Reading 46: understanding fixed income risk and return Flashcards
The largest component of returns for a 7-year zero-coupon bond yielding 8% and held to maturity is:
capital gains.
interest income.
reinvestment income.
The increase in value of a zero-coupon bond over its life is interest income. A zero-coupon bond has no reinvestment risk over its life. A bond held to maturity has no capital gain or loss. (LOS 46.a)
An investor buys a 10-year bond with a 6.5% annual coupon and a YTM of 6%. Before the first coupon payment is made, the YTM for the bond decreases to 5.5%. Assuming coupon payments are reinvested at the YTM, the investor’s return when the bond is held to maturity is:
less than 6.0%.
equal to 6.0%.
greater than 6.0%.
The decrease in the YTM to 5.5% will decrease the reinvestment income over the life of the bond so that the investor will earn less than 6%, the YTM at purchase. (LOS 46.a)
Assuming coupon interest is reinvested at a bond’s YTM, what is the interest portion of an 18-year, $1,000 par, 5% annual coupon bond’s return if it is purchased at par and held to maturity?
$576.95.
$1,406.62.
$1,476.95.
The interest portion of a bond’s return is the sum of the coupon payments and interest earned from reinvesting coupon payments over the holding period.
N = 18; PMT = 50 ; PV = 0; I/Y = 5%; CPT → FV = –1,406.62
(LOS 46.a)
An investor buys a 15-year, £800,000, zero-coupon bond with an annual YTM of 7.3%. If she sells the bond after three years for £346,333 she will have:
a capital gain.
a capital loss.
neither a capital gain nor a capital loss.
The price of the bond after three years that will generate neither a capital gain nor a capital loss is the price if the YTM remains at 7.3%. After three years, the present value of the bond is 800,000 / 1.07312 = 343,473.57, so she will have a capital gain relative to the bond’s carrying value. (LOS 46.a)
A 14% annual-pay coupon bond has six years to maturity. The bond is currently trading at par. Using a 25 basis point change in yield, the approximate modified duration of the bond is closest to:
0.392.
3.888.
3.970.
V– = 100.979
N = 6; PMT = 14.00; FV = 100; I/Y = 13.75; CPT → PV = –100.979
V+ = 99.035
I/Y = 14.25; CPT → PV = –99.035V0 = 100.000
Δy = 0.0025
approx modified duration= 100.979-99.035/2(100)(0.0025)= 3.888
Which of the following measures is lowest for a callable bond?
Macaulay duration.
Effective duration.
Modified duration.
The interest rate sensitivity of a bond with an embedded call option will be less than that of an option-free bond. Effective duration takes the effect of the call option into account and will, therefore, be less than Macaulay or modified duration. (LOS 46.b)
Effective duration is more appropriate than modified duration for estimating interest rate risk for bonds with embedded options because these bonds:
tend to have greater credit risk than option-free bonds.
exhibit high convexity that makes modified duration less accurate.
have uncertain cash flows that depend on the path of interest rate changes.
Because bonds with embedded options have cash flows that are uncertain and depend on future interest rates, effective duration must be used. (LOS 46.c)
A bond portfolio manager who wants to estimate the sensitivity of the portfolio’s value to changes in the 5-year spot rate should use:
a key rate duration.
a Macaulay duration.
an effective duration.
Key rate duration refers to the sensitivity of a bond or portfolio value to a change in one specific spot rate. (LOS 46.d)
Which of the following three bonds (similar except for yield and maturity) has the least Macaulay duration? A bond with:
5% yield and 10-year maturity.
5% yield and 20-year maturity.
6% yield and 10-year maturity.
Other things equal, Macaulay duration is less when yield is higher and when maturity is shorter. The bond with the highest yield and shortest maturity must have the lowest Macaulay duration. (LOS 46.e)
Portfolio duration has limited usefulness as a measure of interest rate risk for a portfolio because it:
assumes yield changes uniformly across all maturities.
cannot be applied if the portfolio includes bonds with embedded options.
is accurate only if the portfolio’s internal rate of return is equal to its cash flow yield.
Portfolio duration is limited as a measure of interest rate risk because it assumes parallel shifts in the yield curve; that is, the discount rate at each maturity changes by the same amount. Portfolio duration can be calculated using effective durations of bonds with embedded options. By definition, a portfolio’s internal rate of return is equal to its cash flow yield. (LOS 46.f)
The current price of a $1,000, 7-year, 5.5% semiannual coupon bond is $1,029.23. The bond’s price value of a basis point is closest to:
$0.05.
$0.60.
$5.74.
PVBP = initial price – price if yield is changed by 1 basis point.
First, we need to calculate the yield so we can calculate the price of the bond with a 1 basis point change in yield. Using a financial calculator: PV = –1,029.23; FV = 1,000; PMT = 27.5 = (0.055 × 1,000) / 2; N = 14 = 2 × 7 years; CPT → I/Y = 2.49998, multiplied by 2 = 4.99995, or 5.00%.
Next, compute the price of the bond at a yield of 5.00% + 0.01%, or 5.01%. Using the calculator: FV = 1,000; PMT = 27.5; N = 14; I/Y = 2.505 (5.01 / 2); CPT→ PV = $1,028.63.
Finally, PVBP = $1,029.23 – $1,028.63 = $0.60. (LOS 46.g)
A bond has a convexity of 114.6. The convexity effect, if the yield decreases by 110 basis points, is closest to:
–1.673%.
+0.693%.
+1.673%.
Convexity effect = 1⁄ 2 × convexity × (ΔYTM)2 = (0.5)(114.6)(0.011)2 =0.00693 = 0.693%
(LOS 46.h)
The modified duration of a bond is 7.87. The approximate percentage change in price using duration only for a yield decrease of 110 basis points is closest to:
–8.657%.
+7.155%.
+8.657%.
–7.87 × (–1.10%) = 8.657%
(LOS 46.i)
Assume a bond has an effective duration of 10.5 and a convexity of 97.3. Using both of these measures, the estimated percentage change in price for this bond, in response to a decline in yield of 200 basis points, is closest to:
19.05%.
22.95%.
24.89%.
Total estimated price change = (duration effect + convexity effect) {[–10.5 × (–0.02)] + [1⁄ 2 × 97.3 × (–0.02)2]} × 100 = 21.0% + 1.95% = 22.95%
(LOS 46.i)
Two bonds are similar in all respects except maturity. Can the shorter-maturity bond have greater interest rate risk than the longer-term bond?
No, because the shorter-maturity bond will have a lower duration.
Yes, because the shorter-maturity bond may have a higher duration.
Yes, because short-term yields can be more volatile than long-term yields.
In addition to its sensitivity to changes in yield (i.e.,duration), a bond’s interest rate risk includes the volatility of yields. A shorter-maturity bond may have more interest rate risk than an otherwise similar longer-maturity bond if short-term yields are more volatile than long-term yields. (LOS 46.j)
