) + (.11) + (-.02)]/4 =.04/4 = .01 = 1% GM = [(1.05)(.90)(1.11)(.98)]1/4 - 1 = 1.00692 - 1 = .00692 = 0.692% 6 Value of account at the end of 30 years = 5000(1.085)30 = $57,791.26 7 Original principal Cumulative simple interest Total interest Cumulative interest-on-interest = 5000 = 30 x 0.085 x 5000 = $12,750.00 = 57,791.26 – 5000 = $52,791.26 = 52,791.26 – 12,750 = $40,041.26 8 Total interest Cumulative interest-on-interest = 57,791.26 – 5000 = $52,791.26 = 52,791.26 – 12,750 = $40,041.26 9 95% of returns will lie between 10% +/- 2 x 14. That is between –18% and 38% 317 CHAPTER 3 SELECTING INVESTMENTS IN A GLOBAL MARKET TRUE/FALSE QUESTIONS (f) 1 The U.S. equity and bond markets have grown in terms of their relative size of the world equity and bond market. (t) 2 Diversification with foreign securities can help reduce portfolio risk. (f) 3 The total domestic return on German bonds is the return that would be experienced by a U.S. investor who owned German bonds. (t) 4 If the exchange rate effect for Japanese bonds is negative, it means that the domestic rate of return will be greater than the U.S. dollar return. (t) 5 Investors who limit themselves to the U.S. equity market experienced rates of return below those in many other countries. (f) 6 It is very important when diversifying that the correlation between rates of return for various countries be high and very stable over time. (t) 7 Municipal bonds are tax-exempt. (f) 8 A Eurobond is an international bond denominated in a currency other than that of the United States. (f) 9 Yields on money market funds are often lower than yields available to individuals investing in CD's because of the fees involved. (f) 10 Income bonds are considered as safe as debentures because they pay higher rates of interest. (t) 11 Warrants are options issued in connection with the sale of fixed income securities. (f) 12 A call option is issued by a firm in conjunction with a convertible bond. (f) 13 For a U.K. based investor with stock investments in the U.S. a weakening dollar will enhance returns in terms of pounds. (t) 14 For a U.S. based investor with stock investments in the U.K. a weakening dollar will enhance returns in dollar terms. 318 MULTIPLE CHOICE QUESTIONS (d) 1 If you are considering investing in German stocks as a means to reduce the risk of your portfolio, the initial factor that you should examine is: a) b) c) d) e) (c) 2 Correlations of returns between U.S. bonds and those of foreign countries differ because of differences in a) b) c) d) e) (c) 3 4 5 A debenture. A warrant. An indenture. A rights certificate. A trustee deed. The correlation between U.S. equities and U.S. government bonds has been a) b) c) d) e) (c) Culture. Political systems. International trade patterns. Language. None of the above. The legal document setting forth the obligations of a bond's issuer is called a) b) c) d) e) (b) The average rate of return of the portfolio when you combine U.S. and German stocks. The standard deviation of the German stocks. The standard deviation of the German stocks compared to the standard deviation of U.S. stocks. The correlation between the rates of return for German stocks and U.S. stocks. The coefficient of variation (CV) of rates of return for German stocks versus the CV of rates of return for U.S. stocks. Strongly positive. Weakly positive. Strong negative. Weakly negative. Indeterminate. U.S. investors should consider constructing global investment portfolios because a) b) c) d) Overseas markets usually outperform U.S. markets. Overseas markets are less risky. Overseas markets offer risk reduction via diversification. Investors will benefit from a stronger dollar 319 e) (d) 6 In order to diversify risk an investor must have investments that that have correlations with other investments in the portfolio that are a) b) c) d) e) (a) 7 b) c) d) e) 8 9 diversifying across countries. diversifying across industries. diversifying across industries and countries. diversifying across U.S. industries. diversifying across U.S. asset classes. Collateralized mortgage obligations (CMOs) offset some of the problems associated with traditional mortgage pass-throughs because a) b) c) d) e) 320 Countries are developing closer trade and economic links. Countries are becoming more segmented. There are fewer barriers to travel. U.S. investors are purchasing more foreign securities. Correlations between bond markets of different countries have been rising. Global portfolio managers can diversify more risk by a) b) c) d) e) (a) low positive zero negative any of the above none of the above Correlations between stock markets in different countries have been rising over time because a) (c) None of the above. They are overcolleralized. They have variable rates. Collateralized by auto-loans. They are deep discount instruments. Collateralized by credit card debt. MULTIPLE CHOICE PROBLEMS USE THE FOLLOWING INFORMATION FOR THE NEXT FIVE PROBLEMS Security U.S. government T-bills Long-term government bonds Long-term corporate bonds Common Stock Small capitalization common stocks (c) 1 What is the maturity premium? a) b) c) d) e) (b) 2 3 4 5 1.66% 12.56% 4.92% 8.80% 10.46% What is the small firm stock risk premium? a) b) c) d) e) (c) 3.76% 1.05% 2.71% 3.25% 4.71% What is the common stock risk premium? a) b) c) d) e) (b) 3.76% 1.05% 2.71% 3.25% 4.70% What is the default premium? a) b) c) d) e) (e) Annual Percentage Return 2.04% 4.75% 5.8% 12.50% 14.60% 1.32% 2.10% 2.50% 3.50% 4.90% If the annual rate of inflation during the period was 4 percent, what was the real rate of return on long-term corporate bonds? 321 a) b) c) d) e) (d) 6 1.16% 1.85% 1.73% 3.50% 4.90% You are trying to decide between a par value corporate bond carrying a coupon rate of 6.25% per year and a par value municipal bond that pays an annual coupon rate of 4.75%. Assuming all other factors are the same and you are in the 28% tax bracket, which bond should you choose and why? a) b) c) d) e) Corporate bond because the after tax yield is 6.25%. Corporate bond because the after tax yield is 4.5%. Municipal bond because the equivalent taxable yield is 6.3%. Municipal bond because the equivalent taxable yield is 6.6%. You will be indifferent between the two because the after tax yields are the same. USE THE FOLLOWING INFORMATION TO ANSWER THE NEXT FIVE PROBLEMS Company Ticker Coupon Gen Elec GE 4.75 (b) 7 8 9 UST 99.544 4.808 62 10 $4.75 $47.50 $4.808 $48.08 $62 $62 $9.954 $48.08 $99.544 $995.44 What is the estimated yield on Treasury securities? a) 4.188% b) 5.428% 322 EST Spread What price would you pay in dollars to purchase this bond? a) b) c) d) e) (a) Last Yield What annual dollar coupon amount will investors receive? a) b) c) d) e) (e) Maturity 9/15/201 4 Last Price Est $ Vol (000's) 158736 c) 5.371% d) 4.132% e) 4.753% (c) 10 What is the current yield for this bond? a) b) c) d) e) (c) 11 What is the capital gains/loss yield on this bond? a) b) c) d) e) (d) 12 13 14 10.83% -28.33% 5.71% -5.71% 10.0% Consider a Germany based investor who purchases U.S. stocks on January 1, 2002. One year later, on January 1, 2003 he sells the German stocks. The total return in local currency is -5%. The exchange rate on January 1, 2002 is $1.05/euro. The exchange rate on January 1, 2003 is $0.90/euro. Calculate the return in euro terms. a) b) c) d) e) (b) -0.038% 0.456% 0.038% -0.456% None of the above Consider a U.S. based investor who purchases German stocks on January 1, 2002. One year later, on January 1, 2003 he sells the German stocks. The total return in local currency is 10%. The exchange rate on January 1, 2002 is $1.05/euro. The exchange rate on January 1, 2003 is $0.90/euro. Calculate the return in dollar terms. a) b) c) d) e) (a) 4.18% 5.88% 4.77% 8.125% 4.063% 10.83% -28.33% 5.71% -5.71% 5.0% An investor based in the U.S. has security investments in the U.K. The 323 exchange over a one year period has gone from $1.85 per pound to $2 per pound. During this same period the investor’s return in dollar terms is calculated to be 10%. Calculate the local currency returns for the U.K. securities ( i.e. in pound terms). a) b) c) d) e) (c) 15 8.11% 1.75% -1.35% -7.5% 10.81% Assume the exchange rate is $1.85 per pound at the beginning of the year and $2 per pound at the end of the year. For an investor based in the U.K. with security investments in the U.S. the exchange rate change is a) b) c) d) e) 8.11% 15% -7.5% -8.11% -15% THE FOLLOWING INFORMATION APPLIES TO THE NEXT TWO PROBLEMS Treasury Bills Maturity Days to Mat May 12 05 181 (c) 16 17 Chg - Ask Yld ? $9997.75 $9997.76 $9887.37 $10002.25 $10002.24 Use the information provided to calculate the ask yield (also known as the investment rate or the bond equivalent rate. a) b) c) d) e) 324 Asked 2.24 Use the information provided above to calculate the ask price for this Treasury bill. a) b) c) d) e) (a) Bid 2.25 2.30% 2.25% 2.24% 3.75% 4.49% CHAPTER 3 ANSWERS TO PROBLEMS 1 Maturity premium = 4.75 – 2.04 = 2.71% 2 Default premium = 5.8 – 4.75 = 1.05% 3 Common stock premium = 12.50 – 2.04 = 10.46%. 4 Small firm premium = 14.60 - 12.50 = 2.10%. 5 Real L-T corporate bond return = (1 + 0.058)/(1 + 0.04) – 1 = 0.0173 or 1.73%. 6 The municipal bond has an equivalent taxable yield of 0.475/(1 – 0.28)= 0.066. This is higher than the bond yield of 0.0625. 7 Annual dollar coupon amount = (1000)(0.0475) = $47.50. 8 Price = $995.44. Or 99.544% of face value of $1000. 9 Estimated yield on 10 year Treasury = 4.808% - 0.62% = 4.188%. 10 Current yield = 47.50/995.44 = 0.0477 or 4.77%. 11 Capital gains yield = 4.808% - 4.77% = 0.038%. 12 Dollar returns = (1 + 0.10)(0.90/1.05) – 1 = -0.0571 or -5.71% 13 Euro returns = (1 - 0.05)(1.1111/0.9524) – 1 = 0.1083 or 10.83%%. 14 Exchange rate change = (2/1.85) -1 = 0.08108 or 8.11% Local currency return = (1 + 0.10)/(1 + 0.08108) – 1 = 0.0175 or 1.75% 15 First restate exchange rates as 1/1.85 = pounds 0.5405 per $ and 1/2.0 = pounds 0.50 per dollar. Exchange rate change = (0.50/0.5405) – 1 = -0.075 or -7.5% 16 Ask price = 10,000 – (0.0224 x 10,000 x 181)/360 = $9887.37 17 Ask yield = ((10000 – 9887.37)/9887.37) x (365/181) = 0.02296 or 2.3% 325 CHAPTER 5 THE ASSET ALLOCATION DECISION TRUE/FALSE QUESTIONS (t) 1 Experts suggest life insurance coverage should be seven to ten times an individual's annual salary. (t) 2 The gifting phase is similar to, and may be concurrent with, the spending phase. (t) 3 Long-term, high-priority goals include some form of financial independence. (f) 4 The investment performance of a portfolio manager of a small Capitalization equity fund should be compared to the performance of the S&P 500 stock index. (f) 5 Risk tolerance is exclusively a function of an individual's psychological makeup. (f) 6 An appropriate investment objective for a typical 25-year-old investor is a lowrisk strategy, such as capital preservation or current income. (f) 7 Marginal tax rate is defined as a person's total tax payment divided by their total income. (t) 8 Investment returns of an IRA investment, including any income, are deferred until the funds are withdrawn from the account. (f) 9 Liquidity needs, time horizon, tax concerns and risk tolerance are all investment constraints. (t) 10 Average tax rate is defined as a person's total tax payment divided by their total income. MULTIPLE CHOICE QUESTIONS (a) 1 Asset allocation is defined as the process of deciding how to allocate an investor’s wealth among a) b) c) d) e) 326 Asset classes, sectors, and countries. Asset classes, sectors and real estate. Asset classes, sectors and derivatives. Asset classes. Sectors. (a) 2 Which of the following is not a life cycle phase? a) b) c) d) e) (e) 3 Which of the following is not a step in the portfolio management process? a) b) c) d) e) (e) 4 5 Develop a policy statement Study current financial and economic conditions Construct the portfolio Monitor investor's needs and market conditions Sell all assets and reinvest the proceeds at least once a year An example of a risk management strategy that involves ‘risk transfer’ is a) b) c) d) e) (c) Discovery phase Accumulation phase Consolidation phase Spending phase Gifting phase Maintaining large cash reserves. Purchasing commodities. Investing largely in bonds. Investing largely in stocks. Purchasing derivative securities. An individual in the consolidation phase of the investment life cycle would a) Have retired and would seek to preserve the real value of their investments. b) Have enough income to cover expenses and excess assets would be used to benefit charities and family. c) Be past the midpoint of their careers and have excess earnings that can be invested in moderately risky investments. d) Be in the early to middle stage of their career, have a small net worth and long investment time horizon. e) None of the above. (d) 6 Which of the following statements is true? a) b) c) d) Stocks are inappropriate investments in a tax deferred account. The only way to maintain purchasing power over time is to invest in bonds. After adjusting for taxes, long-term bonds consistently outperform stocks. Investment in common stocks enables an investor to maintain real value over time. e) None of the above 327 (c) 7 In the U.K. equity allocation in pension fund portfolios stands around 78%. This high level of allocation to equities can be explained by a) b) c) d) e) (e) 8 Research has shown that the asset allocation variation in fund returns across all funds, and particular fund over time. a) b) c) d) e) (a) 9 10 11 90 and 100. 100 and 40. 90 and 40. 40 and 100. 40 and 90. risk and return risk return time horizon liquidity needs Investors can manage risk confronting their wealth using the following a) b) c) d) e) (d) decision explains % of the % of the variation in returns for a In an investment policy statement the objectives of an investor are expressed in terms of a) b) c) d) e) (d) The generous state pensions. The high average age of the population. The historically high inflation. An illiquid stock market. Government regulations. risk avoidance risk anticipation risk transfer all of the above none of the above An individual in the accumulation phase of the investment life cycle would a) Have retired and would seek to preserve the real value of their investments. b) Have enough income to cover expenses and excess assets would be used to benefit charities and family. c) Be past the midpoint of their careers and have excess earnings that can be invested in moderately risky investments. d) Be in the early to middle stage of their career, have a small net worth and long investment time horizon. 328 e) None of the above. 329 MULTIPLE CHOICE PROBLEMS (d) 1 The nominal rate of return for a security is 12.5% per year. If the relevant tax rate is 35% and the rate of inflation is 3.75% per year, calculate the after tax real rate of return for the security. a) b) c) d) e) 8.75% 5.69% 8.43% 3.06% 2.95% USE THE FOLLOWING INFORMATION FOR THE NEXT 4 PROBLEMS As part of a retirement planning exercise, you are comparing a regular IRA with a Roth IRA. The regular IRA contribution is tax deductible. In both cases the contribution amount is $2000. Your time horizon is 25 years and you expect to earn 9.5% percent per year on both types of IRA accounts. Your current tax rate is 20% but you expect you tax rate at retirement to be 15%. (b) 2 Calculate the tax savings generated by the regular IRA at the time of investment. a) b) c) d) e) (c) 3 Calculate the future value, at the end of 25 years, of the tax savings. a) b) c) d) e) (c) 4 $2,900.51 $3,867.35 $2,496.70 $1,248.35 $4,369.23 Calculate the total after tax future value, at the end of 25 years, of the regular IRA contribution and the tax savings. a) b) c) d) e) 330 $300 $400 $700 $100 $200 $19,336.73 $21,833.43 $18,932.92 $16,840.03 $16,436.23 (a) 5 Calculate the total after tax future value, at the end of 25 years, of the Roth IRA contribution. a) b) c) d) e) (e) 6 Your portfolio currently has an asset allocation that is 15% cash, 35% bonds, and 50% stocks. The returns over the past years for cash was 3.5%, bonds 5.75%, and stocks –8.5%. The return on your portfolio for the past year was a) b) c) d) e) (a) 7 8 9 $233,976 $220,515 $250,515 $500,673 $213,321 Assume that you invest $1000 at the end of each quarter for the next 15 years in a mutual fund. The annual rate of interest that you expect to earn in the this account is 8.75%. The amount in the account at the end of 15 years a) b) c) d) e) (d) -5.04% 5.47% 0.25% 5.91% -1.71% The future value of $25,000 invested today, at the end of 20 years assuming an interest rate of 11.5% per year, with semiannual compounding, is a) b) c) d) e) (b) $19,336.73 $21,833.43 $18,932.92 $16,840.03 $16,436.23 $28,790 $121,749 $60,000 $315,000 $115,637 Assuming the investor's marginal tax rate is 28% and he is considering investing in a municipal bond yielding 7%. What is the equivalent taxable yield? a) 5.04% b) 5.47% c) 8.96% 331 d) 9.72% e) 9.80% USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS Assume that you have just retired with $1,000,000 in savings in an investment account. You expect to earn 10% per year on your investments. You plan to withdraw 25% annually at the beginning of each year with interest credited on the remaining balance at the end of the year. (d) 10 Calculate the amount withdrawn at the beginning of the second year. a) b) c) d) e) (d) 11 Calculate the balance in the investment account at the end of the second year (prior to any withdrawals) a) b) c) d) e) (b) 12 13 $750,000 $618,750 $825,000 $680,625 $510,468 Someone in the 15 percent tax bracket can earn 8% on his investments in a taxexempt IRA account. What will be the value of a $10,000 investment after 5 years (assuming annual compounding)? a) b) c) d) e) (c) $148,739 $250,000 $170,156 $206,250 $186,320 $ 6,805 $14,693 $15,528 $20,114 $50,000 Suppose you invest money in a taxable account earning 8% per year. What will be the after-tax value of a $10,000 investment after 5 years if you are in the 15% tax bracket (assuming annual compounding)? a) $10,680 b) $11,765 332 c) $13,895 d) $14,693 e) $15,528 CHAPTER 5 ANSWERS TO MULTIPLE CHOICE PROBLEMS 1. After tax real rate = ([(1 + 0.125)/(1 + 0.0375)]-1)(1-.35) = 0.0548 or 5.48% 2. Tax savings on regular IRA = (2000)(0.2) = 400. 3. FV of tax savings = 400(1 + 0.076)25 = $2496.70 0.095(1 – 0.2) = 0.076 4. Pre tax FV of regular IRA contribution = 2000(1 + 0.095)25 = $19,336.73 After tax FV of regular IRA = $19,336.73(1 – 0.15) = $16,436.22 FV of tax savings = 400(1 + 0.076)25 = $2496.70 Total after tax = $18,932.92 5. After tax FV of Roth IRA contribution = 2000(1 + 0.095)25 = $19,336.73 6. Portfolio return = (.15)(.035)+(.35)(.0575)+(.5)(-.085) = -0.0171 or –1.71% 7. FV = 25,000(1 + .057540) = $233,976 8. (1 .021875 60 ) 1 =$121,749 FV = 1000 .021875 9. Equivalent taxable yield = .07/(1 - .28) = .07/.72 = 9.72% 333 10. Interest rate Withdrawal rate Year Principal 10% 25% outflow Balance 0 $1,000,000.00 $250,000.00 $750,000.00 1 $ 825,000.00 $206,250.00 $618,750.00 2 $ 680,625.00 $170,156.25 $510,468.75 The initial withdrawal is $1,000,000(0.25) = $250,000 The remaining balance of $750,000 earns interest of 10%. At the end of the year it is worth 750,000(1.1) = $825,000 The withdrawal at the beginning of the second year is = 825,000(0.25) = $206,250 11. The remaining balance at the end of the first year = 825,000 – 206,250 = $618,750 This earns interest of 10% and at the end of year 2 is worth = 618,750(1.1) = $680,625 12. $10,000(1 + 0.08)5 = $14,693 13. After-tax yield = Before-tax yield (1 - Tax rate) = 0.08(1 - 0.15) = 0.068 or 6.8% $10,000(1 + 0.068)5 = $13,895 334 CHAPTER 5 APPENDIX MULTIPLE CHOICE QUESTIONS (a) 1 Many endowments are tax-exempt. a) True b) False (b) 2 Cash flows for nonlife insurance companies, such as property and casualty, are similar to cash flows of life insurance companies. a) True b) False (b) 3 The portfolio mixes of institutional investors around the world are approximately the same. a) True b) False (e) 4 In a defined contribution pension plan, a) the plan does not promise to pay the retiree a specific income stream after retirement. b) the plan does promise to pay the retiree a specific income stream after retirement. c) the employee's retirement income is not an obligation of the firm. d) the company carries the risk of paying future pension benefits to retirees. e) Choices a and c (d) 5 Banks typically have short-term investment horizons because a) b) c) d) e) they have a strong need for liquidity. they offer short-term deposit accounts. they are required to by federal and state laws. Choices a and b All of the above 335 CHAPTER 6 ORGANIZATION AND FUNCTIONING OF SECURITIES MARKETS TRUE/FALSE QUESTIONS (t) 1 A continuous market that has price continuity requires depth of buyers and sellers. (f) 2 A market where prices adjust rapidly to new information is considered to be internally efficient. (f) 3 Informational efficiency is where the cost of acquiring information is very cheap. (f) 4 The primary market is where existing issues are traded between current and potential owners. (t) 5 A general obligation (GO) bond is backed by the full taxing power of the municipality. (t) 6 Negotiated, competitive bids, and best efforts are three forms of underwriting arrangements. (t) 7 Secondary markets are important because they provide liquidity to individuals who have purchased issues in the primary market. (f) 8 In a call market, trades occur at any time while the market is open. (t) 9 The U.S. over-the-counter market is the largest segment of the U.S. secondary market in terms of number of issues traded. (f) 10 The third market describes direct trading of securities between parties with no broker intermediary. (f) 11 The fourth market is mainly used by individual investors because it is much cheaper than using a broker. (t) 12 A short seller can only trade on an uptick (or zero uptick) and must pay any dividends to the lender of the stock. (t) 13 The increase in institutional development has caused an increase in the number and size of block trades. (t) 14 Super DOT is an electronic order-routing system through which member firms can transmit market and limit orders directly to the posts where the securities are traded. (t) 15 In the United States commons stocks are quoted in decimals not fractions. 336 (f) 16 Decimalization has increased spread size and caused an increase in transaction costs. MULTIPLE CHOICE QUESTIONS (b) 1 A central limit order book (CLOB) refers to a system where a) b) c) d) e) (b) 2 In a call market, trading for individual stocks a) b) c) d) e) (e) 3 All limit orders are electronically matched. All limit orders are visible to the specialist only. All limit orders are visible to markets makers and specialists. Orders are routed through Super Dot. None of the above. Occurs anytime the market is open. Takes place at specific times. Takes place at the open and close of the trading day. All of the above. None of the above. A pure auction market is one in which a) Dealers provide liquidity by buying and selling shares of stock for themselves. b) Dealers compete against each other to provide the highest bid and lowest asking prices. c) Buyers submit bid prices to sellers. d) Sellers submit ask prices to buyers. e) Buyers and sellers submit bid and ask prices to a central location to be matched. (a) 4 In a negotiated bid, the underwriter carries out the following service(s) a) b) c) d) e) (d) 5 Origination, risk-bearing, and distribution. Origination and risk-bearing. Risk-bearing and distribution. Origination and distribution. Risk-bearing and distribution. Municipal bonds are sold using the following method or methods a) Competitive bid 337 b) c) d) e) (d) 6 When a market externally efficient, it means that a) b) c) d) e) (b) 7 8 Timely and accurate information is available The market is liquid Transaction costs are low Prices adjust rapidly to new information The number of buyers and sellers are the same When a market is internally efficient, it means that a) b) c) d) e) (b) Negotiated sale Private placement All of the above None of the above The market has price continuity. The market has minimal transactions costs The market has good depth The market has more buyers than sellers The market has more sellers than buyers The impact of changing the system for quoting share prices from fractions to decimals has been to a) Increase spread size, increase transaction costs, and increase the number of transactions. b) Decrease spread size, decrease transaction costs, and increase the number of transactions. c) Decrease spread size, decrease transaction costs, and decrease the number of transactions. d) Decrease spread size, increase transaction costs, and increase the number of transactions. e) Decrease spread size, decrease transaction costs and decrease the number of transactions.. (d) 9 Which of the following is not a characteristic of a "good" market? a) b) c) d) e) (b) 338 10 Marketability Price continuity Low transaction costs Few buyers and sellers Informational efficiency A "good" market is one a) In which there is a strong likelihood of insider trading. b) Where prices reflect new information regarding supply and demand factors. c) Where accurate information on cost and volume for past transactions is difficult to obtain. d) Which is illiquid and has high transaction costs. e) All of the above. (e) 11 Which of the following is(are) an underwriting function? a) b) c) d) e) (d) 12 With a best-efforts offering, the investment banker performs all of the following roles: a) b) c) d) e) (c) 13 Origination. Risk-bearing and origination. Distribution and origination. Risk bearing and distribution. Origination, risk bearing and distribution. Designs and plans the security issue. Acquires the total issue through a competitive bid. Accepts the responsibility for reselling the issue. Acts as a broker to sell as many securities it can at a stipulated price. All of the above are true. The basic distinction between a primary and a secondary market is a) Proceeds from sales in the primary market go to the current owner of a security; proceeds in secondary market go to the original owner. b) Primary markets involve direct dealings within regional exchanges. c) Only new securities are sold in the primary market; only outstanding securities are brought and sold in the secondary market. d) Primary markets deal exclusively in bonds; secondary markets deal primarily in common stock. e) There is no difference between a primary and secondary market (a) 14 The underwriting function of ‘origination’ involves a) b) c) d) e) (c) 15 The design and planning of the security issue. Acquiring the total issue through a competitive bid. Accepting the responsibility for reselling the issue. Acting as a broker to sell as many securities it can at a stipulated price. All of the above are true. The underwriting function of ‘risk-bearing’ involves 339 a) b) c) d) e) (a) 16 The design and planning of the security issue. Selling the security issue through a selling syndicate. Accepting the responsibility for reselling the issue. Acting as a broker to sell as many securities it can at a stipulated price. All of the above are true. A dealer market is one in which a) Dealers compete and provide liquidity by buying and selling shares of a security for themselves. b) One dealer sets bid and ask prices at which securities will trade. c) Buyers submit bid prices to sellers. d) Sellers submit ask prices to buyers. e) Buyers and sellers submit bid and ask prices to a central location to be matched. (e) 17 The term ‘third market’ describes the market where dealers and brokers: a) b) c) d) e) (e) 18 The vast majority of trading on regional stock exchanges is in a) b) c) d) e) (e) 19 20 Stocks listed on the NYSE. Stocks listed on the Nasdaq. Dual listed stocks. Stocks with unlisted trading privileges (UTP). Dual listed and UTP stocks. The member of the New York Stock Exchange who acts as a dealer on assigned stocks is known as a a) b) c) d) e) (c) Trade in stocks listed on regional stock exchanges. Trade in stocks through electronic communication networks. Trade in stocks listed on the London Stock Exchange. Trade in stocks through electronic crossing systems. Trade in exchange listed stocks away from the exchanges. Registered trader. Commission broker. Registered dealer. Floor dealer. Specialist. Floor brokers on the NYSE a) Use their membership to buy and sell for their own account. 340 b) Are employees of a member firm and buy and sell for customers of the firm. c) Act as brokers for other members. d) Handle limit and other special orders placed by other brokers on the floor. e) Maintain a fair and orderly market. (a) 21 An order placed specifying the buy or sell price is a a) b) c) d) e) (c) 22 When an investor borrows part of the investment cost it is known as a) b) c) d) e) (e) 23 Limit order. Short sale. Market order. Priced order. Stop loss. A short sale. A fill or kill order. A margin transaction. A limit order. A credit order. Which of the following is not a function of the specialist? a) Acting as a broker who handles the limit orders or special orders placed with member brokers b) Buying and selling securities in order to stabilize the market c) Acting as a dealer in assigned stocks to maintain a fair and orderly market d) Maintain a minimum of $1 million or the value of 15,000 shares of each stock assigned, whichever is greater e) Speculating only for themselves, they do not execute traders for the public nor for other brokers (c) 24 If your broker required a maintenance margin of 25%, it means that a) You may borrow up to 25% of a stock purchase. b) You may borrow up to 75% of a stock purchase. c) The ratio of your equity value to the total value of the position may not fall below 25%. d) The ratio of your equity value to the total value of the position may not fall below 75%. e) None of the above. 341 342 MULTIPLE CHOICE PROBLEMS USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS Assume you deposit $100,000 in a margin account. The margin requirement is 50 percent and commissions are ignored. Shares in Sisco Corp currently sell for $80 per share: (b) 1 What is the value of stock that you can acquire? a) b) c) d) e) (c) 2 What is your profit if the price of Sisco Corp rises to $90? a) b) c) d) e) (c) 3 4 5 $51.25 $43.25 $53.33 $45.33 $83.33 Calculate your percentage rate of return if the shares of Sisco Corp falls to $65. a) b) c) d) e) (b) $50,000 $12,500 $25,000 $100,000 $120,000 If the maintenance margin is 25 percent, to what price can Sisco Corp fall before you receive a margin call? a) b) c) d) e) (d) $100,000 $200,000 $175,000 $150,000 $300,000 -15.00% -25.00% -23.07% -37.50% -30.50% Suppose you buy a round lot of a stock on 55 percent margin when it is selling at $35 a share. The broker charges a 10 percent annual interest rate and commissions are 3 percent of the total stock value on both the purchase and the sale. If at year end you receive a $0.90 per share dividend and sell the stock for 32, what is your rate of return on the investment? 343 a) b) c) d) e) -29.38% -28.00% -26.23% -25.00% -35.00% USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS You decide to sell 100 shares of a stock short when it is selling at its yearly high of $22.25. Your broker tells you that your margin requirement is 55% and that the commission on the sale is $55. While you are short, the stock, Tuna Boat pays a $0.75 per share dividend. At the end of one year you buy shares of the stock to cover your short sale at $18.38 and are charged a commission of $45 and a 9% interest rate on the funds you borrowed. (a) 6 What is your dollar return on the investment? a) b) c) d) e) (d) 7 $121.89 $315.05 $425.50 $637.73 $950.45 What is your rate of return on the investment? a) b) c) d) e) 0.87% 3.87% 5.08% 9.53% 11.87% USE THE FOLLOWING INFORMATION FOR THE NEXT FIVE PROBLEMS You decide to sell short 200 shares of XCorp stock at a price of $75. Your margin deposit is 65%. Commission on the sale is 1.25%. During the year the stock pays a $1.75 per share dividend. Interest on margin debt is 5.25% per year. (d) 8 Calculate your initial investment a) b) c) d) e) 344 $15,000 $5,250.75 $9,750.25 $9,937.50 $15,187.50 (a) 9 At the end of one year you close out your short position by purchasing shares of XCorp at $45 per share. The commission is 1.25%. Calculate your dollar profit. a) b) c) d) e) (c) 10 If at the end of one year you close out your short position by purchasing share of XCorp at $45 per share with commission of 1.25%, what is your rate of return on the investment? a) b) c) d) e) (b) 11 12 -55.92% 10.31% 51.06% 23.1% -33.05% Suppose at the end of one year XCorp is selling at $90 per share and you cover your short position at this price. What is your dollar profit on the investment? (Assume a 1.25% commission on the purchase) a) b) c) d) e) (a) $5,074.38 -$4,038.13 $5250.00 -$5074.38 $4,038.13 $5,074.38 -$4,038.13 $5250.00 -$5074.38 $4,038.13 If you cover your short position at $90 per share. What is your rate of return on the investment? (Assume a 1.25% commission on the purchase) a) b) c) d) e) -40.64% -25.53% 5.21% 72.7% –71.2% USE THE FOLLOWING INFORMATION FOR THE NEXT FIVE PROBLEMS Shares of RossCorp stock are selling for $45 per share. Brokerage commissions are 2% for purchases and 2% for sales. The interest rate on margin debt is 6.25% per year. The maintenance margin is 30%. (e) 13 At the end of one year shares of RossCorp stock are selling for $55 per share and the company paid dividends of $0.85 per share. Assuming that 345 you paid the full cost of the purchase, what is your rate of return if you sell RossCorp stock? a) b) c) d) e) (b) 14 At the end of one year shares of RossCorp stock are selling for $35 per share and the company paid dividends of $0.85 per share. Assuming that you paid the full cost of the purchase, what is your rate of return if you sell RossCorp stock? a) b) c) d) e) (c) 15 16 17 33.05% -33.05% -23.51% -25.35% –40.64% Assume that you purchase 150 shares of RossCorp stock by making a margin deposit of 75%. At what price would you receive a margin call? a) b) c) d) 346 -23.51% 29.35% 23.51% 5.21% 10.06% At the end of one year shares of RossCorp stock are selling for $35 per share and the company paid dividends of $0.85 per share. Assuming that you borrowed 25% of cost of the purchase, what is your rate of return? a) b) c) d) e) (d) -33.05% -23.42% 23.42% 33.05% –25.35% At the end of one year shares of RossCorp stock are selling for $55 per share and the company paid dividends of $0.85 per share. Assuming that you borrowed 25% of cost of the purchase, what is your rate of return? a) b) c) d) e) (b) 18.08% 23.51% 22.32% 14.96% 19.28% $29.39 $26.48 $50.39 $16.07 e) $50.10 CHAPTER 6 ANSWERS TO MULTIPLE CHOICE PROBLEMS 1. If X is the total investment your share will represent 50 percent. Thus .50x = $100,000 and X = $100,000/.50 = $200,000. Since the shares are $80 each, you can purchase ($200,000)/$80 = 2500 shares 2. Profit = (90 - 80)(2500) = $25,000 3. Margin = (Market Value - Debit Balance)/ Market Value where Market Value = Price x Number of Shares = Price x 2500 Debit Balance = Initial Loan Value = (0.5)($80)(2500) = $100,000 0.25 = ((Price x 2500) - $100,000)/(Price x 2500) Price = $53.33 4. Return = (65 – 80)/(0.5 x 80) = -0.375 or -37.5% 5. Initial investment= (.55 x $3,500) + (.03 x $3500) = $2030 Beginning Value of Stock = $3500 Profit = Ending Wealth - Beginning Value of Stock - Transaction Costs - Interest Ending Wealth = Ending Market Value + Dividend= $3200 + $90 = $3290 Transaction Costs = .03 x 3500 + .03 x 3200 = $105.00 + 96 = $201 Interest = .10 x (.45 x $3500) = $157.50 Profit = $3290 - $3500.00 - $201 - $157.50 = - $568.50 Rate of Return = Profit/Initial Investment = -$568.50/$2030 = -28% 347 For problems 6 and 7 Initial investment = (.55 x $2225) + 55 = $1278.75 Cost = $18.38 x 100 = $1838 (without transaction costs) Profit = Total Return - Cost - Transaction Costs - Interest Total Return = Beginning Market Value - Dividend = $2225 - $75 = $2150 Transaction Costs = $55 + $45 = $100.00 Interest = .09 x (.45 x $2225) = $90.11 6. Profit = $2150 - $1838 - $100 - $90.11 = $121.89 7. Rate of Return = $121.89/$1278.75 = 9.53% 8. Initial investment = (0.65)(200)(75) + (0.0125)(200)(75) = $9937.50 9. 10. 11. Dollar profit = 200(75 – 45 – 1.75) – (200)(75)(0.0125) – (200)(45)(0.0125) – (200)(75)(0.35)(0.0525) = $5074.38 Rate of return = 5074.38/9937.50 = 0.5106 or 51.06% Dollar profit = 200(75 – 90 – 1.75) – (200)(75)(0.0125) – (200)(90)(0.0125) – (200)(0.35)(75)(0.0525) = -$4038.13 12. Rate of return = -4038.13/9937.50 = -0.4063 or -40.63% 13. Rate of return = [55- 45 + 0.85 - 1.10 - 0.90]/[45 + 0.90] = 19.28% 14. Rate of return = [35 – 45 + 0.85 -0.70 -0.90]/[45 + 0.90] = -23.42% 348 15. Rate of return = [55-45 + 0.85 -1.10-0.90-(1-.75)(45)(.0625)]/[(0.75)(45) + 0.90] = 23.51% 16. Rate of return = [35-45+0.85-0.70-0.90- (1-.75)(45)(.0625)]/[(0.75)(45)+0.90] = -33.05% 17. 0.30 = [(150)(P) – (0.25)(150)(45)]/[(150)(P)] P = $16.07 CHAPTER 7 349 SECURITY-MARKET INDICATOR SERIES TRUE/FALSE QUESTIONS (t) 1 An aggregate market index can be used as a benchmark to judge the performance of professional money managers. (f) 2 A price-weighted index is the geometric average of the current prices of the sampled securities. (f) 3 The Dow-Jones Industrial Average (DJIA) is a value- weighted average. (f) 4 The DJIA has been criticized because when a stock in the index splits there are more shares outstanding and the importance of the stock in the index increases. (t) 5 Security market indexes have been used to create index funds and exchange traded funds. (f) 6 In a value-weighted index the highest priced stock carries the greatest weight. (t) 7 A value-weighted index contains an automatic adjustment for stock splits. (f) 8 The S&P 500 stock index is an example of an equally-weighted index. (t) 9 An index constructed using small-cap growth stocks would be referred to as a style index . (t) 10 The low correlations between the U.S. and the U.K., and the U.S. and Japan, confirm the benefit of global diversification. (t) 11 The correlations among the U.S. investment-grade-bond series were very high because all rates of return for investment-grade bonds over time are impacted by common macroeconomic variables. 350 MULTIPLE CHOICE QUESTIONS (c) 1 Which of the following is not a use of security market indicator series? a) b) c) d) e) (c) 2 A properly selected sample for use in constructing a market indicator series will consider the sample's source, size and a) b) c) d) e) (a) 3 4 5 Divisor will increase/decrease, index remains the same. Index will increase/decrease, divisor remains the same. Index and divisor will remain the same. Index and divisor will both reflect the changes (immediately). Not enough information provided. An example of a value-weighted stock market indicator series is the a) b) c) d) e) (d) Value. Average beta. Breadth. Variability. Dividend record. What effect does a stock substitution or stock split have on a price-weighted series, such as DJIA? a) b) c) d) e) (d) To use as a benchmark of individual portfolio performance To develop an index portfolio To determine unsystematic risk To determine factors influencing aggregate security price movements To determine systematic risk Dow Jones Industrial Average. Nikkei-Dow Jones Average. Value Line Index. American Stock Exchange Index. Lehman Brothers Index. Which of the following indexes includes the most comprehensive list of stocks? a) b) c) d) e) New York Stock Exchange Composite Index Standard and Poor's 500 Composite Index American Stock Exchange Market Value Index Nasdaq Composite Dow Jones Industrial Average 351 (c) 6 The Value Line Composite Average is based on percent price changes which has been computed using a) b) c) d) e) (e) 7 An arithmetic mean. A harmonic average. A geometric mean. An expected average. A logarithmic average. Which of the following are factors that make it difficult to create and maintain a bond index? a) The universe of bonds is broader than stocks. b) The universe of bonds is constantly changing due to new issues, bond maturities, calls, and bond sinking funds. c) There can be difficulties in correctly pricing bond issues. d) Choices a and c. e) Choices a, b and c. (a) 8 Low correlations between the S&P 500 stock index and the MSCI EAFE suggest a) b) c) d) e) (d) 9 That investors should diversify investment portfolios. That investors should invest only in U.S. stocks. That investors should invest only in Europe. That investors should invest only is Asia. Nothing. Correlations between U.S. investment grade bonds are a) Low because of the equity characteristics of high yield bonds. b) Low because yields on investment grade bonds are determined by systematic interest rate variables. c) High because of the equity characteristics of high yield bonds. d) High because yields on investment grade bonds are determined by systematic interest rate variables. e) None of the above. (a) 10 Correlations between U.S. investment grade bonds and high yield bonds are a) Low because of the equity characteristics of high yield bonds. b) Low because yields on investment grade bonds are determined by systematic interest rate variables. c) High because of the equity characteristics of high yield bonds. d) High because yields on investment grade bonds are determined by systematic interest rate variables. e) None of the above. 352 MULTIPLE CHOICE PROBLEMS USE THE FOLLOWING INFORMATION FOR THE NEXT 12 PROBLEMS Stock W X Y Z 31-Dec-03 31-Dec-0331-Dec-0431-Dec-04 Price Shares Price Shares $ 75.00 10000 $ 50.00 30000 $ 150.00 5000 $ 65.00 15000 $ 25.00 20000 $ 35.00 20000 $ 40.00 25000 $ 50.00 25000 Stocks W and X had 3 for 1 splits on December 31, 2003 at the end of trading. (c) 1 Calculate the price weighted series for Dec 31, 2003, prior to the splits. a) b) c) d) e) (a) 2 Calculate the price weighted series for December 31, 2003 after the splits. a) b) c) d) e) (e) 3 4 72.5 100.0 119.25 121.25 103.57 Calculate the price weighted series for Dec 31, 2004. a) b) c) d) e) (a) 103.57 100.0 72.5 121.25 119.25 121.25 119.25 100.0 72.5 103.57 Calculate the percentage return in the price weighted series for the period Dec 31, 2003 to Dec 31, 2004. a) b) c) d) e) 42.86% 20.00% 21.76% 33.33% 40.00% 353 (d) 5 Calculate the value weighted index for Dec 31, 2003, prior to the splits. Assume a base index value of 100. The base year is Dec 31, 2003. a) b) c) d) e) (c) 6 Calculate the value weighted index for Dec 31, 2003, after the splits. Assume a base index value of 100. The base year is Dec 31, 2003. a) b) c) d) e) (e) 7 8 9 12.68% 47.50% 21.76% 33.33% 40.00% Calculate the unweighted index for Dec 31, 2003, prior to the splits. Assume a base index value of 100. The base year is Dec 31, 2003. a) b) c) d) e) 354 121.25 100.0 81.69 72.5 147.5 Calculate the percentage return in the value weighted index for the period Dec 31, 2003 to Dec 31, 2004. a) b) c) d) e) (a) 72.5 81.69 100.0 147.5 121.25 Calculate the value weighted index for Dec 31, 2004. Assume a base index value of 100. The base year is Dec 31, 2003. a) b) c) d) e) (b) 147.5 81.69 72.5 100.0 121.25 100.0 200.0 150.0 120.0 175.0 (c) 10 Calculate the unweighted index for Dec 31, 2003, after the splits. Assume a base index value of 100. The base year is Dec 31, 2003. a) b) c) d) e) (a) 11 Calculate the unweighted index (geometric mean) for Dec 31, 2004. Assume a base index value of 100. The base year is Dec 31, 2003. a) b) c) d) e) (a) 12 110.0 200.0 100.0 120.0 150.0 146.05 121.25 151.25 148.75 100.25 Calculate the percentage return in the unweighted index (geometric mean) for the period Dec 31, 2003 to Dec 31, 2004. Assume a base index value of 100. The base year is Dec 31, 2003. a) b) c) d) e) 46.05% 21.25% 51.25% 48.75% 100.25% USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS You are given the following information regarding prices for a sample of stocks: Stock A B C (b) Number of Shares 1,000,000 10,000,000 25,000,000 13 PriceT 50 30 20 PriceT+1 60 35 25 Using a price-weighted series approach, what is the percentage change in the series for the period from T to T + 1. a) 1.20% 355 b) c) d) e) (d) 14 Using a value-weighted series approach, what is the percentage change in the series for the period from T to T + 1. a) b) c) d) e) (c) 20.00% 21.76% 33.33% 40.00% 15 1.22% 20.00% 20.55% 21.76% 33.33% Construct an unweighted series (arithmetic mean) assuming $1,000 is invested in each stock. What is the percentage change in wealth for this portfolio? a) b) c) d) e) 1.21% 20.00% 20.56% 21.76% 33.33% USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS Price COMPANY Day 1 Day 2 Day 3 Day 4 Shares A 12 10 8 9 B 23 22 26 25 *Split at Close of Day 2 (c) 16 17 B 350 350 350 350 C 250 250 250** 750 **Split at Close of Day 3 13.000 19.000 29.000 87.000 100.000 Calculate a Dow Jones Industrial Index for Day 4. a) 11.2389 356 A 500 500* 1000 1000 Calculate a Dow Jones Industrial Index for Day 1. a) b) c) d) e) (c) C 52 55 51 19 b) c) d) e) (e) 18 21.3343 31.2389 41.6890 None of the above Calculate a Standard & Poor's Index for Day 3 if the base period is Day 1 with an initial index value is 100. a) b) c) d) e) 90.351 91.035 95.234 101.628 110.351 CHAPTER 7 ANSWERS TO MULTIPLE CHOICE PROBLEMS 1 PRICE WEIGHTED SERIES DEC 2003 = (75 + 150 + 25 + 40)/4 = 72.5 2 POST SPLIT SERIES = 72.5 = (25 + 50 + 25 + 40)/X The new divisor, X = 1.931 3 PRICE WEIGHTED SERIES DEC 2004 = (50 + 65 + 35 + 50)/1.931 = 103.57 4 Return on series = (103.57 – 72.5)/72.5 = 42.86% 5 Value weighted series Dec 2003 = 750000 750000 500000 1000000 x100 100 750000 750000 500000 1000000 6 Value weighted post split = 100. Not affected by splits. 7 Value weighted series Dec 2004 = 1500000 975000 700000 1250000 x100 147.5 750000 750000 500000 1000000 8 9 SINCE THE BASE VALUE IS 100 AND THE CURRENT INDEX VALUE IS 147.5, the percentage return is 47.5%. The index value Dec 2003 is 100 357 10 Post split the index value is 100 11 Index Dec 2004 = (2 + 1.3 + 1.40 + 1.25)1/4 (100) = 146.05 12 The return on the index is 46.05% 13 Given a three security series and a price change from period T to T+1, the percentage change in the price weighted series would be A B C Sum Divisor Average Period T $50 30 20 $100 3 33.33 Period T+1 $60 35 25 $120 3 40.00 Percentage change = (40.00 - 33.33)/33.33 = 20.00% 14 Period T Stock Price/Share A $50 B 30 C 20 Total # of Shares 1,000,000 10,000,000 25,000,000 Market Value $50,000,000 300,000,000 500,000,000 $850,000,000 Period T+1 Stock Price/Share A $60 B 35 C 25 Total # of Shares 1,000,000 10,000,000 25,000,000 Market Value $60,000,000 350,000,000 625,000,000 $1,035,000,000 Percentage change = (1,035 – 850)/850 = 21.76% 15 Period T Stock Price/Share A $50 B 30 C 20 Total Period T+1 Stock Price/Share A $ 60 B 35 C 25 358 # of Shares Market Value 20.00 $1,000.00 33.33 1,000.00 50.00 1,000.00 $3,000.00 # of Shares 20.00 33.33 50.00 Market Value $1,200.00 1,166.55 1,250.00 Total $3,616.55 Percentage change = (3,616.55 - 3,000)/3,000 = 20.56% 16 Day 1 Index = (12 + 23 + 52)/3.0000 = 29.000 17 Day 2 Index = (10 + 22 + 55)/3.0000 = 29.000 Adjusted Day 2 Index = (5 + 22 + 55)/X = 29.000 X = 2.8276 (new divisor) Day 3 Index = (8 + 26 + 51)/2.8276 = 30.0608 Adjusted Day 3 Index = (8 + 26 + 17)/Y = 30.0608 Y = 1.6966 (new divisor) Day 4 Index = (9 + 25 + 19)/1.6966 = 31.2389 18 Base = ($12 x 500) + ($23 x 350) + ($52 x 250) = $27,050 Day 3 ($8 x 1000) + ($26 x 350) + ($51 x 250) = $29,850 Index = ($29,850/$27,050) x 100 = 110.351 CHAPTER 8 359 AN INTRODUCTION TO PORTFOLIO MANAGEMENT TRUE/FALSE QUESTIONS (t) 1 Risk is defined as the uncertainty of future outcomes. (t) 2 A basic assumption of the Markowitz model is that investors base decisions solely on expected return and risk. (t) 3 The yield spread between yields on AAA bonds and BAA bonds is evidence that investors are risk averse. (t) 4 Standardizing the covariance by the individual standard deviation yields the correlation coefficient. (t) 5 The covariance is a measure of the degree to which two variables (e.g., rates of return) move together over time relative to their means. (f) 6 For a two stock portfolio containing Stocks i and j, the correlation coefficient of returns (ri,j) is equal to the square root of the covariance (covi,j). (f) 7 To reduce the standard deviation of a portfolio it is necessary to increase the relative weight of assets with low volatility (small standard deviation of returns). (t) 8 Increasing the correlation among assets in a portfolio results in an increase in the standard deviation of the portfolio. (f) 9 A basic assumption of portfolio theory is that an investor would want to maximize risk subject to a given level of return. (t) 10 Most investors hold a diversified portfolio in order to reduce portfolio risk. (f) 11 other. 360 Most assets of the same type have negative covariances of returns with each MULTIPLE CHOICE QUESTIONS (a) 1 The optimal portfolio is identified at the point of tangency between the efficient frontier and the a) b) c) d) e) (d) 2 An individual investor’s utility curves specify the tradeoffs he or she is willing to make between a) b) c) d) e) (c) 3 4 approaches a horizontal straight line. bends out. bends in. approaches a vertical straight line. none of the above. A portfolio manager is considering adding another security to his portfolio. The correlations of the 5 alternatives available are listed below. Which security would enable the highest level of risk diversification a) b) c) d) e) (b) high risk and low risk assets. high return and low return assets. covariance and correlation. return and risk. efficient portfolios. As the correlation coefficient between two assets decreases, the shape of the efficient frontier a) b) c) d) e) (d) highest possible utility curve. lowest possible utility curve. middle range utility curve. steepest utility curve. flattest utility curve. 5 0.0 0.25 -0.25 -0.75 1.0 A positive covariance between two variables indicates that a) b) c) d) the two variables move in different directions. the two variables move in the same direction. the two variables are low risk. the two variables are high risk. 361 e) the two variables are risk free. (c) 6 A positive relationship between expected return and expected risk is consistent with a) b) c) d) e) (d) 7 What information must you input to a computer program in order to derive the portfolios that make up the efficient frontier a) b) c) d) e) (d) 8 investors being risk seekers. investors being risk avoiders. investors being risk averse. all of the above. none of the above. Expected returns, covariances and correlations. Standard deviations, variances and covariances. Expected returns, standard deviations and variances. Expected returns, variances and correlations. Covariances, correlations and variances. The Markowitz model is based on several assumptions regarding investor behavior. Which of the following is an assumption of the Markowitz model? a) Investors consider investment alternative as being represented by a joint probability distribution of expected returns over some holding period. b) Investors minimize one-period expected utility. c) Investors estimate the risk of the portfolio on the basis of their utility functions. d) Investors base decisions solely on expected return and risk. e) None of the above. (a) 9 As the correlation coefficient between two assets increases, the shape of the efficient frontier a) b) c) d) e) (d) 10 The probability of an adverse outcome is the a) b) c) d) 362 approaches a horizontal straight line. bends out. bends in. approaches a vertical straight line. none of the above. Statistics. Variance. Random. Risk. definition of: e) Semivariance. (c) 11 Which of the following is a measure of risk? a) b) c) d) e) (b) 12 Semivariance, when applied to portfolio theory, is concerned with the a) b) c) d) e) (a) 13 14 Square root of deviations from the mean. Deviations below the mean. Deviations above the mean. All deviations (above and below the mean). Summation of the squared deviations from the mean. With low, zero or negative correlations it is possible to derive portfolios that have a) b) c) d) e) (d) Range of standard deviations Expected return Standard deviation Covariance Correlation Lower risk than the individual securities in the portfolio. Lower risk than the highest risk individual security in the portfolio. Higher risk than the individual securities that make up the portfolio. Higher risk than the highest risk individual security in the portfolio. None of the above. Which of the following statements are correlation coefficient is false? a) The values range between -1 to +1. b) A value of +1 implies that the returns for the two stocks move together in a completely linear manner. c) A value of -1 implies that the returns move in a completely opposite direction. d) A value of zero means that the returns are zero. e) None of the above (that is, all statements are true) (a) 15 In a two stock portfolio, if the correlation coefficient between two stocks were to decrease over time everything else remaining constant the portfolio's risk would a) b) c) d) e) Decrease. Remain constant. Increase. Fluctuate positively and negatively. Be a negative value. 363 (d) 16 Given the following correlations between pairs of stocks, a portfolio constructed from which pair will have the lowest standard deviation? Correl(A,B) = 0, Correl(C,D) = 1, Correl(E,F) = 0.75, Correl(G,H) = -0.75, Correl(I,J) = -0.50. a) b) c) d) e) (c) 17 Given a portfolio of stocks the envelope curve containing the set of best possible combinations is known as the a) b) c) d) e) (d) 18 19 Expected security returns. Standard deviations of expected returns. Correlations of expected returns. All of the above. None of the above. A portfolio is considered to be efficient if: a) b) c) d) e) 364 Efficient portfolio. Utility curve. Efficient frontier. Last frontier. Capital asset pricing model. Estimation error refers to potential errors that arise from estimating a) b) c) d) e) (a) Pair A,B Pair C,D Pair E,F Pair G,H Pair I,J No other portfolio offers higher expected returns with the same risk. No other portfolio offers lower risk with lower expected return. There is no portfolio with a higher return. There is no portfolio with lower risk. None of the above MULTIPLE CHOICE PROBLEMS (d) 1 Consider two securities, A and B. Security A and B have a correlation coefficient of 0.65. Security A has standard deviation of 12, and security B has standard deviation of 25. Calculate the covariance between these two securities. a) b) c) d) e) (a) 2 300 461.54 261.54 195 200 Calculate the expected return for a three asset portfolio with the following Asset A B C a) b) c) d) e) (c) 3 Exp. Ret. 0.0675 0.1235 0.1425 Given the following weights and expected security returns, calculate the expected return for the portfolio. a) b) c) d) e) 4 Weight 0.25 0.35 0.40 11.71% 11.12% 15.70% 14.25% 6.75%. Weight .20 .25 .30 .25 (d) Std. Dev 0.12 0.1675 0.1835 Expected Return .06 .08 .10 .12 .085 .090 .092 .097 None of the above the standard deviation for stock A is 0.15 and for stock B, it is 0.20. The covariance between returns for these stocks is 0.01. The correlation coefficient between these two stocks is: a) -0.125 b) 0.195 c) -0.285 365 d) 0.333 e) 0.405 USE THE FOLLOWING INFORMATION FOR THE NEXT TWO PROBLEMS Given: E(R1) = .10 E(SD1) = .03 W1 = .30 (d) 5 6 W2 = .70 Calculate the expected return of the two stock portfolio. a) b) c) d) e) (c) E(R2) = .15 E(SD2) = .05 .105 .115 .125 .135 None of the above Calculate the expected standard deviation of the two stock portfolio when the correlation is 0.40. a) b) c) d) e) .0016 .0160 .0395 .1558 .3950 USE THE FOLLOWING INFORMATION FOR THE NEXT FOUR PROBLEMS Given the following information about two stocks: E(R1) = 0.12 E(SD1) = 0.08 (a) 7 Calculate the expected return a two stock portfolio when w1 = 0.75. a) b) c) d) e) (d) 366 8 E(R2) = 0.16 E(SD2) = 0.15 0.13 0.136 0.14 0.125 0.16 Calculate the expected standard deviation of a two stock portfolio when w1 = 0.75 and the covariance between stock 1 and stock 2 is -0.009. a) b) c) d) e) (b) 9 Calculate the expected return a two stock portfolio when w1 = 0.60. a) b) c) d) e) (c) 10 0.1025 0.0705 0.0906 0.0404 0.0623 0.13 0.136 0.14 0.125 0.16 Calculate the expected standard deviation of a two stock portfolio when w1 = 0.60 and the covariance between stock 1 and stock 2 is 0.8. a) b) c) d) e) 0.1025 0.0705 0.0906 0.0404 0.0623 CHAPTER 8 ANSWERS TO MULTIPLE CHOICE PROBLEMS 1. Cov(A, B) = (0.65)(12)(25) = 195 2. E(R) = (0.25)(0.0675) + (0.35)(0.1235) + (0.40)(0.1425) = 0.1171 or 11.71% 3. E(R) = (0.20)(0.06) + (0.25)(0.08) + (0.30)(0.10) + (0.25)(0.12) = 0.092 or 9.2% 4. Correlation = (0.01)(0.15 x 0.20) = 0.3333 5. E(R) = (.3 x .10) + (.7 x .15) = .135 6. SD= [(.3)2(.03)2+ (.7)2(.05)2+ 2(.3)(.7)(.03)(.05)(.4)]1/2 = 0.03947 7. 8. E(R) = (.75 x .12) + (.25 x .16) = 0.13 SD = [(.75)2(.04)2+ (.25)2(.06)2+ 2(.75)(.25)(-.0009)]1/2 = 0.0404 9. 10. E(R) = (.60 x .12) + (.40 x .16) = 0.136 SD= [(.6)2(.04)2+ (.4)2(.06)2+ 2(.6)(.4)(.8)]1/2 = 0.0906 367 CHAPTER 9 AN INTRODUCTION TO ASSET PRICING MODELS TRUE/FALSE QUESTIONS (t) 1 One of the assumptions of Capital Market Theory is that investors can borrow or lend at the risk-free rate. (f) 2 An assumption of Capital Market Theory is that buying or selling of assets entails no taxes, but entails significant transaction costs. (t) 3 A risky asset is an asset with uncertain future returns, and uncertainty (or risk) is measured by the variance or standard deviation of returns. (t) 4 The standard deviation of a portfolio that combines the risk-free asset with risky assets is the linear proportion of the standard deviation of the risky asset portfolio. (t) 5 The Capital Market Line (CML) is the line from the intercept point that represents the risk-free rate tangent to the original efficient frontier. (t) 6 The market portfolio consists of all risky assets. (f) 7 All portfolios on the CML are perfectly negatively correlated, which means that all portfolios on the CML are perfectly negatively correlated with the completely diversified market portfolio since it lies on the CML. (t) 8 Diversification reduces the unsystematic risk in a portfolio. (f) 9 The Capital Asset Pricing Model (CAPM) is a technique for determining the expected risk on an asset. (t) 10 Beta is a standardized measure of systematic risk. (t) 11 Multifactor models of risk and return can be broadly grouped into models that use macroeconomic factors and models that use microeconomic factors. (f) 12 Arbitrage Pricing Theory (APT) specifies the exact number of risk factors and their identity 368 MULTIPLE CHOICE QUESTIONS (d) 1 Which of the following is not an assumption of the Capital Market Theory? a) b) c) d) e) (e) 2 The market portfolio consists of all a) b) c) d) e) (c) 3 4 New York Stock Exchange stocks. International stocks and bonds. Stocks and bonds. U.S. and non-U.S. stocks and bonds. Risky assets. The separation theorems divides decisions on a) b) c) d) e) (d) All investors are Markowitz efficient investors. All investors have homogeneous expectations. There are no taxes or transaction costs in buying or selling assets. There are no risk-free assets. All investors have the same one period time horizon. from decisions on . Lending, borrowing Risk, return Investing, financing Risky assets, risk free assets Buying stocks, buying bonds When identifying undervalued and overvalued assets, which of the following statements is false? a) An asset is properly valued if its estimated rate of return is equal to required rate of return. b) An asset is considered overvalued if its estimated rate of return is below required rate of return. c) An asset is considered undervalued if its estimated rate of return is above required rate of return. d) An asset is considered overvalued if its required rate of return is below estimated rate of return. e) None of the above (that is, all are true statements) (b) 5 its its its its Utilizing the security market line an investor owning a stock with a beta of (-2) would expect the stock's return to in a market that was expected to decline 10 percent. a) Rise or fall an indeterminate amount b) Rise by 20.0% 369 c) Fall by 20.0% d) Rise by 10.2% e) Fall by 10.2% (d) 6 The Capital Market Line (CML) refers to the efficient formed by creating portfolios that a) b) c) d) e) (e) 7 Invest solely in the market portfolio M. Lend at the risk free asset and invest in the market portfolio. Borrow at the risk free asset and invest in the market portfolio. Lend and borrow at the risk free rate and invest in the market portfolio. Short sell the market portfolio. As the number of stocks in a portfolio increases a) The expected return of the portfolio increases because systematic decreases. b) The expected return of the portfolio increases because unsystematic decreases. c) The standard deviation of the portfolio increases because systematic increases. d) The standard deviation of the portfolio decreases because systematic increases. e) The standard deviation of the portfolio decreases because unsystematic decreases. (a) 8 9 10 risk risk Risk and required return on an asset. Systematic risk and required return on an asset. Risk and return on a diversified portfolio of assets. Unsystematic risk and required return on an asset Systematic risk and required return on a diversified portfolio of assets. Confidence risk. Maturity risk. Expected inflation risk. Call risk. Return difference between small capitalization and large capitalization stocks. In a multifactor model, confidence risk represents a) Unanticipated changes in the level of overall business activity. 370 risk In a macro-economic based risk factor model the following factor would be one of many appropriate factors a) b) c) d) e) (d) risk The Security Market Line (SML) represents the relation between a) b) c) d) e) (a) risk b) Unanticipated changes in investors’ desired time to receive payouts. c) Unanticipated changes in short term and long term inflation rates. d) Unanticipated changes in the willingness of investors to take on investment risk. e) None of the above. (b) 11 In a multifactor model, time horizon risk represents a) b) c) d) Unanticipated changes in the level of overall business activity. Unanticipated changes in investors’ desired time to receive payouts. Unanticipated changes in short term and long term inflation rates. Unanticipated changes in the willingness of investors to take on investment risk. e) None of the above. (e) 12 In a micro-economic based risk factor model the following factor would be one of many appropriate factors a) b) c) d) e) Confidence risk. Maturity risk. Expected inflation risk. Call risk. Return difference between small capitalization and large capitalization stocks. MULTIPLE CHOICE PROBLEMS (b) 1 Consider an asset that has a beta of 1.5. The return on the risk-free asset is 6.5% and the expected return on the stock index is 15%. The estimated return on the asset is 20%. Calculate the alpha for the asset. a) b) c) d) e) (b) 2 19.25% 0.75% –0.75% 9.75% 9.0% The table below provides factor risk sensitivities and factor risk premia for a three factor model for a particular asset where factor 1 is MP the growth rate in U.S. industrial production, factor 2 is UI the difference between actual and expected inflation, and factor 3 is UPR the unanticipated change in bond credit spread. Risk Factor Factor Sensitivity(β) Risk Premium(λ) 371 MP UI UPR 1.76 -0.8 0.87 0.0259 -0.0432 0.0149 Calculate the expected excess return for the asset. a) b) c) d) e) (a) 3 The variance of returns for a risky asset is 25%. The variance of the error term, Var(e) is 8%. What portion of the total risk of the asset, as measured by variance, is unsystematic? a) b) c) d) e) (c) 4 5 5.2% 8.0% 3.2% 4.0% 1.2% An investor wishes to construct a portfolio by borrowing 35% of his original wealth and investing all the money in a stock index. The return on the risk-free asset is 4.0% and the expected return on the stock index is 15%. Calculate the expected return on the portfolio. a) b) c) d) e) 372 32% 8% 68% 25% 75% An investor wishes to construct a portfolio consisting of a 40% allocation to a stock index and a 60% allocation to a risk free asset. The return on the risk-free asset is 2% and the expected return on the stock index is 10%. The standard deviation of returns on the stock index 8%. Calculate the expected standard deviation of the portfolio. a) b) c) d) e) (b) 12.32% 9.32% 4.56% 6.32% 8.02% 18.25% 18.85% 9.50% 15.00% 11.15% (d) 6 An investor wishes to construct a portfolio consisting of a 70% allocation to a stock index and a 30% allocation to a risk free asset. The return on the risk-free asset is 4.5% and the expected return on the stock index is 12%. Calculate the expected return on the portfolio. a) b) c) d) e) (d) 7 A stock has a beta of the stock is 1.1. The risk free rate is 2.5% and the return on the market is 12%. The estimated return for the stock is 14%. According to the CAPM you should a) b) c) d) e) (b) 8 9 10 1.0 0.0 -1.0 0.5 -0.5 The expected return for a stock, calculated using the CAPM, is 10.5%. The market return is 9.5% and the beta of the stock is 1.50. Calculate the implied risk-free rate. a) b) c) d) e) (d) Sell because required return is 9.95%. Sell because required return is 16.5%. Buy because required return 11.5%. Buy because required return is 12.95%. Short because it is undervalued. Consider a risky asset that has a standard deviation of returns of 15. Calculate the correlation between the risky asset and a risk free asset. a) b) c) d) e) (a) 8.25% 16.50% 17.50% 9.75% 14.38% 7.50% 13.91% 17.50% 21.88% 14.38% The expected return for a stock, calculated using the CAPM, is 25%. The risk free rate is 7.5% and the beta of the stock is 0.80. Calculate the implied return on the market. a) 7.50% b) 13.91% c) 17.50% 373 d) 21.88% e) 14.38% (c) 11 The expected return for Zbrite stock calculated using the CAPM is 15.5%. The risk free rate is 3.5% and the beta of the stock is 1.2. Calculate the implied market risk premium. a) b) c) d) e) (d) 12 5.5% 6.5% 10.0% 15.5% 12.0% Calculate the expected return for Express Inc. which has a beta of .69 when the risk free rate is.09 and you expect the market return to be .14. a) b) c) d) e) 0.05% 13.91% 10.92% 12.45% 14.25% USE THE FOLLOWING INFORMATION FOR THE NEXT THREE PROBLEMS You expect the risk-free rate (RFR) to be 5 percent and the market return to be 9 percent. You also have the following information about three stocks. STOCK X Y Z (b) 13 BETA 1.50 0.50 2.00 CURRENT PRICE $ 22 $ 40 $ 45 EXPECTED PRICE $ 23 $ 43 $ 49 EXPECTED DIVIDEND $ 0.75 $ 1.50 $ 1.00 What are the expected (required) rates of return for the three stocks (in the order X, Y, Z)? a) b) c) d) e) (a) 374 14 16.50%, 5.50%, 22.00% 11.00%, 7.00%, 13.00% 7.95%, 11.25%, 11.11% 6.20%, 2.20%, 8.20% 15.00%, 3.50%, 7.30% What are the estimated rates of return for the three stocks (in the order X, Y, Z)? a) b) c) d) e) (e) 15 7.95%, 11.25%, 11.11% 6.20%, 2.20%, 8.20% 16.50%, 5.50%, 22.00% 11.00%, 7.00%, 13.00% 15.00%, 3.50%, 7.30% What is your investment strategy concerning the three stocks? a) b) c) d) e) Buy stock Y, it is undervalued. Buy stock X and Z, they are undervalued. Sell stocks X and Z, they are overvalued. Sell stock Y, it is overvalued. Choices a and c USE THE FOLLOWING INFORMATION FOR THE NEXT FOUR PROBLEMS Year 1 2 3 4 5 6 (a) 16 17 18 0.4255 0.5929 5.6825 9.4163 0.3333 Compute the correlation coefficient between GBC and the Market Index. a) b) c) d) e) (b) Return for Market 12 13 17 -15 -8 9 Compute the beta for GBC Company using the historic returns presented above. a) b) c) d) e) (e) Return for GBC 25 10 5 -13 11 -20 0.4255 0.5929 5.6825 9.4163 0.3333 Compute the intercept of the characteristic line 375 a) b) c) d) e) (d) 19 0.4255 1.013 1.4385 0.5875 0.5219 The equation of the characteristic line is a) b) c) d) e) RGBC + 1.013 = 0.4255(RMarket) RGBC = 1.013 - 0.4255(RMarket) RMarket = 1.013 + 0.4255(RGBC) RGBC = 1.013 + 0.4255(RMarket) RMarket = 1.013 - 0.4255(RMarket) CHAPTER 9 ANSWERS TO PROBLEMS 1 6.5 + 1.5(15 – 6.5) = 19.25% alpha = 20 –19.25 = 0.75% 2 The table below shows the relevant calculations Risk Factor Factor Sensitivity(β) MP 1.76 UI -0.8 UPR 0.87 Expected return Risk Premium(λ) 0.0259 -0.0432 0.0149 (β)x(λ) 0.0456 0.0346 0.013 0.1232 3 8%/25% = 0.32. = 32% unsystematic. 4 0.4(0.08) = 0.032 or 3.2% 5 -0.35(4) + 1.35(15) = 18.85% 6 E(R)= 0.3(4.5) + 0.7(12) = 9.75% 7 E(R)= 2.5 + 1.1(12 – 2.5) = 12.95%. Buy the stock is undervalued. 8 The correlation between a risky asset and a risk-free asset is always zero. 9 10.5 = X + 1.5(9.5 – X). X = 7.5%. 376 10 25 = 7.5 + 0.8(X). X = 14.38%. Return on market = 14.38 + 7.5 = 21.88% 11 15.5 = 3.5 + 1.2(X). X = 10%. 12 k = .09 + .69 (.14 - .09) = .1245 = 12.45% For problems 13 - 15 STOCK REQUIRED ESTIMATED EVALUATION X .05 + 1.50(.09 - .05) = 11% (23 - 22 + 0.75)/22 = 7.95% Overvalued Y .05 + 0.50(.09 -.05) = 7% (43 - 40 + 1.50)/40 = 11.25% Undervalued Z .05 + 2.00(.09 - .05) = 13% (49 - 45 + 1.00)/45 = 11.11% Overvalued For problems 16 – 19 The table below shows the relevant calculations. 16 (1) (2) (3) Year 1 2 3 4 5 6 Total Average Variance Std. Dev. Covariance Correlation Beta GBC 25 10 5 -13 11 -20 18 3.0000 Market 12 13 17 -15 -8 9 28 4.67 (4) GBC (R-E(R ))2 484.00 49.00 4.00 256.00 64.00 529.00 1386.00 (5) Market (R-E(R ))2 53.73 69.39 152.03 386.91 160.53 18.75 841.33 277.20 16.65 168.27 12.97 (6) GBC R-E(R ) 22.00 7.00 2.00 -16.00 8.00 -23.00 (7) Market R-E(R ) 7.33 8.33 12.33 -19.67 -12.67 4.33 (8) (6) x (7) 161.26 58.31 24.66 314.72 -101.36 -99.59 358.00 71.60 0.33 0.4255 Beta for GBC Computer is computed as follows: Beta = Cov(GBC, Market)/ VarianceMarket Beta = 18.40/82 = 0.2244 17 The correlation coefficient can be computed as follows: 377 Correlation = Cov(GBC, Market)/(SDGBC x SDMarket) = 71.6/(16.65 x 12.97) = 0.33 Where: SDGBC = [1386/5]1/2 = 16.65 SDMarket = [841.33/5]1/2 = 12.97 Cov(GBC, Market) = 358/5 = 71.60 18 The alpha or intercept of the characteristic line is computed as follows: alpha = 3.0 - [(0.4255)(4.67)] = 1.013% 19 378 RGBC = 1.013 + 0.4255(RMarket)