Question

Suppose that the yield curve shows that the one-year bond yield is 6 percent, the two-year yield is 5 percent, and the three-year yield is 5 percent. Assume that the risk premium on the one-year bond is zero, the risk premium on the two-year bond is 1 percent, and the risk premium on the three-year bond is 2 percent.

a. What are the expected one-year interest rates next year and the following year?

The expected one-year interest rate next year = %

The expected one-year interest rate the following year = %

Answer 1

Expected one year interest rate for future periods can be calculated using current long term interest rate available using the formula

here R_l  represents current Long term interest rate for n years

R_s(n-1)   represents current interest rate for (n-1) years

R_sn   represents expected one year interest for n^th period and  

n represents no. of year .

Suppose we have current long term interest rate for 3 years and also current interest for 2 years form thsi we can find out expected one year interest rate for 3 year .

From the data given in question we have tabulated

Periods in Years	Bond Yeild (%)	Risk premium (%)	Interest Rate (%) WN1
1	6	0	6
2	5	1	4
3	5	2	3

WN 1 :

Risk premuim of bond is difference between anticipateed yeild from bond and risk free rate offered one  government securities

Risk Premuim = Yeild - Risk free rate

using the above formula ,

we get

For first year,

RP₁=6%-R_f1

0=6%-R_f1

R_f1 =6%

For 2nd year,

RP2=5%-R_f2

1%=5%-R_f2

R_f2 =4%

For 3rd year,

RP3=5%-R_f3

2%=5%-R_f3

R_f3 =3%

As now we have Risk free rate for different maturity periods we can canculated expeted interest for one year using the below formula

(1+0.04)² =(1+0.06)¹(1+R_s2)

1.0816=1.06*(1+R_s2)

(1+R_s2)=1.0816/1.06

(1+R_s2)=1.0204

R_s2 = 1.0204-1

R_s2 =0.0204=2.04%

Thus we get the expected one-year interest rate next year = 2.04%

Similarly for finding out the expected one-year interest rate following year ,i.e R_s2

(1+0.03)³ =(1+0.04)² (1+ R_s3)

1.092727= 1.0816 *(1+ R_s3)

(1+ R_s3) =1.092727/1.0816

(1+ R_s3)=1.01029

R_s3 = 1.01029-1

R_s3 = 0.01029=1.029%

Thus ,the expected one-year interest rate following year =1.029%

Final Answer

the expected one-year interest rate next year = 2.04%

the expected one-year interest rate following year =1.029%