1

Assignment 2 Winter 2022

Problem 1 Assume you have the option to buy one of three bonds. All have the same degree of default risk and mature in 15 years. The first is a zero-coupon bond that pays $1,000 at maturity. The second has a 7 percent coupon rate and pays the $70 coupon once per year. The third has a 9 percent coupon rate and pays the $90 coupon once per year.

a. If all three bonds are now priced to yield 8 percent to maturity, what are their prices? b. If you expect their yields to maturity to be 8 percent at the beginning of next year, what will

their prices be then? What is your before-tax holding period return on each bond? If your tax bracket is 30 percent on ordinary income and 20 percent on capital gains income, what will your after-tax rate of return be on each? Assume you do not sell the bonds.

c. Recalculate your answer to (b) under the assumption that you expect the yields to maturity on each bond to be 7 percent at the beginning of next year.

d. Re-do the calculations in parts b and c above, assuming you will sell the bonds at the end of the year.

Problem 2

A University endowment fund has sought your advice on its fixed-income portfolio strategy.

The characteristics of the portfolios current holdings are listed below:

Market Credit Maturity Coupon Modified Value of Bond Rating (yrs.) Rate (%) Duration Convexity Position

A Cnd. Govt. 3 0 2.727 9.9 $30,000 B A1 10 8 6.404 56.1 $30,000 C Aa2 5 12 3.704 18.7 $30,000 D Agency 7 10 4.868 32.1 $30,000 E Aa3 12 0 10.909 128.9 $30,000

$150,000

a) Calculate the modified duration for this portfolio.

b) Suppose you learn that the modified duration of the endowment’s liabilities is 6.5 years.

Identify whether the bond portfolio is: i) immunized against interest rate risk, ii) exposed to net

price risk, or iii) exposed to net re-investment risk. Briefly explain what will happen to the net

position of the endowment fund if in the future there is a significant parallel upward shift in the

yield curve.

c) Your current active view for the fixed income market over the coming months is that Treasury

yields will decline and corporate credit spreads will also decrease. Briefly discuss how you

could restructure the existing portfolio to take advantage of this view.

2

Problem 3

A 20-year maturity bond with a 10% coupon rate (paid annually) currently sells at a yield to

maturity of 9%. A portfolio manager with a 2-year horizon needs to forecast the total return on

the bond over the coming 2 years. In 2 years, the bond will have an 18-year maturity. The analyst

forecasts that 2 years from now, 18-year bonds will sell at yield to maturity of 8%, and that

coupon payments can be reinvested in short-term securities over the coming 2 years at a rate of

7%.

a) What is the 2-year return on the bond b) What will be the rate of return the manager forecasts that in 2 years the yield on 18-year bonds

will be 10%, and that the reinvestment rate for coupons will be 8%?

Problem 4

Shares of XYZ Corp. pay a $2 dividend at the end of every year on December 31. An investor buys

two shares of the stock on January 1 at a price of $20 each, sells one of those shares for $22 a

year later, on the next January 1, and sells the second share an additional year later for $19. Find

the dollar- and time-weighted rates of return on the 2-year investment.

Problem 5 An analyst wants to evaluate portfolio X, consisting entirely of U.S. common stocks, using both the Treynor and Sharpe measures of portfolio performance. The following table provides the average annual rate of return for portfolio X, the market portfolio (as measured by the S&P 500), and U.S. Treasury bills during the past 8 years:

Average Annual Rate of Return

Standard Deviation of Return

Beta

Portfolio X 10% 18% 0.60

S&P 500 12% 13% 1.00

T-bills 6% N/A N/A

1. Calculate the Treynor and Sharpe measures for both portfolio X and the S&P 500. Briefly explain whether portfolio X underperformed, equalled, or outperformed the S&P 500 on a risk-adjusted basis using both the Treynor measure and the Sharpe ratio.

2. On the basis of the performance of portfolio X relative to the S&P 500 calculated in part (a), briefly explain the reason for the conflicting results when using the Treynor measure versus the Sharpe ratio.

3

Problem 6 Assume a 4-year Euro-note, with a $100,000 face value, a coupon rate of 10% and a convexity of 63.29. Today's YTM is 11.5%. Coupon frequency and compounding frequency are assumed to be annual. (a.) What is the duration of this bond? (b.) What is the exact price change in dollars if interest rates decrease by 50 basis points? (c.) Use the duration model to calculate the approximate price change in dollars if interest rates decrease by 50 basis points. (d.) What does convexity measure? Incorporate convexity to calculate the approximate price change in dollars if interest rates decrease by 50 basis points. Problem 7 The WorldValue fund has value weights on asset classes and returns as given in the table below. There are four major asset classes: Europe, Pacific, Emerging and North America. The table also shows the weights and returns of the fund's benchmark portfolio, the World Index.

(a.) How did the World Value fund perform compared with the benchmark, over-performance or under-performance? (b.) Provide a performance attribution of World Value's return in terms of its broad asset class allocation and stock selection relative to the benchmark.