Question

1. Suppose the yields on government bonds are as follows: 1-year = .01; 2-year = .02; 3-year = .05. According to the expectations theory, what is the implied 1-year forward yield on a 1-year government bond?

2. Suppose we have a zero coupon bond with a yield of 6% and 5 years to maturity, use duration to estimate its price if interest rates fall by 1%.

3. If the 5-year treasury rate was 2.5% and the 5-year TIPS yield was 1.2%, what is the estimated 5-year inflation rate?

4. Suppose the spot US$ yen exchange rate is .0089; the annual US$ rate is .011; the annual yen rate is .003, what is the 1-year forward rate?

Answer 1

1.

1 year rate = 1% = S1

2 year rate = 2% = S2

1 year forward yield on 1 year bond = 1f1

(1+S2)^2 = (1+S1)^1 * (1+1f1)

So

1f1 = (1+S2)^2 / (1+S1)^1 - 1

1f1 = (1.02)^2 / (1.01)^1 - 1 = 3.009%

2. Zero coupon bond has duration which is equals to its maturity

So since maturity is 5 years, duration is 5

So 1% fall in interest rate will cause 5% increase in the price of the bond

Par value = 1000

yield = 6%

time = 5 years

Value of bond = par value / ( 1+ yield )^ time

Value of bond = 1000 / ( 1.06)^5 = $747.26

So new value of bond = 1.05% of 747.26 = $784.62 approx

3.

Treasury rate = 2.5%

TIPS yield = 1.2%

So inflation = 2.5% - 1.2% = 1.3%

4. Spot rate 0.0089 $ per yen

US rate = 1.1%

Japan rate = 0.3%

Forward rate = spot rate * (1+US rate ) / (1 +japan rate )

Forward rate = 0.0089 * 1.011 / 1.003 = 0.008970 $ per yen

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