1. You are planning to offset a single-payment liability with an immunized bond portfolio. Your liability is due in three years and amounts to $600,000. You have decided to form your portfolio by using bonds A and B. Bond A and B have five and two year time-to-maturity, respectively. Bond A is a pure-discount bond while Bond B has a coupon rate of 12% and makes annual coupon payments. If both bonds have face values of $1,000 and yields-to-maturity of 10%, how many units of each bond should you purchase to form your immunized portfolio? In other words, you need to find your total dollar investment today and the way you need to allocate this amount between bonds A and B by finding how many units of each bond you should buy today.
- Suppose that a 1-year zero-coupon bond with face value of $1,000 sells at $934.58, while a 2-year zero-coupon bond with face value of $1,000 sells at $826.45. You are considering the purchase of a 2-year-maturity bond making annual coupon payments. The face value of the bond is $1,000, and the coupon rate is 14% per year.
- What is the price of this 2-year 14% coupon bond?
- What is the forward rate for the second year, f12?
- Consider the following information regarding the performance of a money manager in a recent month. The table represents the actual return of each sector of the manager’s portfolio in column 1, the fraction of portfolio allocated to each sector in column 2, the benchmark sector allocations in column 3, and the returns of sector indices in column 4.
Actual Return / Actual Weight / Benchmark Weight / Benchmark Index Return
Equity / 8.0% / 0.7 / 0.6 / 10.0% (S&P 500)
Bonds / 2.0% / 0.2 / 0.3 / 3.0% (Salomon Index)
Cash / 1.0% / 0.1 / 0.1 / 1.0%
a. What was the manager’s return in the month? What was her overperformance or underperformance?
b.What was the contribution of security selection to relative performance?
c.What was the contribution of asset allocation to relative performance? Confirm that the sum of selection and allocation contributions equals her total “excess” return relative to the benchmark.
2. Dr. Hannibal began September 2006 with a portfolio valued at $20,000 and made a contribution to and a withdrawal from this portfolio over the next three months. Information regarding amounts and dates of these cash flows and the portfolios market value at various dates is shown below:Date / Portfolio Value before
Contribution or Withdrawal / Contribution(+)
or Withdrawal (-) / Portfolio Value after
Contribution or Withdrawal
End of August 2006 / $ 20,000 / $ 0 / $ 20,000
End of September 2006 / $ 24,000 / $ 2,400 / $ 26,400
End of October 2006 / $ 19,800 / $ -3,800 / $ 16,000
End of November 2006 / $ 18,400 / $ 0 / $ 18,400
a.Write down the equation needed to calculate the dollar-weighted return for the three-month period. Do not try to solve it.
b.Calculate the time-weighted return for the three-month period using geometric average.
c.Calculate the time-weighted return for the three-month period using arithmetic average.