Question

a)The yields of four zero-coupon bonds of varying maturities are as follows: Maturity YTM 1 6.1% 2 6.2% 3 6.3% 4 6.4% If you expect the implied term structure to be the same next year as it is this year, what is the expected return on the 2-year zero coupon bond over the coming year? Please express your answer in percent, rounded to the nearest basis point.

b)The maturities and yields of three zero-coupon bonds are as follows:

Maturity	YTM
1	4%
2	5%
3	6%

Next year, you expect the yields on zero-coupon bonds to be as follows:

Maturity	YTM
1	5%
2	6%
3	7%

c)What is your expectation of the rate of return on a 3-year zero-coupon bond over the coming year? Please express your answer in percent rounded to the nearest basis point.

d)The 1-year rate is currently 2%, and the expected 1-year rate a year from now is 1%. If the liquidity preference theory holds and the liquidity premium for the 2-year rate is 1.0%, what should the 2-year rate be? (Assume that the liquidity premium for the 1-year rate is 0.0%) Please express your answer in percent rounded to the nearest basis point.

If the 1-year rate is currently 3%, and the 2-year rate is 4.5%, what is the expected 1-year rate a year from now if the expectations hypothesis holds? Please express your answer in percent rounded to the nearest basis point.

Answer 1

a). Assuming a maturity value of 1,000 for the ZCBs, the price of a 2-year ZCB today is

1,000/(1+2 year YTM)^2 = 1,000/(1+6.20%)^2 = 886.65

If the term structure remains same the next year also, then the price of a 2-year ZCB held till next year will be

1,000/(1+ 1 year YTM) = 1,000/(1+6.10%) = 942.51

Expected return on the 2-year ZCB = (next year price/current price) -1

= (942.51/886.65) - 1 = 6.30%

b). A 3-year ZCB held today is giving a return of 6%. Next year, the ZCB will have a maturity of 2 years so its return will be 6% (as per the expected yields next year), so the expected return on the 3-year ZCB over the coming year has to be 6.00%.

c). 2-year rate (as per the liquidity preference theory) = (current 1-year rate + expected 1-year rate next year)/2 + 2-year liquidity premium

= (2%+1%)/2 + 1% = 2.50%

d). As per the expectations hypothesis,

2-year rate = (current 1-year rate + expected 1-year rate)/2

4.5% = (3% + x)/2

expected 1-year rate = 6.00%