Suppose the yield to maturity on a one-year zero-coupon bond is 8%. The yield to

Question

Suppose the yield to maturity on a one-year zero-coupon bond is 8%. The yield to maturity on a two-year zero-coupon bond is 10%. Answer the following questions (use annual compounding):

(a) According to the Expectations Hypothesis, what is the expected one-year rate in the marketplace for year 2?

(b) Consider an investor who only wants to invest for a year. She expects the yield to maturity on a one-year zero to be 6% next year. In which one will she choose to invest for a year: the one-year zero-coupon bond or the two-year zero-coupon bond? [Hint: compare the holding period return for both bonds]

(c) If all investors behave like the investor in (b), what will happen to the equilibrium term structure according to the Expectations Hypothesis?

Explanation / Answer

As per expectation theory,

a) (Y1 + Y2)/2 = Yield (2 years)

=>> Y2 = 2* 10%-8% = 12%

b) expexted(Y2) = 6%, Yeild on 2Y bond after one year (Using expectations threory) = 2*10%- 6% = 14%

Can also calculate using (1.10^2)/1.06 -1 [ for precision]

= Yeild on one year bond = 8%

Hence, the investor should invest in 2 year bond and should sell it after one year

c) In case all the investors behave like investor in b) the demand for 2 year bond will increase resulting in increase in price of bond and thus decrease in 2Y (2nd year yeild). Thus at equilibrium 2Y would be equal to 6% only

1Y = 8% (as before)

Thus 2 year yeild = (8% + 6% )/2 = 7%

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