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If the plan in the previous problem wants to fund and immunize its position fully, how much of its portfolio should it allocate to one-year zero-coupon bonds and perpetuities, respectively, if these are the only two assets? Funding the plan?.

“A pension plan is obligated to make disbursements of \(1 million, \)2 million, and $1 million at the end of the next three years, respectively.”

Short Answer

Expert verified

Answer

90.48% in zero-coupon bonds and 9.52% in perpetuity

Step by step solution

01

Step by Step Solution Step 1: Calculation of duration of the perpetuity

CF = $1m, $2m and $1m

Time = 3 years.

y = Yield to maturity = 10%

Formulae for duration of perpetuity = (1 + y) / 1 = 1.10/0.10 = 11 Years

02

Calculation of the weight of the zero-coupon bond

To find the weight (w) of zero coupon bond = (w x 1)[(1 – w) x 11]

w = 9.048 / 10

= 0.9048

Thus, 90.48% should be invested in zero-coupon bonds and 9.52% perpetuity.

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Most popular questions from this chapter

Noah Kramer, a fixed-income portfolio manager based in the country of Sevista, is considering the purchase of a Sevista government bond. Kramer decides to evaluate two strategies for implementing his investment in Sevista bonds.

Table 11.6 gives the details of the two strategies, and Table 11.7 contains the assumptions that apply to both strategies.

Before choosing one of the two bond investment strategies, Kramer wants to analyze how the market value of the bonds will change if an instantaneous interest rate shift occurs immediately after his investment.

The details of the interest rate shift are shown in Table 11.8. Calculate, for the instantaneous interest rate shift shown in Table 11.8, the percent change in the market value of the bonds that will occur under each strategy.

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

A bond currently sells for \(1,050, which gives it a yield to maturity of 6%. Suppose that if the yield increases by 25 basis points, the price of the bond falls to \)1,025. What is the duration of this bond?

Question: The yield curve is upward-sloping. Can you conclude that investors expect short-term interest rates to rise? Why or why not?

Question: Masters Corp. issues two bonds with 20-year maturities. Both bonds are callable at \(1,050. The first bond is issued at a deep discount with a coupon rate of 4% and a price of \)580 to yield 8.4%. The second bond is issued at par value with a coupon rate of 8.75%.

a. What is the yield to maturity of the par bond? Why is it higher than the yield of the discount bond?

b. If you expect rates to fall substantially in the next two years, which bond would you prefer to hold?

c. In what sense does the discount bond offer “implicit call protection”?

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