Question

You are given the following yield curve (spot rates at different maturities) Note : All rates are semiannuallycompounded.  The annual coupon rate of a one-year bond is 6%. The coupons are paid semiannually and the face value of the bond is $100. The price of this bond is____________ (take three digits after the decimal point). The forward rate at which one can lend or borrow money 0.5 year from today for a period of 0.5 year (0.5f0.5) is__________ %( take three digits after the decimal point).  The expected six-month spot rate, six months from today assuming that risk premia is 0.5% per year is____________ % ( take three digits after the decimal point).

Maturity	Spot Rate
0.5	4%
1	4.5%
1.5	5%
2	5.5%
2.5	6%
3	6.5%
3.5	7%
4	7.5%

Answer 1

Semi-annual Coupon amount =$100*6%/2 = $3

Discount rate for 1st coupon =4%/2 =2%

Discount rate for 2nd coupon and principal repayment =4.5%/2 =2.25%

So, price of bond = 3/1.02+ 3/1.0225^2+100/1.0225^2 =$101.458

The forward rate 0.5 year from today for a period of 0.5 year (0.5f0.5) is given as

= 2* ((1+1 year spot rate/2)^2/(1+0.5 year spot rate/2) -1)

= 2* ( (1+0.0225)^2/1.02 - 1 )

= 0.050012 or 5.001%

The expected six-month spot rate, six months from today assuming that risk premia is 0.5% per year is

= 5.001%+0.5% = 5.501%