Chapter 4 - Problem Set.pdf

# For bond c the holding period is also shorter than

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For Bond C, the holding period is also shorter than the years to maturity, the higher interest rate results in a rate of capital loss of 9.1%, even though it has a higher current yield of 9% compared to that of Bond A, the rate of return is negative (-0.1%). For Bond D, although the holding period is shorter than the years to maturity, the higher interest rate does not result any capital loss because the coupon rate is exactly the same as the new interest rate such that the bond can be sold at par in the next period, in this case, the rate of return equals to the current yield of 12%. Bond D will be chosen because its offers the highest rate of return on the 1,000 dollars investment.

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ECO349 2011 Winter Chapter 4 Problem Set Michael Ho 8/8 5. Suppose an investor pays \$925.93 to purchase a bond with a face value of \$1,000, coupon rate 10%, and five years to maturity. Assume the current interest rate is 10% and expected to rise by 2% each year in the next five years . The rate of inflation is expected to be 2% in the next twelve months. If the investor only plans to hold on to this bond for one year and then sell it at the beginning of next year, then what is the real rate of return for this investment? (Hint: All cash flows must be discounted to the beginning of time t for the precise calculation of the real rate of return and hence the current yield is irrelevant.) Face Value ( F ) 1,000.00 Coupon Rate 10% Purchase Price ( P t ) 925.93 Future Bond Price ( P t+1 ) 864.53 = 89.29 + 78.32 + 67.52 + 57.22 + 572.19 Capital Gain/Loss ( g) -61.40 = 864.53 925.93 Discounted g -55.82 = -61.50/(1+10%) Discounted Coupon Payment from Year 1 90.91 Discounted Return (RET) 35.09 = 90.91 + (-55.82) Rate of Return 3.79% = 35.09/925.93 Expected Rate of Inflation ( π e ) 2.00% Real Rate of Return 1.79% = 3.79% - 2% Years to Maturity 1 2 3 4 5 Coupon Payment ( C ) 100.00 100.00 100.00 100.00 100.00 Interest Rate ( i ) 10% 12% 14% 16% 18% Discounted Coupon Payment 90.91 89.29 78.32 67.52 57.22 Discounted Face Value 572.19 Coupon Payment = Face Value × Coupon Rate = 1,000 × 10% = 100 90.91 = 100/(1 + 10%) 89.29 = 100/(1 + 12%) 78.32 = 100/[(1 + 12%) × (1 + 14%)] 67.52 = 100/[(1 + 12%) × (1 + 14%) × (1 + 16%)] 57.22 = 100/[(1 + 12%) × (1 + 14%) × (1 + 16%) × (1 + 18%)] 572.19 = 100/[(1 + 12%) × (1 + 14%) × (1 + 16%) × (1 + 18%)]
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