# Solutions 10 = 10% \$40 1 +

### Solutions 10 = 10% \$40 1 +

Solutions to Chapter 10 Introduction to Risk, Return, and the Opportunity Cost of Capital capital gain + dividend (\$44 ? \$40) + \$2 = = 0. 15 = 15.

0% initial share price \$40 1. Rate of return = Dividend yield = dividend/initial share price = \$2/\$40 = 0. 05 = 5% Capital gains yield = capital gain/initial share price = \$4/\$40 = 0. 10 = 10% 2. Dividend yield = \$2/\$40 = 0. 05 = 5% The dividend yield is unaffected; it is based on the initial price, not the final price. Capital gain = \$36 – \$40 = ? \$4 Capital gains yield = –\$4/\$40 = –0.

We Will Write a Custom Essay Specifically
For You For Only \$13.90/page!

order now

10 = –10% capital gain + dividend (\$38 ? 40) + \$2 = = 0% initial share price \$40 1 + nominal rate of return 1+ 0 ? 1 = ? 1 = ? 0. 0385 = ? 3. 85% 1 + inflation rate 1 + 0. 04 3.

a. Rate of return = Real rate of return = Rate of return = b. (\$40 ? \$40) + \$2 = 0. 05 = 5% \$40 1 + nominal rate of return 1. 05 ? 1 = ? 1 = 0. 0096 = 0.

96% 1 + inflation rate 1. 04 Real rate of return = Rate of return = c. (\$42 ? \$40) + \$2 = 0. 10 = 10% \$40 1 + nominal rate of return 1.

10 ? 1 = ? 1 = 0. 0577 = 5. 77% 1 + inflation rate 1. 04 Real rate of return = 10-1 4. Real rate of return = 1 + nominal rate of return ? 1 1 + inflation rate 1.

95 ? = 0. 0833 = 8. 33% 1. 80 Costaguana: Real return = U. S.

: Real return = 1. 12 ? 1 = 0. 0980 = 9. 80% 1. 02 The U.

S. provides the higher real rate of return despite the lower nominal rate of return. Notice that the approximate relationship between real and nominal rates of return is valid only for low rates: real rate of return ? nominal rate of return – inflation rate This approximation incorrectly suggests that the Costaguanan real rate was higher than the U. S. real rate. 5.

We use the following relationship: Real rate of return = 1 + nominal rate of return ? 1 1 + inflation rateAsset class Treasury bills Treasury bonds Common stocks Nominal rate of return 4. 0% 5. 3% 11. 7% Inflation rate 3.

0% 3. 0% 3. 0% Real rate of return 0. 97% 2. 23% 8. 45% 6. The nominal interest rate cannot be negative.

If it were, investors would choose to hold cash (which pays a rate of return equal to zero) rather than buy a Treasury bill providing a negative return. On the other hand, the real expected rate of return is negative if the inflation rate exceeds the nominal return. 7. Average price of Quarter stocks in market 1 902. 50 2 866. 67 3 888. 33 4 876.

67 Index (using DJIA method) 100. 00 96. 03 98. 43 97. 4 Total market value of stocks 628,880 608,260 607,760 569,100 Index (using S&P method) 100. 00 96. 72 96.

64 90. 49 10-2 8. a.

b. c. For the period 1900-2004, Average rate of return = 11. 7% (See Table 10-1) For the period 1900-2004, Average risk premium = 7. 6% (See Table 10-1) For the period 1900-2004, Standard deviation of returns = 20. 0%.

(See Table 10-5) 9. a. Year 2000 2001 2002 2003 2004 b. c. Stock market return -10.

89 -10. 97 -20. 86 31.

64 12. 62 T-bill return 5. 89 3. 83 1.

65 1. 02 1. 20 Average Risk premium -16. 78 -14. 80 -22. 51 30. 62 11.

42 -2. 41 Deviation from mean -14. 37 -12. 39 -20. 10 33. 03 13.

3 Squared deviation 206. 4969 153. 5121 404. 0100 1,090.

9809 191. 2689 409. 2538 The average risk premium was: -2. 41% The variance (the average squared deviation from the mean) was 409.

2538 (without correcting for the lost degree of freedom). Therefore: standard deviation = 409. 2538 = 20. 23% 10.

In early 2004, the Dow was substantially more than three times its 1990 level. Therefore, in 2004, a 40-point movement was far less significant in percentage terms than it was in 1990. We would expect to see more 40-point days in 2004 even if market risk as measured by percentage returns is no higher than it was in 1990. 1.

Investors would not have invested in bonds during the period 1977-1981 if they had expected to earn negative average returns. Unanticipated events must have led to these results. For example, inflation and nominal interest rates during this period rose to levels not seen for decades. These increases, which resulted in large capital losses on long-term bonds, were almost certainly unanticipated by investors who bought those bonds in prior years. The results for this period demonstrate the perils of attempting to measure ‘normal’ maturity (or risk) premiums from historical data.

While experience over long periods may be a reasonable guide to normal premiums, the realized premium over short periods may contain little information about expectations of future premiums. 10-3 12. If investors become less willing to bear investment risk, they will require a higher risk premium to compensate them for holding risky assets. Security prices of risky investments will fall until the expected rates of return on those securities rise to the now-higher required rates of return. 13. Based on the historical risk premium of the S&P 500 (7. 6 percent) and the current level of the risk-free rate (about 3.

percent), one would predict an expected rate of return of 11. 1 percent. If the stock has the same systematic risk, it also should provide this expected return. Therefore, the stock price equals the present value of cash flows for a one-year horizon.

P0 = \$2 + \$50 = \$46. 80 1. 111 14. Boom: \$5 + (\$195 ? \$80) = 150. 00% \$80 \$2 + (\$100 ? \$80) = 27.

50% \$80 \$0 + (\$0 ? \$80) = ? 100. 00% \$80 Normal: Recession: r= 150 + 27. 50 + (? 100) = 25.

83% 3 1 1 1 ? (150 ? 25. 83) 2 + ? (27. 50 ? 25. 83) 2 + ? (? 100 ? 25. 83) 2 = 10,418.

06 3 3 3 Variance = Standard deviation = variance = 102. 07% 15.The bankruptcy lawyer does well when the rest of the economy is floundering, but does poorly when the rest of the economy is flourishing and the number of bankruptcies is down. Therefore, the Leaning Tower of Pita is a risk-reducing investment. When the economy does well and the lawyer’s bankruptcy business suffers, the stock return is excellent, thereby stabilizing total income. 10-4 16.

Boom: \$0 + (\$18 ? \$25) = ? 28. 00% \$25 \$1 + (\$26 ? \$25) = 8. 00% \$25 \$3 + (\$34 ? \$25) = 48. 00% \$25 Normal: Recession: r= (? 28) + 8 + 48 = 9. 33% 3 1 1 1 ? (? 28 ? 9. 33) 2 + ? (8 ? 9. 33) 2 + ? (48 ? 9.

33) 2 = 963. 6 3 3 3 Variance = Standard deviation = variance = 31. 04% Portfolio Rate of Return Boom: (? 28 + 150)/2 = 61. 00% Normal: (8 + 27.

5)/2 = 17. 75% Recession: (48 –100)/2 = –26. 0% Expected return = 17.

58% Standard deviation = 35. 52% 17. a.

Interest rates tend to fall at the outset of a recession and rise during boom periods. Because bond prices move inversely with interest rates, bonds provide higher returns during recessions when interest rates fall. rstock = 0. 2 ? (? 5%) + (0. 6 ? 15%) + (0. 2 ? 25%) = 13. 0% rbonds = (0.

2 ? 14%) + (0. 6 ? 8%) + (0. 2 ? 4%) = 8. 4% Variance(stocks) = 0. ? (? 5? 13)2 + 0. 6 ? (15? 13)2 + 0.

2 ? (25 – 13)2 = 96 Standard deviation = 96 = 9. 80% Variance(bonds) = 0. 2 ? (14? 8. 4)2 + 0.

6 ? (8? 8. 4)2 + 0. 2 ? (4? 8. 4)2 = 10. 24 Standard deviation = 10. 24 = 3. 20% b.

c. Stocks have both higher expected return and higher volatility. More risk averse investors will choose bonds, while those who are less risk averse might choose stocks.

10-5 18. a. Recession Normal economy Boom (? 5% ? 0.

6) + (14% ? 0. 4) = 2. 6% (15% ? 0. 6) +(8% ? 0.

4) = 12. 2% (25% ? 0. 6) + (4% ? 0. 4) = 16. 6% b. Expected return = (0.

2 ? 2. 6%) + (0. 6 ? 2. 2%) + (0.

2 ? 16. 6%) = 11. 16% Variance = 0. 2 ? (2.

6 – 11. 16)2 + 0. 6 ? (12. 2 – 11. 16)2 + 0.

2 ? (16. 6 – 11. 16)2 = 21. 22 Standard deviation = c. 21. 22 = 4.

61% The investment opportunities have these characteristics: Stocks Bonds Portfolio Mean Return 13. 00% 8. 40% 11. 