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Question: The yield to maturity on one-year zero-coupon bonds is 8%. The yield to maturity on two-year zero-coupon bonds is 9%.

a. What is the forward rate of interest for the second year?

b. If you believe in the expectations hypothesis, what is your best guess as to the expected value of the short-term interest rate next year?

c. If you believe in the liquidity preference theory, is your best guess as to next year’s short-term interest rate higher or lower than in ( b )?

Short Answer

Expert verified

Answer

a. 10.01%

b. 10.01%

c. Less than 10.01%

Step by step solution

01

Calculation of forward rates of interest

The forward rate (f2) makes the return from rolling over one-year bonds the same as the return from investing in the two-year maturity bond and holding to maturity:

The formulae for Forward rate of interest: 1 + fn = (1+yn)n / (1 + yn-1)n-1

Substituting the value in the formulae =

(1 + 8%) x (1 + f2) = (1 + 9%)2

f2 = 0.1001

= 10.01%

02

Evaluation of expected value of the short-term interest rate next year

As per the expectations hypothesis, the forward rate equals the expected value of the short-term interest rate next year, so the best guess would be 10.01%.

03

Evaluation of next year’s short-term interest rate

As per the liquidity preference hypothesis, the forward rate exceeds the expected short-term interest rate next year, so the best guess would be less than 10.01%.

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Most popular questions from this chapter

You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are essentially going to resemble level perpetuities of $1 million per year. The interest rate is 10%. You plan to fully fund the obligation using 5-year and 20-year maturity zero-coupon bonds.

a. How much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position?

b. What must be the face value of the two zeros to fund the plan?

Question: Now suppose the bond in the previous question is selling for 102. What is the bond’s yield to maturity? What would the yield to maturity be at a price of 102 if the bond paid its coupons only once per year?

Question: A two-year bond with par value \(1,000 making annual coupon payments of \)100 is priced at $1,000. What is the yield to maturity of the bond? What will be the realized compound yield to maturity if the one-year interest rate next year turns out to be:

( a ) 8%,

( b ) 10%,

( c ) 12%?

Pension funds pay lifetime annuities to recipients. If a firm remains in business indefinitely, the pension obligation will resemble perpetuity. Suppose, therefore, that you are managing a pension fund with responsibilities to make perpetual payments of $2 million per year to beneficiaries. The yield to maturity on all bonds is 16%.

a. If the duration of 5-year maturity bonds with coupon rates of 12% (paid annually) is four years and the time of 20-year maturity bonds with coupon rates of 6% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both entire fund and immunize your obligation?

b. What will be the par value of your holdings in the 20-year coupon bond?

The following multiple-choice problems are based on questions that appeared in past CFA examinations.

a. A bond with a call feature:

(1) Is attractive because the immediate receipt of principal plus premium produces a high return.

(2) Is more apt to be called when interest rates are high because the interest saving will be greater.

(3) Will usually have a higher yield to maturity than a similar non-callable bond.

(4) None of the above.

b. In which one of the following cases is the bond selling at a discount?

(1) Coupon rate is greater than current yield, which is greater than yield to maturity.

(2) Coupon rate, current yield, and yield to maturity are all the same.

(3) Coupon rate is less than current yield, which is less than yield to maturity.

(4) Coupon rate is less than current yield, which is greater than yield to maturity.

c. Consider a five-year bond with a 10% coupon selling at a yield to maturity of 8%. If interest rates remain constant, one year from now the price of this bond will be:

(1) Higher

(2) Lower

(3) The same

(4) Par

d. Which of the following statements is true?

(1) The expectations hypothesis indicates a flat yield curve if anticipated future short term rates exceed current short-term rates.

(2) The basic conclusion of the expectations hypothesis is that the long-term rate is equal to the anticipated short-term rate.

(3) The liquidity hypothesis indicates that, all other things being equal, longer maturities will have higher yields.

(4) The liquidity preference theory states that a rising yield curve necessarily implies that the market anticipates increases in interest rates

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