21
CHAPTER 4
UNDERSTANDING
FIXED‑INCOME RISK
AND RETURN
PROBLEMS
ese questions were developed by Danny Hassett, CFA (Cedar Hill, TX, USA), Lou Lemos,
CFA Institute.
1. A “buy-and-hold” investor purchases a fixed-rate bond at a discount and holds the securi-
ty until it matures. Which of the following sources of return is least likely to contribute to
the investor’s total return over the investment horizon, assuming all payments are made as
scheduled?
A. Capital gain
B. Principal payment
C. Reinvestment of coupon payments
2. Which of the following sources of return is most likely exposed to interest rate risk for an
investor of a fixed-rate bond who holds the bond until maturity?
A. Capital gain or loss
B. Redemption of principal
C. Reinvestment of coupon payments
3. An investor purchases a bond at a price above par value. Two years later, the investor sells
the bond. e resulting capital gain or loss is measured by comparing the price at which
the bond is sold to the:
A. carrying value.
B. original purchase price.
C. original purchase price value plus the amortized amount of the premium.
22 Part I: Learning Objectives, Summary Overview, and Problems
e following information relates to Problems 4–6
An investor purchases a nine-year, 7% annual coupon payment bond at a price equal to par
value. After the bond is purchased and before the first coupon is received, interest rates increase
to 8%. e investor sells the bond after five years. Assume that interest rates remain unchanged
at 8% over the five-year holding period.
4. Per 100 of par value, the future value of the reinvested coupon payments at the end of the
holding period is closest to:
A. 35.00.
B. 40.26.
C. 41.07.
5. e capital gain/loss per 100 of par value resulting from the sale of the bond at the end of
the five-year holding period is closest to a:
A. loss of 8.45.
B. loss of 3.31.
C. gain of 2.75.
6. Assuming that all coupons are reinvested over the holding period, the investor’s five-year
horizon yield is closest to:
A. 5.66%.
B. 6.62%.
C. 7.12%.
7. An investor buys a three-year bond with a 5% coupon rate paid annually. e bond, with
a yield-to-maturity of 3%, is purchased at a price of 105.657223 per 100 of par value.
Assuming a 5-basis point change in yield-to-maturity, the bond’s approximate modified
duration is closest to:
A. 2.78.
B. 2.86.
C. 5.56.
8. Which of the following statements about duration is correct? A bond’s:
A. effective duration is a measure of yield duration.
B. modified duration is a measure of curve duration.
C. modified duration cannot be larger than its Macaulay duration.
9. An investor buys a 6% annual payment bond with three years to maturity. e bond has
a yield-to-maturity of 8% and is currently priced at 94.845806 per 100 of par. e bond’s
Macaulay duration is closest to:
A. 2.62.
B. 2.78.
C. 2.83.
10. e interest rate risk of a fixed-rate bond with an embedded call option is best measured by:
A. effective duration.
B. modified duration.
C. Macaulay duration.
11. Which of the following is most appropriate for measuring a bond’s sensitivity to shaping
risk?
A. Key rate duration
B. Effective duration
C. Modified duration
Chapter 4 Understanding Fixed‑Income Risk and Return 23
12. A Canadian pension fund manager seeks to measure the sensitivity of her pension lia-
bilities to market interest rate changes. e manager determines the present value of the
liabilities under three interest rate scenarios: a base rate of 7%, a 100 basis-point increase
in rates up to 8%, and a 100 basis-point drop in rates down to 6%. e results of the
manager’s analysis are presented below:
Interest Rate Assumption Present Value of Liabilities
6% CAD510.1 million
7% CAD455.4 million
8% CAD373.6 million
e effective duration of the pension fund’s liabilities is closest to:
A. 1.49.
B. 14.99.
C. 29.97.
13. Which of the following statements about Macaulay duration is correct?
A. A bond’s coupon rate and Macaulay duration are positively related.
B. A bond’s Macaulay duration is inversely related to its yield-to-maturity.
C. e Macaulay duration of a zero-coupon bond is less than its time-to-maturity.
14. Assuming no change in the credit risk of a bond, the presence of an embedded put option:
A. reduces the effective duration of the bond.
B. increases the effective duration of the bond.
C. does not change the effective duration of the bond.
15. A bond portfolio consists of the following three fixed-rate bonds. Assume annual coupon
payments and no accrued interest on the bonds. Prices are per 100 of par value.
Bond Maturity
Market
Value Price Coupon
Yield-to-
Maturity
Modified
Duration
A 6 years 170,000 85.0000 2.00% 4.95% 5.42
B 10 years 120,000 80.0000 2.40% 4.99% 8.44
C 15 years 100,000 100.0000 5.00% 5.00% 10.38
e bond portfolio’s modified duration is closest to:
A. 7.62.
B. 8.08.
C. 8.20.
16. A limitation of calculating a bond portfolio’s duration as the weighted average of the yield
durations of the individual bonds that compose the portfolio is that it:
A. assumes a parallel shift to the yield curve.
B. is less accurate when the yield curve is less steeply sloped.
C. is not applicable to portfolios that have bonds with embedded options.
24 Part I: Learning Objectives, Summary Overview, and Problems
17. Using the information below, which bond has the greatest money duration per 100 of par
value assuming annual coupon payments and no accrued interest?
Bond
Time-to-
Maturity
Price Per 100
of Par Value Coupon Rate
Yield-to-
Maturity
Modified
Duration
A 6 years 85.00 2.00% 4.95% 5.42
B 10 years 80.00 2.40% 4.99% 8.44
C 9 years 85.78 3.00% 5.00% 7.54
A. Bond A
B. Bond B
C. Bond C
18. A bond with exactly nine years remaining until maturity offers a 3% coupon rate with
annual coupons. e bond, with a yield-to-maturity of 5%, is priced at 85.784357 per
100 of par value. e estimated price value of a basis point for the bond is closest to:
A. 0.0086.
B. 0.0648.
C. 0.1295.
19. e “second-order” effect on a bond’s percentage price change given a change in
yield-to-maturity can be best described as:
A. duration.
B. convexity.
C. yield volatility.
20. A bond is currently trading for 98.722 per 100 of par value. If the bond’s yield-to-maturity
(YTM) rises by 10 basis points, the bond’s full price is expected to fall to 98.669. If the
bond’s YTM decreases by 10 basis points, the bond’s full price is expected to increase to
98.782. e bond’s approximate convexity is closest to:
A. 0.071.
B. 70.906.
C. 1,144.628.
21. A bond has an annual modified duration of 7.020 and annual convexity of 65.180. If
the bond’s yield-to-maturity decreases by 25 basis points, the expected percentage price
change is closest to:
A. 1.73%.
B. 1.76%.
C. 1.78%.
22. A bond has an annual modified duration of 7.140 and annual convexity of 66.200. e
bond’s yield-to-maturity is expected to increase by 50 basis points. e expected percent-
age price change is closest to:
A. –3.40%.
B. –3.49%.
C. –3.57%.
23. Which of the following statements relating to yield volatility is most accurate? If the term
structure of yield volatility is downward sloping, then:
A. short-term rates are higher than long-term rates.
B. long-term yields are more stable than short-term yields.
C. short-term bonds will always experience greater price uctuation than long-term
bonds.
Chapter 4 Understanding Fixed‑Income Risk and Return 25
24. e holding period for a bond at which the coupon reinvestment risk offsets the market
price risk is best approximated by:
A. duration gap.
B. modified duration.
C. Macaulay duration.
25. When the investor’s investment horizon is less than the Macaulay duration of the bond
she owns:
A. the investor is hedged against interest rate risk.
B. reinvestment risk dominates, and the investor is at risk of lower rates.
C. market price risk dominates, and the investor is at risk of higher rates.
26. An investor purchases an annual coupon bond with a 6% coupon rate and exactly 20 years
remaining until maturity at a price equal to par value. e investor’s investment horizon is
eight years. e approximate modified duration of the bond is 11.470 years. e duration
gap at the time of purchase is closest to:
A. –7.842.
B. 3.470.
C. 4.158.
27. A manufacturing company receives a ratings upgrade and the price increases on its fixed-
rate bond. e price increase was most likely caused by a(n):
A. decrease in the bond’s credit spread.
B. increase in the bond’s liquidity spread.
C. increase of the bond’s underlying benchmark rate.