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一、求这本书中的第13章和第16章中文教材讲解
二、求以下习题的来源以及中文讲解
谢谢大神
1. Supposethat the share price of a share always either goes up by 20% or falls by 30%over the next year, whatever the current level. The chances of an upward moveare 0.75 and the chances of a downward move are 0.25. The stock pays nodividends. a. Suppose you know nothing about the recentperformance of the stock. What is the expected rate of return on the stock? The expectedreturn is the probability weighted average of the good outcome, +20%, and thebad outcome, -30%. This is: 0.75 x （+20%） + 0.25 x（ –30%） = +7.55% b. Suppose further than you now discover thatover the past five years the return on the stock have been +20%, +20%, +30%,-30%, -30%. What do you now think the expected return for the next year is? The current price level is irrelevantto the chances of good and bad outcomes: no matter where prices arethere is a 75% chance of a return of 20% and a 25% chance of a return of –30%.Since the current price level is irrelevant to future returns then pastreturns, which determine where the current price level is, also are irrelevant.So the expected next period return is always +7.5% regardless of recentreturns. 2. In an economy, aggregate dividends paid bycompanies are expected to grow in line with GDP. The trend rate of growth of GDPis 2.5% per annum. The required rate of return on equities股本回报率 equals a saferate plus a risk premium. The safe (real) rate is 3%, and the risk premium is5%. a. What would you expect the dividend priceratio (or dividend yield) to be? If dividends grow at rate g and are discounted at ratere the value of equities, which is the present discounted value offuture dividends, is given by P = D / (re – g) If the safe rate is 3% and the risk premium is 5% then re = 0.03 + 0.05 = 0.08 With g = 0.025 we then have: P = D /(0.08 – 0.025) So D/P =0.055 and the dividend yield is 5.5%. b. By how much would the stock market priceschange if the risk premium increased to 6%? If the risk premium rises to 6% then: re = 0.03 + 0.06 = 0.09 P = D / (0.09 – 0.025) The ratio of this new level of stock prices to thelevel with a risk premium of 5% is: (0.08 – 0.025) / (0.09 – 0.025) = 0.85 Thus stock prices fall by about 15% when the riskpremium increases from 5% to 6%.（1.25increase 25%） 3. Suppose your weight fluctuates randomly from monthto month; it is as likely to go up as down. Your current weight is 161 pounds.Looking back at records of your weight over the past year the pattern is: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 150 145 148 153 157 155 158 160 161 159 159 161 a. What is your best guess on the profile ofmonthly weights over the next 12 month? Your weightfollows a random walk – it is as likely to go up as to go down. Your best guess as to your weight one monthahead is that it is equal to your current weight. It follows that your bestguess today as to your weight two months ahead – and indeed for all futuremonths – is also today’s weight. Thus your profile of expected future weightsover the next 12 months is flat at the current weight of 161 pounds. b. How volatile is the path of actual monthlyweights over the next year likely to be relative to your estimated profile? Your actual weight will certainly deviate from thecurrent weight of 161 pounds. Looking at the past pattern of changes in weightfrom one month to the next we have: Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec -5 +3 +5 +4 -2 +3 +2 +1 -2 0 +2 The variance of these monthly changes is 9 pounds. Thestandard deviation is 3 pounds. Over a twelve month horizon the spread of weightsaround you current best guess should reflect this standard deviation of monthlyweight changes. On a twelve month ahead horizon the standard deviation ofweight around the central forecast of 161 pounds is the square root of 12 timesthe monthly standard deviation of 3 pounds.
1.Calculate the price of the following bonds on theassumption that the yield to maturity is 7% for all maturity dates: a. Abond with exactly 10 years to maturity that pays no coupon and has a face value of $100 P = $100/ (1+.07)10 = $ 50.83 b. Abond that pays an annual coupon worth 5% of face value and will pay a couponevery year for 10 years and then be redeemed for $100 P = $5 /(1.07) + $5 / (1.07)2 + $5 /(1.07)3 + $5 /(1.07)4 + $5 / (1.07)5 + $5 / (1.07)6 + $5 / (1.07)7 + $5 /(1.07)8 + $5 / (1.07)9 + $5 / (1.07)10 +$100 / (1.07)10 = $85.95 c. A bond that pays an annual coupon worth 7%of face value and will pay a coupon every year for 10 years and then beredeemed for $100 P = $7 /(1.07) + $7 / (1.07)2 + $7 /(1.07)3 + $7 /(1.07)4 + $7 / (1.07)5 + $7 / (1.07)6 + $7 / (1.07)7 + $7 /(1.07)8 + $7 / (1.07)9 + $7 / (1.07)10 +$100 / (1.07)10 = $100.00 d. Abond that pays an annual coupon worth 9% of face value and will pay a couponevery year for 10 years and then be redeemed for $100 P= $9 / (1.07) + $9 / (1.07)2 + $9 / (1.07)3 + $9 / (1.07)4 + $9 / (1.07)5+ $9 / (1.07)6 +$9 / (1.07)7 + $9 / (1.07)8 + $9 / (1.07)9 + $9 / (1.07)10 +$100 / (1.07)10 = $114.05 2. Consider each of thebonds you priced in exercised 1. Calculate the percentage change in the priceof each bond between the start of the year and the start of the following year.Assume the yield to maturity remain at a constant level of 7% throughout. Nowadd the coupon yield (the ratio of coupon to price) to the percentage change inprice. What do the one-year returns on each bond look like? (The one-yearreturns are the percentage change in price plus the coupon yield) BOND A Price at the endof year 1: P= $100/ (1+.07)9 = $ 54.39 The change inprice of bond a is $54.39 - $50.83 This is apercentage change of 7% [ ($54.39 -$50.83)/ $50.83] Since the bondpays no coupon this capital gain is the one-year return on the bond. BOND B Price at the end of year 1: P = $5 /(1.07) + $5 / (1.07)2 + $5 /(1.07)3 + $5 /(1.07)4 + $5 / (1.07)5 + $5 / (1.07)6 + $5 / (1.07)7 + $5 /(1.07)8 + $5 / (1.07)9 + $100 / (1.07)9 = $86.97 The change in price of bond b is $86.97 - $85.95. This is a percentage change of 1.19%. [($86.97 - $85.95)/ $85.95] The coupon yield is 5/85.95 = 5.81%. The sum of coupon yield plus capital gain(percentage change in price) is 7%. This is the one-year return on the bond. BOND C Price at the end of year 1: P = $7 / (1.07) + $7 / (1.07)2 + $7 / (1.07)3 + $7 / (1.07)4 + $7 / (1.07)5+ $7 / (1.07)6 + $7 / (1.07)7 + $7 /(1.07)8 + $7 / (1.07)9 + $100/ (1.07)9 = $100.00 The change in price of bond b is $100 - $100. This is a percentage change of 0%. The coupon yield is 7/100 = 7%. The sum of coupon yield plus capital gain (percentagechange in price) is 7%. Thisis the one-year return on the bond. BOND D Price at the end of year 1: P = $9 / (1.07) + $9 / (1.07)2 + $9 / (1.07)3 + $9 / (1.07)4 + $9 / (1.07)5+ $9 / (1.07)6 + $9 / (1.07)7 + $9 /(1.07)8 + $9 / (1.07)9 + $100 / (1.07)9 = $113.03 The change in price of bond b is $113.03 - $114.05 This is a percentage change of -0.89% [($113.03 - $114.05)/ $114.05] The coupon yield is 9/114.05 = 7.89%. The sum of coupon yield plus capital loss (percentage change in price) is7%. This is the one-year return on the bond. Note that the one year return on all bonds is the sameat 7%, which is the discount rate. 3. The central bank in acountry has set the short-term interest rate at 6%. It is widely expected thatthe short term rate will stay at this level for a year and then rise to 7% fora year before moving back to an equilibrium level of 6.5%, where it is expectedto remain from two years ahead indefinitely. Assuming the expectations theoryis true, what would you expect the yield to be on government bonds ofmaturities from 1 year up to 10 years? The following table showsthe path for the short-term rate (column 1). The second column is theaverage of the short-term rate over the period from today to the relevantperiod ahead. This is what the yield on(zero coupon) bonds of the relevant maturity would be approximately equal tounder the expectations theory of the yield curve.
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