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ECON_134b_-_HPR_Section_Problem_Solutions

# ECON_134b_-_HPR_Section_Problem_Solutions - Thus Nom rate...

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Q5. Here’s a breakdown of payments for a TIPS with a coupon rate a 4%: Time Inflation Par Value Coupon Payment Principal Repayment Total Payment 0 1000.0 0 1 2% 1020.00 40.80 0 40.80 2 3% 1050.60 42.02 0 42.02 3 1% 1061.11 42.44 1061.11 1103.55 What were the real and nominal rates of return in years 1, 2, and 3? A: It appears that the book assumes that the TIPS is selling at par. So basically they’ve set the coupon rate = yield to maturity. The TIPS will make sure that we earn a real yield of 4% by adjusting the par value of the bond to account for inflation. For example, in Year 1, the par value increases by 2% (1020-1000/1000 = 2%). The coupon payment will therefore also increase because it’s tied to the par value of the TIPS. We need to figure out our rate of return under this format. Let’s do nominal first because it’s more intuitive. What we need to do is figure out what we “earn” in each year. You’re going to get a return on your investment from two things: money from the coupon and the increase in the price of the TIPS.
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Unformatted text preview: Thus, Nom rate of return = (End Price-Beg Price + Coupon)/Beg Price Now, note that because this thing is selling at par, End price = Ending par value and Beg Price = Beg Par Value (because both the coupon and the nominal yield are growing at the inflation rate) Thus, Nom rate of return (Year 1) = (1020-1000+40.80)/1000 = 6.08% In years 2 and 3, the par value and (thus the coupon) will increase by the inflation rates for that period, 3% and 1%. Remember that the beg price for year 2 will be 1020, not 1000. Nom rate of return (year 2) = (1050.6 - 1020+40.80*1.03)/1020 = 7.12% Nom rate of return (3) = (1061.11 - 1050.6+42.02*1.01)/1050.6 = 5.04% Now, use the inflation formula to get the real rate of return: Year 1: (1+0.0608)/(1+0.02) = 1.04 Year 2: (1+0.0712)/(1+0.03) = 1.04 Year 3: (1+0.0504)/(1+0.01) = 1.04 The real rate of return is 4% each year. Not a coincidence!...
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ECON_134b_-_HPR_Section_Problem_Solutions - Thus Nom rate...

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