Week 7 | Bonds (Finance)

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  Chapter 10 Answers to critical thinking and concepts review questions 1.  They all wish they had! Since they didn’t, it must have been the case that the stellar performance was not foreseeable, at least not by most. 2.  As in the previous question, it’s easy to see after the fact that the investment was terrible, but it  probably wasn’t so easy ahead of time. 3.  No, shares are riskier. Some investors are highly risk averse, and the extra possible return doesn’t attract them relative to the extra risk. 4.  On average, the only return that is earned is the required return—investors buy assets with returns in excess of the required return (positive NPV), bidding up the price and thus causing the return to fall to the required return (zero NPV); investors sell assets with returns less than the required return (negative NPV), driving the price lower and thus the causing the return to rise to the required return (zero NPV). 5.  The market is not weak-form efficient. 6.  Yes, historical information is also public information; weak form efficiency is a subset of semi-strong form efficiency. 7.  Ignoring trading costs, on average, such investors merely earn what the market offers; the trades all have zero NPV. If trading costs exist, then these investors lose by the amount of the costs. 8.  Unlike gambling, the shares market is a positive sum game; everybody can win. Also, speculators provide liquidity to markets and thus help to promote efficiency. 9.  The EMH only says, that within the bounds of increasingly strong assumptions about the information processing of investors, that assets are fairly priced. An implication of this is that, on average, the typical market participant cannot earn excessive profits from a particular trading strategy. However, that does not mean that a few particular investors cannot outperform the market over a particular investment horizon. Certain investors who do well for a period of time get a lot of attention from the financial press, but the scores of investors who do not do well over the same period of time generally get considerably less attention. 10.   a.  If the market is not weak-form efficient, then this information could be acted on and a profit earned from following the price trend. Under (2), (3), and (4), this information is fully impounded in the current price and no abnormal profit opportunity exists. b.  Under (2), if the market is not semistrong-form efficient, then this information could be used to buy the shares ‘cheap’ before the rest of the market discovers the financial statement anomaly. Since (2) is stronger than (1), both imply that a profit opportunity exists; under (3) and (4), this information is fully impounded in the current price and no profit opportunity exists. c.  Under (3), if the market is not strong form efficient, then this information could be used as a  profitable trading strategy, by noting the buying activity of the insiders as a signal that the shares is underpriced or that good news is imminent. Since (1) and (2) are weaker than (3), all three imply that a profit opportunity exists. Note that this assumes the individual who sees the insider trading is the only one who sees the trading. If the information about the trades made by company management is public information, under (3) it will be discounted  in the shares price and no profit opportunity exists. Under (4), this information does not signal any profit opportunity for traders; any pertinent information the manager-insiders may have is fully reflected in the current share price. Solutions to questions and problems  NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each  problem is found without rounding during any step in the problem.  Basic questions (1–18) 1.  The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. The return of these shares is:  R  = [($69 – 61) + 1.40] / $61  R  = 0.1541, or 15.41% The dividend yield is the dividend divided by price at the initial period price, so: Dividend yield = $1.40 / $61 Dividend yield = 0.0230, or 2.30% And the capital gains yield is the increase in price divided by the initial price, so: Capital gains yield = ($69 – 61) / $61 Capital gains yield = 0.1311, or 13.11% 2.  Using the equation for total return, we find:  R  = [($54 – 61) + 1.40] / $61  R  = –0.0918, or –9.18% And the dividend yield and capital gains yield are: Dividend yield = $1.40 / $61 Dividend yield = 0.0230, or 2.30% Capital gains yield = ($54 – 61) / $61 Capital gains yield = –0.1148, or –11.48% Here’s a question for you: Can the dividend yield ever be negative? No, that would mean you were paying the company for the privilege of owning the shares, however, it has happened on  bonds. 3.  To calculate the dollar return, we multiply the number of shares owned by the change in price  per share and the dividend per share received. The total dollar return is: Dollar return = 250($76.45 – 68.12 + 0.85) Dollar return = $2295 4.   a.  The total dollar return is the change in price plus the coupon payment, so: Total dollar return = $949 – 941 + 75   Total dollar return = $83 b.  The nominal percentage return of the bond is:  R  = [($949 – 941) + 75] / $941  R  = 0.0882, or 8.82%  Notice here that we could have simply used the total dollar return of $83 in the numerator of this equation. c.  Using the Fisher Effect equation, the real rate of return was: (1 +  R ) = (1 + r  )(1 + h ) r   = (1.0882 / 1.04) – 1 r   = 0.0464, or 4.64% 7. The average return is the sum of the returns, divided by the number of returns. The average return for each stock was:   %8.40or .0840, 523.09.17.21.14. 1       N  x X   N ii     %40.15or .1540, 545.12.17.05.32. 1       N  yY   N ii  Remembering back to ‘sadistics’, we calculate the variance of each stock as:                            058030.154.45.154.12.154.17.154.05.154.32. 151029580.084.23.084.09.084.17.084.21.084.14. 1511 222222 222222 122       Y  X  N ii X   N  x x         The standard deviation is the square root of the variance, so the standard deviation of each stock is:     X   = (0.02958) 1/2     X   = 0.1720, or 17.20%    Y   = (0.058030) 1/2      Y   = 0.2409, or 24.09% 9.   a . To find the average return, we sum all the returns and divide by the number of returns, so: Arithmetic average return = (–0.12 +0.21 + 0.27 + 0.06 + 0.17)/5 Arithmetic average return = 0.1180, or 11.80% b . Using the equation to calculate variance, we find:   Variance = 1/4[(–0.12 – 0.118) 2  + (0.21 – 0.118) 2  + (0.27 – 0.118) 2  + (0.06 – 0.118) 2  + (0.17 – 0.118) 2 ] Variance = 0.02357 So, the standard deviation is: Standard deviation = (0.02357) 1/2  Standard deviation = 0.1535, or 15.35% 21.  To calculate the arithmetic and geometric average returns, we must first calculate the return for each year. The return for each year is:  R 1  = ($107.11 – 99.15 + 1.60) / $99.15 = 0.0964, or 9.64%  R 2  = ($91.65 – 107.11 + 2.00) / $107.11 = –0.1257, or –12.57%  R 3  = ($127.16 – 91.65 + 2.20) / $91.65 = 0.4115, or 41.15%  R 4  = ($162.15 – 127.16 + 2.60) / $127.16 = 0.2956, or 29.56%  R 5  = ($192.60 – 162.15 + 3.00) / $162.15 = 0.2063, or 20.63% The arithmetic average return was:  R A  = (0.0964 – 0.1257 + 0.4115 + 0.2956 + 0.2063)/5  R A = 0.1768, or 17.68% And the geometric average return was:  R G  = [(1 + 0.0964)(1 – 0.1257)(1 + 0.4115)(1 + 0.2956)(1 + 0.2063)] 1/5  – 1  R G  = 0.1616, or 16.16% 22. To find the real return, we need to use the Fisher Effect equation. Re-writing the Fisher Effect equation to solve for the real return, we get: r   = [(1 +  R )/(1 + h )] – 1 So, the real return each year was: Quarter Bank Bills CPI Real return Mar-88 2.70% 1.70% 0.98%Jun-88 2.82% 1.90% 0.90%Sep-88 3.27% 1.80% 1.44%Dec-88 3.51% 2.00% 1.48%Mar-89 3.77% 1.00% 2.74%Jun-89 4.34% 2.50% 1.80%Sep-89 4.51% 2.30% 2.16%Dec-89 4.66% 1.80% 2.81%Total 29.58% 15.00% 14.32%  a.  The average return for bank bills over this period was: Average return = 0.0.2958 / 8
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