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i Safari File Edit View History Bookmarks Window Help 61% i O. Fri 1 1:09:16 AM aE Chegg Study Guided Solutions a HW 6 Fantasy Football Yahool Sports Saved Help Save & Exit Submit Check my work Suppose that you buy a 1-year maturity bond with a coupon of 8.6% paid annually. If you buy the bond at its face value, what real rate of return will you earn if the inflation rate is 3%? 5%210.40%? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.) 9.09 points Real Rate of Return 3% 5% 10.40% eBook Print Bond

Explanation / Answer

When you buy the bond at face value, this implies coupon = yield to maturity.

Hence, YTM or rate of return of bond = 8.6%. This is the nominal rate of return

Based on Fischer relation,

(1 + Nominal Rate) = (1 + Real rate) * (1 + Inflation)

a) Inflation Rate = 3%

(1 + 8.6%) = (1 + Real rate) * (1 + 3%)

(1 + Real rate) = 1.0544

Real Rate = 5.44%

b) Inflation Rate = 5%

(1 + 8.6%) = (1 + Real rate) * (1 + 5%)

(1 + Real rate) = 1.0343

Real Rate = 3.43%

c) Inflation Rate = 10.40%

(1 + 8.6%) = (1 + Real rate) * (1 + 10.40%)

(1 + Real rate) = 0.9837

Real Rate = - 1.63%

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Some texts mention Fischer relation as,

Nominal Rate = Real rate + Inflation.

This is an approximation and a simplied version of the above mentioned formula, which take you to approximate results.

Based on this relation, when Inflation = 3%, Real rate = 8.6% - 3% = 5.6%

when Inflation = 5%, Real rate = 8.6% - 5% = 3.6%

when Inflation = 10.4%, Real rate = 8.6% - 10.4% = -1.8%

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