Chapter 05

3. Award: 10.00 points Problems? Adjust credit for all students. Suppose your expectations regarding the stock price are as follows: State of the Market Probability Ending Price HPR (including dividends) Boom 0.35 $ 140 44.5% Normal growth 0.30 110 14.0 Recession 0.35 80 −16.5 Use the equations and to compute the mean and standard deviation of the HPR on stocks. Note: Do not round intermediate calculations. Round your answers to 2 decimal places. Mean 14.00 % Standard deviation 25.52 % Explanation: E(r) = [0.35 × 44.5%] + [0.30 × 14.0%] + [0.35 × (−16.5%)] = 0.1400 or 14% σ 2 = [0.35 × (44.5 − 14) 2 ] + [0.30 × (14 − 14) 2 ] + [0.35 × (−16.5 − 14) 2 ] = 651.175 = 0.2552 or 25.52% The mean is unchanged, but the standard deviation has increased, as the probabilities of the high and low returns have increased. Worksheet Difficulty: 2 Intermediate Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 05: Risk, Return, and the Historical Record > Chapter 05 Problems - Algorithmic & Static References

6. Award: 10.00 points Problems? Adjust credit for all students. The continuously compounded annual return on a stock is normally distributed with a mean of 20% and standard deviation of 30%. With 95.44% confidence, we should expect its actual return in any particular year to be between which pair of values? Hint : Refer to Figure 5.4 . Which pair of values? −40.0% and 80.0% Explanation: With probability 95.44%, the value of a normally distributed variable will fall within 2 standard deviations of the mean; that is, between −40% and 80%. Simply add and subtract 2 standard deviations to and from the mean. Worksheet Difficulty: 2 Intermediate Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 05: Risk, Return, and the Historical Record > Chapter 05 Problems - Algorithmic & Static References

9. Award: 10.00 points Problems? Adjust credit for all students. Suppose that the inflation rate is expected to be 3% in the near future using the historical data provided in Table 5.3 and Table 5.5 , what would be your predictions for the following? Note: Round your answers to 2 decimal places. a. The T-bill rate? 3.38 % b. The expected rate of return on the Big/Value portfolio? 15.40 % c. The risk premium on the stock market? Remains unchanged Explanation: From Table 5.3, the average real rate on T-bills has been 0.38%. a. T-bills: 0.38% real rate + 3% inflation = 3.38% b. Expected return on Big/Value: 3.38% T-bill rate + 12.02% historical risk premium (from Table 5.5) = 15.40% c. The risk premium on stocks remains unchanged. A premium, the difference between two rates, is a real value, unaffected by inflation. Worksheet Difficulty: 2 Intermediate Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 05: Risk, Return, and the Historical Record > Chapter 05 Problems - Algorithmic & Static References

11. Award: 10.00 points Problems? Adjust credit for all students. You are faced with the probability distribution of the HPR on the stock market index fund given in spreadsheet 5.1 of the text. Suppose the price of a put option on a share of the index fund with exercise price of $110 and time to expiration of 1 year is $12. Required: a. What is the probability distribution of the HPR on the put option? b. What is the probability distribution of the HPR on a portfolio consisting of one share of the index fund and a put option? c. In what sense does buying the put option constitute a purchase of insurance in this case?  Required A Required C  Complete this question by entering your answers in the tabs below. What is the probability distribution of the HPR on a portfolio consisting of one share of the index fund and a put option? Note: Round your answers to 2 decimal places. Required A Required B Required C $ STOCK + PUT State of the Economy Probability Ending Price + Put + Dividend HPR Stock + Put Excellent 0.25 131.00 17.00 % Good 0.45 114.00 1.80 % Poor 0.25 113.50 1.30 % Crash 0.05 112.00 0.00 % Explanation: a. Probability distribution of the HPR on the stock market and put: Remember that the cost of the index fund is $100 per share, cash dividends are from Spreadsheet 5.1 (and vary each year), and the cost of the put option is $12. b. The cost of one share of the index fund plus a put option is $112. The probability distribution of the HPR on the portfolio is: HPR: Excellent = ($131 − $112) ÷ $112 = 17.0% Good = ($114 − $112) ÷ $112 = 1.8% Poor = ($113.50 − $112) ÷ $112 = 1.3% Crash = ($112 − $112) ÷ $112 = 0.0% c. Buying the put option guarantees the investor a minimum HPR of 0.0% regardless of what happens to the stock's price. Thus, it offers insurance against a price decline. Worksheet Difficulty: 3 Challenge Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 05: Risk, Return, and the Historical Record > Chapter 05 Problems - Algorithmic & Static References

13. Award: 10.00 points Problems? Adjust credit for all students. Consider these long-term investment data: The price of a 10-year $100 par value zero-coupon inflation-indexed bond is $84.49. A real-estate property is expected to yield 2% per quarter (nominal) with a SD of the (effective) quarterly rate of 10%. Compute the annual rate on the real (i.e., inflation-indexed) bond. Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Real bond annual rate 1.70 % Explanation: Total return of the bond is ($100 ÷ $84.49) = 1.1836. With t = 10, the annual rate on the real bond is EAR = 1.1836 1/10 − 1 = 1.70%. Total return of the bond is ($100 ÷ $84.49) = 1.1836. With t = 10, the annual rate on the real bond is EAR = 1.1836 1/10 − 1 = 1.70%. Worksheet Difficulty: 3 Challenge Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 05: Risk, Return, and the Historical Record > Chapter 05 Problems - Algorithmic & Static References

16. Award: 10.00 points Problems? Adjust credit for all students. You invested in a 3-month certificate of deposit at your bank. Your investment was $1,768, and at the end of the term you will receive $1,962. Required: a. What is the holding period return (HPR) on your investment? Note: Round your final percentage answer to 2 decimal places. HPR 10.97 % b. What is the annual percentage rate (APR)? Note: Round your final percentage answer to 2 decimal places. APR 43.89 % c. What is the effective annual rate (EAR)? Note: Round your final percentage answer to 2 decimal places. EAR 51.66 % Explanation: a. The HPR equals (1,962 – 1,768) ÷ 1,768 = 10.97%. b. The APR is the 3-month rate times the number of three-month periods in one year. APR = 10.97% × (12/3) = 43.89% c. The EAR is calculated as EAR = 51.66% Worksheet Difficulty: 1 Basic Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 05: Risk, Return, and the Historical Record > Chapter 05 Additional Algorithmic Problems References

19. Award: 10.00 points Problems? Adjust credit for all students. The common stock of Perforated Pool Liners, Incorporated now sells for $38.00 per share. The table below shows the anticipated stock price and the dividend to be paid one year from now. Both the price and the dividend will depend on the level of growth experienced by the firm. State Probability, p(s) End-of-Year Price Annual Dividend Super high growth 0.105 $50 $3 High growth 0.192 $50 $3 Normal growth 0.396 $56 $2 Low growth 0.172 $46 $2 No growth 0.135 $46 $0 Required: a. Calculate the holding period return (HPR) for each of the possible states, assuming a one-year holding period. Note: Negative amounts should be indicated by a minus sign. Round your answer to 2 decimal places. Super high growth 39.47 % High growth 39.47 % Normal growth 52.63 % Low growth 26.32 % No growth 21.05 % b. What is the expected return for a holder of Perforated Pool Liners stock? Note: Round your answer to 2 decimal places. Expected HPR 39.93 % c. What is the standard deviation of the returns? Note: Round your answer to 2 decimal places. Standard deviation 12.00 % Explanation: a. The holding period return (HPR) for each state is calculated as State End-of-Year Price Annual Dividend HPR Super high growth $50 $3 (50+3−38)/38 = 39.47% High growth $50 $3 (50+3−38)/38 = 39.47% Normal growth $56 $2 (56+2−38)/38 = 52.63% Low growth $46 $2 (46+2−38)/38 = 26.32% No growth $46 $0 (46+0−38)/38 = 21.05% b. The expected return is = (0.105 × 39.47%) + (0.172 × 39%) + (0.396 × 53%) + (0.172 × 26.320%) + (0.105 × ( 21.05%)) = 39.93% c. The standard deviation is the square root of the variance. The variance is given by the formula since there are 5 possible outcomes. The calculations are shown in the table below. Each column in the table has a column number at the top (indicated in parentheses), which is used to indicate how the column is used in calculations. (1) (2) (3) (4) (5) (6) State Probability p( s ) HPR (from part a) HPR − E( r ) (4) squared (2) × (5) Super high growth 0.105 39.47% −0.46% 0.000021 0.000002 High growth 0.192 39.47% −0.46% 0.000021 0.000004 Normal growth 0.396 52.63% 12.70% 0.016122 0.006384 Low growth 0.172 26.32% −13.62% 0.018546 0.003190 No growth 0.135 21.05% −18.88% 0.035651 0.004813 Variance 0.014394 Standard deviation 12.00% Worksheet Difficulty: 2 Intermediate Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 05: Risk, Return, and the Historical Record > Chapter 05 Additional Algorithmic Problems References

20. Award: 10.00 points Problems? Adjust credit for all students. You earned a nominal rate of return equal to 11.10% on your investments last year. The annual inflation rate was 2.90%. Required: a. What was your approximate real rate of return? Note: Round your answer to 2 decimal places. Approximate real rate of return 8.20 % b. What was your exact real rate of return? Note: Round your answer to 2 decimal places. Real rate of return 7.97 % Explanation: a. The approximate rate of return equals the nominal rate minus the inflation rate: r R − i = 11.10% − 2.90% = 8.20%. b. The exact real rate of return is calculated from the equation r = 7.97%. Worksheet Difficulty: 1 Basic Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 05: Risk, Return, and the Historical Record > Chapter 05 Additional Algorithmic Problems ≅ References

21. Award: 10.00 points Problems? Adjust credit for all students. If the real interest rate is 3.70% per year and the expected inflation rate is 1.40%, what is the nominal interest rate according to the Fisher equation? Note: Round your answer to 2 decimal places. Nominal interest rate 5.10 % Explanation: The Fisher equation shows the relationship R = r + E ( i ). In this case, R = 3.70% + 1.40% = 5.10%. Worksheet Difficulty: 1 Basic Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 05: Risk, Return, and the Historical Record > Chapter 05 Additional Algorithmic Problems References

22. Award: 10.00 points Problems? Adjust credit for all students. Your firm recently lent Arlington Enterprises $23,140,000 for one year at an interest rate of 12.50%. Inflation during the year is expected to be 2.90%. Answer the following questions to gauge the impact of inflation on the real interest to be paid. Note: Round all answers to 2 decimal places. Required: a. How much interest income will your firm receive from the transaction, calculated the traditional way? $ Interest income 2,892,500.00 b. What is the approximate real rate of interest? Approximate real rate of interest 9.60 % c. What is the real portion of the interest income? $ Real portion of interest income 2,221,440.00 d. By how much will interest income be understated due to inflation? $ Understated interest 671,060.00 Explanation: a. Interest income = 12.50% × $23,140,000 = $2,892,500.00 b. The approximate real rate of interest = 12.50% − 2.90% = 9.60% c. The real portion of the interest income = 9.60% × $23,140,000 = $2,221,440.00 d. Interest income will be understated by 2.90% × $23,140,000 = $671,060.00 due to inflation. Worksheet Difficulty: 1 Basic Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 05: Risk, Return, and the Historical Record > Chapter 05 Additional Algorithmic Problems References

1. Award: 10.00 points 2. Award: 10.00 points 3. Award: 10.00 points 4. Award: 10.00 points Over the past year, you earned a nominal rate of interest of 12% on your money. The inflation rate was 3% over the same period. The exact actual growth rate of your purchasing power was: 9.0%. 10.0%. 5.0%. 8.7%. 15.0%. r = (1 + R )÷(1 + i) − 1 = 1.12÷1.03 − 1 = 0.087, or 8.7%. References Multiple Choice Difficulty: 2 Intermediate Over the past year, you earned a nominal rate of interest of 9% on your money. The inflation rate was 3% over the same period. The exact actual growth rate of your purchasing power was: 6.0%. 10.0%. 5.8%. 4.8%. 15.0%. r = (1 + R )/(1 + i ) − 1 = 1.09/1.03 − 1 = 0.058, or 5.8%. References Multiple Choice Difficulty: 2 Intermediate A year ago, you invested $1,000 in a savings account that pays an annual interest rate of 9%. What is your approximate annual real rate of return if the rate of inflation was 2% over the year? 5% 10% 7% 3% None of the options are correct. 9% − 2% = 7%. References Multiple Choice Difficulty: 1 Basic A year ago, you invested $10,000 in a savings account that pays an annual interest rate of 5%. What is your approximate annual real rate of return if the rate of inflation was 1.5% over the year? 3.5% 10% 7% 4% None of the options are correct. 5% − 1.5% = 3.5%. References Multiple Choice Difficulty: 1 Basic                        

5. Award: 10.00 points 6. Award: 10.00 points 7. Award: 10.00 points 8. Award: 10.00 points If the annual real rate of interest is 6%, and the expected inflation rate is 2%, the nominal rate of interest would be approximately: 1%. 8%. 20%. 15%. None of the options are correct. 6% + 2% = 8%. References Multiple Choice Difficulty: 1 Basic If the annual real rate of interest is 3.0%, and the expected inflation rate is 4.0%, the nominal rate of interest would be approximately: 3.7%. 7.0%. 2.5%. − 1.2%. None of the options are correct. 3% + 4% = 7%. References Multiple Choice Difficulty: 1 Basic You purchased a share of stock for $25. One year later, you received $1 as a dividend and sold the share for $29. What was your holding-period return? 45% 20% 5% 40% None of the options are correct. HPR = (P sell − P buy + Div) ÷ P buy = ($29 − $25 + $1) ÷ $25 = 0.20 or 20% References Multiple Choice Difficulty: 2 Intermediate You purchased a share of stock for $68. One year later, you received $5.00 as a dividend and sold the share for $74.50. What was your holding-period return? 12.50% 16.91% 13.65% 11.80% None of the options are correct. HPR = (P sell − P buy +Div) ÷ P buy = ($74.50 − $68.00 + $5.00) ÷ $68 = 0.1691 or 16.91% References Multiple Choice Difficulty: 2 Intermediate                        

9. Award: 10.00 points 10. Award: 10.00 points 11. Award: 10.00 points 12. Award: 10.00 points Which of the following determine(s) the level of real interest rates? I. The supply of savings by households and business firms II. The demand for investment funds III. The government's net supply and/or demand for funds I only II only I and II only I, II, and III None of the options are correct. The value of savings by households is the major supply of funds; the demand for investment funds is a portion of the total demand for funds; the government's position can be one of either net supplier or net demander of funds. The above factors constitute the total supply and demand for funds, which determine real interest rates. References Multiple Choice Difficulty: 2 Intermediate Which of the following statement(s) is(are) true ? I. The real rate of interest is determined by the supply and demand for funds. II. The real rate of interest is determined by the expected rate of inflation. III. The real rate of interest can be affected by actions of the Fed. IV. The real rate of interest is equal to the nominal interest rate plus the expected rate of inflation. I and II only I and III only III and IV only II and III only I, II, III, and IV only The expected rate of inflation is a determinant of nominal, not real, interest rates. Real rates are determined by the supply and demand for funds, which can be affected by the Fed. References Multiple Choice Difficulty: 2 Intermediate Which of the following statement(s) is(are) true ? Nominal interests account for inflation. The nominal rate of interest is almost never greater than the real rate of interest. Certificates of deposit offer a guaranteed real rate of interest. None of the options are true. All of the options are true. References Multiple Choice Difficulty: 2 Intermediate Other things equal, an increase in the government budget deficit: drives the interest rate down. drives the interest rate up. might not have any effect on interest rates. increases business prospects. None of the options are correct. An increase in the government budget deficit, other things equal, causes the government to increase its borrowing, which increases the demand for funds and drives interest rates up. References Multiple Choice Difficulty: 2 Intermediate                        

13. Award: 10.00 points 14. Award: 10.00 points 15. Award: 10.00 points 16. Award: 10.00 points Ceteris paribus, a decrease in the demand for loans: drives the interest rate down. drives the interest rate up. might not have any effect on interest rates. results from an increase in business prospects and a decrease in the level of savings. increases the quantity demanded for loans. A decrease in demand, ceteris paribus, always drives interest rates down. An increase in business prospects would increase the demand for funds. The savings level affects the supply of, not the demand for, funds. References Multiple Choice Difficulty: 2 Intermediate The holding-period return (HPR) on a share of stock is equal to: the capital gain yield during the period plus the inflation rate. the capital gain yield during the period plus the dividend yield. the current yield plus the dividend yield. the dividend yield plus the risk premium. the change in stock price. The HPR of any investment is the sum of the capital gain and the cash flow over the period, which for common stock is the capital gain yield during the period plus the dividend yield. References Multiple Choice Difficulty: 2 Intermediate Historical records regarding return on stocks, Treasury bonds, and Treasury bills between 1926 and 2021 show that: stocks offered investors greater rates of return than bonds and bills. stock returns were less volatile than those of bonds and bills. bonds offered investors greater rates of return than stocks and bills. bills outperformed stocks and bonds. Treasury bills always offered a rate of return greater than inflation. The historical data show that, as expected, stocks offer a greater return and greater volatility than the other investment alternatives. Inflation sometimes exceeded the T-bill return. References Multiple Choice Difficulty: 1 Basic If the interest rate paid by borrowers and the interest rate received by savers accurately reflect the realized rate of inflation, borrowers gain and savers lose. savers gain and borrowers lose. both borrowers and savers lose. neither borrowers nor savers gain nor lose. both borrowers and savers gain. If the described interest rate accurately reflects the rate of inflation, both borrowers and lenders are paying and receiving, respectively, the real rate of interest; thus, neither group gains. References Multiple Choice Difficulty: 2 Intermediate                        

17. Award: 10.00 points 18. Award: 10.00 points 19. Award: 10.00 points You have been given this probability distribution for the holding-period return for KMP stock: Stock of the Economy Probability HPR Boom 0.30 18% Normal growth 0.50 12% Recession 0.20 –5% What is the expected holding-period return for KMP stock? 10.40% 9.32% 11.63% 11.54% 10.88% HPR = 0.30 × (18%) + 0.50 × (12%) + 0.20 × ( − 5%) = 10.4%. References Multiple Choice Difficulty: 2 Intermediate You have been given this probability distribution for the holding-period return for KMP stock: Stock of the Economy Probability HPR Boom 0.30 18% Normal growth 0.50 12% Recession 0.20 –5% What is the expected standard deviation for KMP stock? 6.91% 8.13% 7.79% 7.25% 8.85% σ = [0.30 × (18% − 10.4%) 2 + 0.50 × (12% − 10.4%) 2 + 0.20 × (−5% − 10.4%) 2 ] 0.5 = 8.13%. References Multiple Choice Difficulty: 3 Challenge You have been given this probability distribution for the holding-period return for KMP stock: Stock of the Economy Probability HPR Boom 0.30 18% Normal growth 0.50 12% Recession 0.20 –5% What is the expected variance for KMP stock? 0.6604% 0.6996% 0.7704% 0.6372% 0.7845% 2 = 0.30 × (18% − 0.104) 2 + 0.5 × (12% − 0.104) 2 + 0.20 × (−5% − 0.104) 2 = 0.6604%. References Multiple Choice Difficulty: 3 Challenge                  

20. Award: 10.00 points 21. Award: 10.00 points 22. Award: 10.00 points 23. Award: 10.00 points If the nominal return is constant, the after-tax real rate of return: declines exponentially as the inflation rate increases. increases as the inflation rate increases. declines as the inflation rate declines. increases exponentially as the inflation rate decreases. declines as the inflation rate increases and increases as the inflation rate decreases. Inflation rates have an inverse effect on after-tax real rates of return. References Multiple Choice Difficulty: 2 Intermediate The risk premium for common stocks: must always be zero, for investors would be unwilling to invest in common stocks. must always be positive, in theory. is negative, as common stocks are risky. cannot be zero, for investors would be unwilling to invest in common stocks and must always be positive, in theory. cannot be zero, for investors would be unwilling to invest in common stocks and is negative, as common stocks are risky. If the risk premium for common stocks were zero or negative, investors would be unwilling to accept the lower returns for the increased risk. References Multiple Choice Difficulty: 2 Intermediate If a portfolio had a return of 18%, the risk-free asset return was 5%, and the standard deviation of the portfolio's excess returns was 34%, the risk premium would be: 13%. 18%. 49%. 12%. 29%. 18% − 5% = 13%. References Multiple Choice Difficulty: 2 Intermediate You purchase a share of Duke Energy Stock stock for $90. One year later, after receiving a dividend of $3, you sell the stock for $92. What was your holding-period return? 4.44% 2.22% 3.33% 5.56% None of the options are correct. HPR = (P sell − P buy + Div) ÷ P buy = ($92 − $90 + $3) ÷ $90 = 0.0556 = 5.56% References Multiple Choice Difficulty: 2 Intermediate                        

24. Award: 10.00 points 25. Award: 10.00 points 26. Award: 10.00 points 27. Award: 10.00 points Coca Cola stock has the following probability distribution of expected prices one year from now: State Probability Price 1 25% $ 50 2 40% $ 60 3 35% $ 70 If you buy Coca Cola today for $55 and it will pay a dividend during the year of $4 per share, what is your expected holding period return on Coca Cola? 17.72% 18.89% 17.91% 18.18% HPR = ∑ pr 3 obability × P sell - P buy + Div P buy = (0.25 × ($50 − $55 + $4) ÷ $55 ) + (0.40 × ($60 − $55 + $4) ÷ $55) + (0.35 × ($70 − $55 + $4) ÷ $55 = 0.1818, or 18.18% References Multiple Choice Difficulty: 3 Challenge Which of the following factors would not be expected to affect the nominal interest rate? The supply of loans The demand for loans The coupon rate on previously issued government bonds The expected rate of inflation Government spending and borrowing The nominal interest rate is affected by supply, demand, government actions, and inflation. Coupon rates on previously issued government bonds reflect historical interest rates but should not affect the current level of interest rates. References Multiple Choice Difficulty: 1 Basic If a portfolio had a return of 11%, the risk-free asset return was 6%, and the standard deviation of the portfolio's excess returns was 25%, the risk premium would be: 14%. 6%. 35%. 21%. 5%. 11% − 6% = 5%. References Multiple Choice Difficulty: 2 Intermediate In words, the real rate of interest is approximately equal to: the nominal rate minus the inflation rate. the inflation rate minus the nominal rate. the nominal rate times the inflation rate. the inflation rate divided by the nominal rate. the nominal rate plus the inflation rate. The actual relationship is (1 + real rate) = (1 + nominal rate) ÷ (1 + inflation rate). This can be approximated by the equation: Real rate = nominal rate − inflation rate. References Multiple Choice Difficulty: 1 Basic                       

28. Award: 10.00 points 29. Award: 10.00 points 30. Award: 10.00 points 31. Award: 10.00 points If the Federal Reserve lowers the Fed Funds rate, ceteris paribus, the equilibrium levels of funds lent will _________, and the equilibrium level of real interest rates will _________. increase; increase increase; decrease decrease; increase decrease; decrease reverse direction from their previous trends; reverse direction from their previous trends A lower Fed Funds rate would encourage banks to make more loans, which would increase the money supply. The supply curve would shift to the right and the equilibrium level of funds would increase while the equilibrium interest rate would fall. References Multiple Choice Difficulty: 2 Intermediate "Bracket Creep" happens when: tax liabilities are based on real income and there is a negative inflation rate. tax liabilities are based on real income and there is a positive inflation rate. tax liabilities are based on nominal income and there is a negative inflation rate. tax liabilities are based on nominal income and there is a positive inflation rate. too many peculiar people make their way into the highest tax bracket. A positive inflation rate typically leads to higher nominal income. Higher nominal income means people will have higher tax liabilities and in some cases will put them in higher tax brackets. This can happen even when real income has declined. References Multiple Choice Difficulty: 2 Intermediate The holding-period return (HPR) for a stock is equal to: the real yield minus the inflation rate. the nominal yield minus the real yield. the capital gains yield minus the tax rate. the capital gains yield minus the dividend yield. the dividend yield plus the capital gains yield. HPR consists of an income component and a price change component. The income component on a stock is the dividend yield. The price change component is the capital gains yield. References Multiple Choice Difficulty: 1 Basic You have been given this probability distribution for the holding-period return for Cheese, Incorporated stock: Stock of the Economy Probability HPR Boom 0.20 24% Normal growth 0.45 15% Recession 0.35 8% Assuming that the expected return on Cheese's stock is 14.35%, what is the standard deviation of these returns? 4.72% 6.30% 4.38% 5.74% None of the options are correct. = [0.20 × (24% − 14.35%) 2 + 0.45 × (15% − 14.35%) 2 + 0.35 × (8% − 14.35%) 2 ] 0.5 = 5.74%. References Multiple Choice Difficulty: 2 Intermediate                        

32. Award: 10.00 points 33. Award: 10.00 points 34. Award: 10.00 points 35. Award: 10.00 points An investor purchased a bond 45 days ago for $985. He received $15 in interest and sold the bond for $980. What is the holding-period return on his investment? 1.02% 0.50% 1.92% 0.01% HPR = (P sell − P buy + Coupon) ÷ P buy = ($980 − $985 + $15) ÷ $985 = 0.0102 = 1.02% References Multiple Choice Difficulty: 1 Basic An investor purchased a bond 63 days ago for $980. He received $17 in interest and sold the bond for $987. What is the holding-period return on his investment? 1.52% 2.45% 1.92% 2.68% HPR = (P sell − P buy + Coupon) ÷ P buy = ($987 − $980 + $17) ÷ $980 = 0.0245 = 2.45% References Multiple Choice Difficulty: 1 Basic Over the past year, you earned a nominal rate of interest of 8% on your money. The inflation rate was 3.5% over the same period. The exact actual growth rate of your purchasing power was: 15.55%. 4.35%. 5.02%. 4.81%. 15.04%. r = ((1 + R ) ÷ (1 + i )) − 1 = (1.08 ÷ 1.035) − 1 = 0.0435 = 4.35%. References Multiple Choice Difficulty: 2 Intermediate Over the past year, you earned a nominal rate of interest of 14% on your money. The inflation rate was 2% over the same period. The exact actual growth rate of your purchasing power was: 11.76%. 16.00%. 15.02%. 14.32%. r = (1 + R ) ÷ (1 + i ) − 1 = 1.14 ÷ 1.02 − 1 = 0.1176 = 11.76%. References Multiple Choice Difficulty: 2 Intermediate                     

36. Award: 10.00 points 37. Award: 10.00 points 38. Award: 10.00 points 39. Award: 10.00 points Over the past year, you earned a nominal rate of interest of 12.5% on your money. The inflation rate was 2.6% over the same period. The exact actual growth rate of your purchasing power was: 9.15%. 9.90%. 9.65%. 10.52%. r = (1 + R ) ÷ (1 + i ) − 1 = 1.125 ÷ 1.026 − 1 = 0.965 = 9.65% References Multiple Choice Difficulty: 2 Intermediate A year ago, you invested $1,000 in a savings account that pays an annual interest rate of 6%. What is your approximate annual real rate of return if the rate of inflation was 2% over the year? 4% 2% 6% 3% 6% − 2% = 4%. References Multiple Choice Difficulty: 1 Basic A year ago, you invested $10,000 in a savings account that pays an annual interest rate of 3%. What is your approximate annual real rate of return if the rate of inflation was 4% over the year? 1% − 1% 7% 3% 3% − 4% = − 1%. References Multiple Choice Difficulty: 1 Basic A year ago, you invested $2,500 in a savings account that pays an annual interest rate of 5.7%. What is your approximate annual real rate of return if the rate of inflation was 1.6% over the year? 4.1% 2.5% 2.9% 1.6% 5.7% − 1.6% = 4.1%. References Multiple Choice Difficulty: 1 Basic                    

40. Award: 10.00 points 41. Award: 10.00 points 42. Award: 10.00 points 43. Award: 10.00 points A year ago, you invested $2,500 in a savings account that pays an annual interest rate of 3.5%. What is your approximate annual real rate of return if the rate of inflation was 5.5% over the year? 0.9% − 2.0% 5.9% 2.0% 3.5% − 5.5% = − 2.0% References Multiple Choice Difficulty: 1 Basic A year ago, you invested $12,000 in an investment that produced a return of 16%. What is your approximate annual real rate of return if the rate of inflation was 4% over the year? 18% 2% 12% 15% 16% − 4% = 12%. References Multiple Choice Difficulty: 1 Basic If the annual real rate of interest is 2.5%, and the expected inflation rate is 1.0%, the nominal rate of interest would be approximately: 3.5%. 2.5%. 1%. 6.8%. None of the options are correct. 2.5% + 1.0% = 3.5%. References Multiple Choice Difficulty: 1 Basic If the annual real rate of interest is 2.5%, and the expected inflation rate is 3.4%, the nominal rate of interest would be approximately: 5.9%. 0.9%. –0.9%. 7%. None of the options are correct. 2.5% + 3.4% = 5.9%. References Multiple Choice Difficulty: 1 Basic                      

44. Award: 10.00 points 45. Award: 10.00 points 46. Award: 10.00 points 47. Award: 10.00 points If the annual real rate of interest is 4%, and the expected inflation rate is 2%, the nominal rate of interest would be approximately: 6%. 3%. 1%. 5%. None of the options are correct. 4% + 2% = 6%. References Multiple Choice Difficulty: 1 Basic You purchased a share of stock for $12. One year later, you received $0.50 as a dividend and sold the share for $13.25. What was your holding-period return? 9.75% 10.65% 11.75% 14.58% None of the options are correct. HPR = (P sell − P buy + Div) ÷ P buy = ($13.25 − $12.00 + $0.50) / $12.00 = 0.1458 = 14.58% References Multiple Choice Difficulty: 2 Intermediate You purchased a share of stock for $120. One year later, you received $1.82 as a dividend and sold the share for $136. What was your holding-period return? 15.67% 22.12% 18.85% 13.24% None of the options are correct. HPR = (P sell − P buy + Div) ÷ P buy = ($136 − $120 + $1.82) ÷ $120 = 0.1485 References Multiple Choice Difficulty: 2 Intermediate You purchased a share of stock for $65. One year later, you received $2.37 as a dividend and sold the share for $63. What was your holding-period return? 0.57% − 0.26% − 0.89% 5.70% None of the options are correct. HPR = (P sell − P buy + Div) ÷ P buy = ($63 − $65 + $2.37) ÷ $65 = 0.0057 = 0.57% References Multiple Choice Difficulty: 2 Intermediate                        

48. Award: 10.00 points 49. Award: 10.00 points 50. Award: 10.00 points You have been given this probability distribution for the holding-period return for a stock: Stock of the Economy Probability HPR Boom 0.40 22% Normal growth 0.35 11% Recession 0.25 –9% What is the expected holding-period return for the stock? 11.67% 8.33% 9.56% 12.4% None of the options are correct. HPR = ∑ 3 probablity × HPR state = 0.40 × 0.22 + 0.35 × 0.11 + 0.25 × ( − 0.09) = 0.104 References Multiple Choice Difficulty: 2 Intermediate You have been given this probability distribution for the holding-period return for a stock: Stock of the Economy Probability HPR Boom 0.40 22% Normal growth 0.35 11% Recession 0.25 − 9% What is the expected standard deviation for the stock? 2.07% 9.96% 7.04% 1.44% None of the options are correct. = [0.40 × (22% − 10.4%) 2 + 0.35 × (11% − 10.4%) 2 + 0.25 × (-9% − 10.4%) 2 ] 0.5 = 12.17% References Multiple Choice Difficulty: 3 Challenge You have been given this probability distribution for the holding-period return for a stock: Stock of the Economy Probability HPR Boom 0.40 22% Normal growth 0.35 11% Recession 0.25 − 9% What is the expected variance for the stock? 1.42% 1.90% 1.77% 1.48% None of the options are correct. 2 = 0.40 (22% − 0.104) 2 + 0.35 (11% − 0.104) 2 + 0.25 (−9% − 0.104) 2 = 1.48% References Multiple Choice Difficulty: 3 Challenge                  

51. Award: 10.00 points 52. Award: 10.00 points 53. Award: 10.00 points 54. Award: 10.00 points Which of the following measures of risk best highlights the potential loss from extreme negative returns? Standard deviation Variance Upper partial standard deviation Value at risk (VaR) None of the options are correct. Only VaR measures potential loss from extreme negative returns. References Multiple Choice Difficulty: 2 Intermediate Over the past year, you earned a nominal rate of interest of 3.6% on your money. The inflation rate was 3.1% over the same period. The exact actual growth rate of your purchasing power was: 3.6%. 3.1%. 0.48%. 6.7%. r = (1 + R ) ÷ (1 + I ) − 1; 1.036 ÷ 1.031 − 1 = 0.48%. References Multiple Choice Difficulty: 2 Intermediate A year ago, you invested $1,000 in a savings account that pays an annual interest rate of 4.3%. What is your approximate annual real rate of return if the rate of inflation was 3% over the year? 4.3% − 1.3% 7.3% 3.0% None of the options are correct. 4.3% − 3.0% = 1.3%. References Multiple Choice Difficulty: 1 Basic If the annual real rate of interest is 3.5%, and the expected inflation rate is 3.5%, the nominal rate of interest would be approximately: 0.0%. 3.5%. 12.3%. 7.0%. 3.5% + 3.5% = 7.0%. References Multiple Choice Difficulty: 1 Basic                      

55. Award: 10.00 points 56. Award: 10.00 points 57. Award: 10.00 points You purchased a share of CSCO stock for $20. One year later, you received $2 as a dividend and sold the share for $31. What was your holding-period return? 45% 50% 60% 40% None of the options are correct. HPR = (P sell − P buy + Div) ÷ P buy = ($31 − $20 + $2) ÷ $20 = 0.65 = 65% References Multiple Choice Difficulty: 2 Intermediate You have been given this probability distribution for the holding-period return for GM stock: Stock of the Economy Probability HPR Boom 0.40 30% Normal growth 0.40 11% Recession 0.20 –10% What is the expected holding-period return for GM stock? 10.4% 11.4% 12.4% 13.4% 14.4% HPR = ∑ 3 Probability × HPR state = 0.40 × 0.30 + 0.40 × 0.11 + 0.20 × ( − 0.10) = 0.144 = 14.4% References Multiple Choice Difficulty: 2 Intermediate You have been given this probability distribution for the holding-period return for GM stock: Stock of the Economy Probability HPR Boom 0.40 30% Normal growth 0.40 11% Recession 0.20 –10% What is the expected standard deviation for GM stock? 16.91% 16.13% 13.79% 15.25% 14.87% σ = [0.40 (30% − 14.4%) 2 + 0.40 × (11% − 14.4%) 2 + 0.20 × (−10% − 14.4%) 2 ] 0.5 = 14.87%. References Multiple Choice Difficulty: 3 Challenge                  

58. Award: 10.00 points 59. Award: 10.00 points 60. Award: 10.00 points 61. Award: 10.00 points You have been given this probability distribution for the holding-period return for GM stock: Stock of the Economy Probability HPR Boom 0.40 30% Normal growth 0.40 11% Recession 0.20 − 10% What is the expected variance for GM stock? 200.00% 2.21% 246.37% 14.87% 16.13% 2 = 0.40 (30% − 14.4%) 2 + 0.40 × (11% − 14.4%) 2 + 0.20 (−10% − 14.4%) 2 = 2.21%. References Multiple Choice Difficulty: 3 Challenge You purchase a share of CAT stock for $90. One year later, after receiving a dividend of $4, you sell the stock for $97. What was your holding-period return? 14.44% 12.22% 13.33% 5.56% HPR = (P sell − P buy + Div) ÷ P buy = ($97 − $90 + $4) ÷ $90 = 0.1222 = 12.22% References Multiple Choice Difficulty: 2 Intermediate When comparing investments with different horizons, the _________ provides the more accurate comparison. arithmetic average effective annual rate average annual return historical annual average The effective annual rate provides the more accurate comparison of investments with different horizons because it expresses the returns in a common period. References Multiple Choice Difficulty: 1 Basic Annual percentage rates (APRs) are computed using: simple interest. compound interest. either simple interest or compound interest. best estimates of expected real costs. None of the options are correct. APRs use simple interest. References Multiple Choice Difficulty: 1 Basic                      

62. Award: 10.00 points 63. Award: 10.00 points 64. Award: 10.00 points 65. Award: 10.00 points If an investment provides a 2% return semi-annually, its effective annual rate is: 2.00%. 4.00%. 4.02%. 4.04%. None of the options are correct. EAR = 1.02 2 − 1 = 0.0404, or 4.04% References Multiple Choice Difficulty: 2 Intermediate If an investment provides a 1.25% return quarterly, its effective annual rate is: 5.23%. 5.09%. 4.02%. 4.04%. EAR = 1.0125 4 − 1 = 0.0509, or 5.09% References Multiple Choice Difficulty: 2 Intermediate If an investment provides a 0.78% return monthly, its effective annual rate is: 9.36%. 9.63%. 10.02%. 9.77%. EAR = 1.0078 12 − 1 = 0.0977, or 9.77% References Multiple Choice Difficulty: 2 Intermediate If an investment provides a 3% return semi-annually, its effective annual rate is: 3%. 6%. 6.06%. 6.09%. EAR = 1.03 2 − 1 = 0.0609, or 6.09% References Multiple Choice Difficulty: 2 Intermediate                     

66. Award: 10.00 points 67. Award: 10.00 points 68. Award: 10.00 points 69. Award: 10.00 points If an investment provides a 2.1% return quarterly, its effective annual rate is: 2.1%. 8.4%. 8.56%. 8.67%. EAR = 1.021 4 − 1 = 0.0867, or 8.67% References Multiple Choice Difficulty: 2 Intermediate Skewness is a measure of: how fat the tails of a distribution are. the downside risk of a distribution. the asymmetry of a distribution. the dividend yield of the distribution. None of the options are correct. One potentially important departure from normality relates to any asymmetry in the probability distribution of returns. The standard measure of this sort of asymmetry is called the skew of the distribution. References Multiple Choice Difficulty: 2 Intermediate Kurtosis is a measure of: how fat the tails of a distribution are. the downside risk of a distribution. the normality of a distribution. the dividend yield of the distribution. Kurtosis is a measure of how fat the tails of a distribution are. References Multiple Choice Difficulty: 2 Intermediate When a distribution is positively skewed, standard deviation overestimates risk. standard deviation correctly estimates risk. standard deviation underestimates risk. the tails are fatter than in a normal distribution. None of the options are correct. When a distribution is positively skewed, standard deviation overestimates risk. References Multiple Choice Difficulty: 2 Intermediate                      

70. Award: 10.00 points 71. Award: 10.00 points 72. Award: 10.00 points 73. Award: 10.00 points When a distribution is negatively skewed, standard deviation overestimates risk. standard deviation correctly estimates risk. standard deviation underestimates risk. the tails are fatter than in a normal distribution. None of the options are correct. When a distribution is negatively skewed, standard deviation underestimates risk. References Multiple Choice Difficulty: 2 Intermediate If a distribution has "fat tails," it exhibits: positive skewness. negative skewness. a kurtosis of zero. positive kurtosis. positive skewness and kurtosis. Kurtosis is a measure of the tails of a distribution, or "fat tails." References Multiple Choice Difficulty: 2 Intermediate If a portfolio had a return of 8%, the risk-free asset return was 3%, and the standard deviation of the portfolio's excess returns was 20%, the Sharpe measure would be: 0.08. 0.03. 0.20. 0.11. 0.25. SR = (0.08 − 0.03) ÷ 0.20 = 0.25 References Multiple Choice Difficulty: 2 Intermediate If a portfolio had a return of 12%, the risk-free asset return was 4%, and the standard deviation of the portfolio's excess returns was 25%, the Sharpe measure would be: 0.12. 0.04. 0.32. 0.16. 0.25. SR = (0.12 − 0.04) ÷ 0.25 = 0.32 References Multiple Choice Difficulty: 2 Intermediate                        

74. Award: 10.00 points 75. Award: 10.00 points 76. Award: 10.00 points 77. Award: 10.00 points If a portfolio had a return of 15%, the risk-free asset return was 5%, and the standard deviation of the portfolio's excess returns was 30%, the Sharpe measure would be: 0.20. 0.35. 0.45. 0.33. 0.25. SR = (0.15 − 0.05) ÷ 0.30 = 0.33 References Multiple Choice Difficulty: 2 Intermediate If a portfolio had a return of 12%, the risk-free asset return was 4%, and the standard deviation of the portfolio's excess returns was 25%, the risk premium would be: 8%. 16%. 32%. 21%. 29%. 12% − 4% = 8%. References Multiple Choice Difficulty: 2 Intermediate _________ is a risk measure that indicates vulnerability to extreme negative returns. Value at risk Upper partial standard deviation Standard deviation Variance None of the options are correct. Value at risk and lower partial standard deviation are risk measures that indicate vulnerability to extreme negative returns. References Multiple Choice Difficulty: 3 Challenge _________ is a risk measure that indicates vulnerability to extreme negative returns. Value at risk Lower partial standard deviation Expected shortfall All of the options are correct. All of the options are risk measures that indicate vulnerability to extreme negative returns. References Multiple Choice Difficulty: 3 Challenge                       

78. Award: 10.00 points 79. Award: 10.00 points 80. Award: 10.00 points 81. Award: 10.00 points The most common measure of loss associated with extremely negative returns is: upper partial standard deviation. value at risk. expected windfall. negative standard deviation. None of the options are correct. The most common measure of loss associated with extremely negative returns is value at risk. References Multiple Choice Difficulty: 3 Challenge Practitioners often use a _________% VaR, meaning that _________% of returns will exceed the VaR, and _________% will be worse. 25; 75; 25 75; 25; 75 1; 99; 1 95; 5; 95 80; 80; 20 Practitioners often use a 1% VaR, meaning that 99% of returns will exceed the VaR, and 1% will be worse. References Multiple Choice Difficulty: 3 Challenge When assessing tail risk by looking at the 1% worst-case scenario, the VaR is the: most realistic, as it is the most complete measure of risk. most pessimistic, as it is the most complete measure of risk. most optimistic, as it is the most complete measure of risk. most optimistic, as it takes the highest return (smallest loss) of all the cases. None of the options are correct. When assessing tail risk by looking at the 1% worst-case scenario, the VaR is the most optimistic as it takes the highest return (smallest loss) of all the cases. References Multiple Choice Difficulty: 3 Challenge When assessing tail risk by looking at the 1% worst-case scenario, the most realistic view of downside exposure would be: expected shortfall. value at risk. unconditional tail expectation. expected shortfall and value at risk. expected shortfall and unconditional tail expectation. When assessing tail risk by looking at the 1% worst-case scenario, the most realistic view of downside exposure would be expected shortfall (or conditional tail expectation). References Multiple Choice Difficulty: 3 Challenge                        

82. Award: 10.00 points 83. Award: 10.00 points 84. Award: 10.00 points 85. Award: 10.00 points A portfolio generates a Sharpe ratio of 0.83. Which of the following benchmark Sharpe ration would be considered show the portfolio over performed? 0.81 0.79 0.65 0.62 All of the options are correct. A higher Sharpe ratio indicates over performance. References Multiple Choice Difficulty: 2 Intermediate The best measure of a portfolio’s risk adjusted performance is the _________. return standard deviation Jensen alpha Sharpe measure All of the options are correct. The Sharpe ratio is the only measurement that factors in risk adjusted returns. References Multiple Choice Difficulty: 2 Intermediate Which combination of returns and standard deviation provides the highest Sharpe ratio? Assume a 3% risk free rate. return = 12%, standard deviation = 20% return = 15%, standard deviation = 22% return = 21%, standard deviation = 25% return = 25%, standard deviation = 35% None of the options are correct. SR = (0.21 − 0.03 ) ÷ 0.25 = 0.72 References Multiple Choice Difficulty: 2 Intermediate A(n) _________ can be used to show the possible outcomes from a normal distribution function. bell curve cumulative normal function event tree confidence level None of the options are correct. An event tree diagrams possible outcomes over time and represents the normal distribution. References Multiple Choice Difficulty: 3 Challenge                        

86. Award: 10.00 points In a two tailed normal distribution function, what is the confidence level created at 2 standard deviations? 68.26% 95.44% 99.74% 86.85% 72.50% This is a general rule of statistics. References Multiple Choice Difficulty: 3 Challenge      