4. The one-year interest rate over the next 10 years will be: 3%,45%, 6%, 7.5%,

Question

4. The one-year interest rate over the next 10 years will be: 3%,45%, 6%, 7.5%, 9%, 10.5%, 13%, 14.5%, 16%, and 17.5%. a. Using the expectations theory, what will be the interest rates on a three year bond, a six year bond and a nine year bond? b. A liquidity premium of 10 basis points is required for each year of bond maturity. Using the liquidity premium theory, what will be the interest rates on a three year bond, a six year bond and a nine year bond? 5. If the interest rates on one to five-year bonds are currently 4%, 5%, 6%, 7% and 8%, predict what the one year interest rate will be two years from now.

Explanation / Answer

4)

a. 3 year bond rate = r1+r2+r3/3 = 3+4.5+6/3 = 4.5%

    6 year bond rate = r1+r2+r3+r4+r5+r6/6 = 3+4.5+6+7.5+9+10.5/6 = 6.75%

   9 year bond rate = r1+r2+r3+r4+r5+r6+r7+r8+r9/9 = 3+4.5+6+7.5+9+10.5+13+14.5+16/9 = 9.33%

we can also do it in more approximate way;

3 year bond rate:

(1+r)^3=(1.03)*(1.045)*(1.06);

Calculate for r, we get r = 4.4928%

Similarly for

6 year bond rate

(1+r)^6=(1.03)*(1.045)*(1.06)*(1.075)*(1.09)*(1.105)

We get r = 6.7193%

For 9 year bond rate r = 9.2502%

b)

3 year bond rate

   we have to add the premium

(1+r) ^ 3 = (1.03)*(1.045)*(1.06) +0.003 = 4.5843%

0.003 is because per year 10 basis point(0.1%) so for 3 years it is 0.3%(0.003)

for 6 years it is 0.006

for 9 years it is 0.009

same way for 6 years bond r = 6.7914%

9 year bond rate r = 9.2993%

5)

one year rate one year from now = r11 = [(1+r2)^2/(1+r1)] - 1

r1 = rate at year one

r2 = rate at year 2

r11 = [(1+r2)^2/(1+r1)] - 1 = [(1.05)^2/(1.04)] - 1 = 6.009%

hence one year rate 2 years from now

= [(1+r3)^3 / (1+r1) * (1+r11)] - 1= [(1.06)^3 / (1.04)*(1.06009)] -1 = 8.029%

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