Suppose that an investor observes the following prices and yields to maturity on

Question

Suppose that an investor observes the following prices and yields to maturity on zero coupon government bonds.

Maturity Price Yield to Maturity

1 year 97.50 2.548%

2 years 94.25 2.983

3 years 91.75 2.891

The prices are per 100 of par value; the YTM are stated on a semiannual bond basis.

A) Compute the 1y1y and 2y1y implied forward rates, stated on a semiannual bond basis.

B) The investor has a three year investment horizon and is choosing between buying the two year zero and reinvesting in another one year zero in 2 years or buying and holding to maturity the three year zero. The investor decides to buy the 2 year bond. Based on the is decision what is the minimum YTM the investor expects on one year zeros two years from now?

Explanation / Answer

(A) The "1y1y" implies forward rate is 3.419%.

A =2 (period), B = 4 (period), B-A = 2(period) , z2= 0.02548/2, (per period) and z4= 0.02983/2 (per period).

So, (1 + 0.02548/2)2X(1+IFR2,2)2 = (1+0.02983/2)4, IFR2,2= 0.017095, x2 = 0.03419.

The "2y1y" implies forward rate is 2.707%.

A =4 (period), B = 6 (period), B-A = 2(period) , z4= 0.02983/2, (per period) and z6= 0.02891/2 (per period).

So, (1 + 0.02983/2)4X(1+IFR4,2)2 = (1+0.02891/2)6, IFR4,2= 0.013536, x2 = 0.02707.

(B) Here the answer would be 2.707%. The investors view is that the one-year yield in two-years will be greater than or equal to 2.707%.

The "2y1y" implies forward rate is 2.707% is the breakeven reinvestment rate. If the investor expects the one-year rate in two-years to be less than that, the investor would prefer to buy the three-year zero. If the investor expects the one-year rate in two-years to be greater than 2.707%, the investor might prefer to buy the two-year zero and reinvest the cash flow.

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