Which two spot interest rates are needed to find a two-year forward rate expecte

Question

Which two spot interest rates are needed to find a two-year forward rate expected three years from now?

A. three- and five-year rates

B. two- and three-year rates

C. two- and five-year rates

D. five- and seven-year rates

E. one- and two-year rates

An issuer of a callable bond is more likely to exercise a call option after a(n) ____.

A. reduction of the company's stock price

B. increase in the company's stock price

C. increase in interest rates

D. downgrade of the bond's rating

E. decrease in interest rates

Explanation / Answer

Answer to Q.1 - Option A

This is an application of pure expectations hypothesis for interest rates.

You need to calculate 2-year interest rate 3 -year from now.

This implies, by pure expectation hypothesis,

(1 + 5yr rate)5 = (1 + 3yr rate)3 * (1 + 2yr rate)2

Now, we need to calculate the 2yr rate, so we will need 3 yr and 5 yr rate, per equation above.

Answer to Q.2 - Option E

When the interest rates decline, price of the bond will increase (relationship between bond price and interest rates). Now, this decrease in interest rates would compel the company to call this bond, and refinance with another issue, since now the company can issue bonds at lower interest rates (or lower coupon payments). Basically, company would look to improve its operating performance by reducing the interest expense it incurs.

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