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55. fixed income risk and return
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The largest component of returns for a 7-year zero-coupon bond yielding 8% and held to maturity is:
A. capital gains.
B. interest income.
C. reinvestment income.
B
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.
An investor buys a 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:
A. less than 6.0%.
B. equal to 6.0%.
C. greater than 6.0%.
A
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.
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:
A. 0.392.
B. 3.888.
C. 3.970.
B
idk.... calc doesnt show the correct answer...
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?
A. $576.95
B. $1,406.62.
C. $1,476.95.
B
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
Effective duration is more appropriate than modified duration for estimating interest rate risk for bonds with embedded options because these bonds:
A. tend to have greater credit risk than option-free bonds.
B. exhibit high convexity that makes modified duration less accurate.
C. have uncertain cash flows that depend on the path of interest rate changes.
C
Because bonds with embedded options have cash flows that are uncertain and depend on future interest rates, effective duration must be used.
Which of the following three bonds (similar except for yield and maturity) has the least Macaulay duration? A bond with:
A. 5% yield and 10-year maturity.
B. 5% yield and 20-year maturity.
C. 6% yield and 1 0-year maturity.
C
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.
Portfolio duration has limited usefulness as a measure of interest rate risk for a portfolio because it:
A. assumes yield changes uniformly across all maturities.
B. cannot be applied if the portfolio includes bonds with embedded options.
C. is accurate only if the portfolio's internal rate of return is equal to its cash flow yield.
A
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.
The current price of a $1,000, seven-year, 5.5% semiannual coupon bond is $1,029.23. The bond's price value of a basis point is closest to:
A. $0.05.
B. $0.60.
C. $5.74.
B
First, use calc to get I/Y of 5%.
Second, add .01% to get 5.01% as I/Y.
Last, find new the PV (in semi annual) and get the difference of 0.6 (1029.23 - 1028.63)
Why is the duration of callable bond less than that of an otherwise identical option-free bond? The value of the call option:
A. increases when YTM increases.
B. decreases when YTM increases.
C. decreases when bond price increases.
B
When the YTM of a callable bond falls, the increase in price is less than for an option free bond because both bond price and the value of the call option increase. Callable bond value = straight bond value- call option value.
Which of the following measures is lowest for a callable bond?
A. Macaulay duration.
B. Effective duration.
C. Modified duration.
B
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.
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:
A. -8.657%.
B. +7.155%.
C. +8.657%.
C
-7.87 x (-1.10%) = 8.657%
A bond has a convexity of 114.6. The convexity effect, if the yield decreases by 110 basis points, is closest to:
A. -1.673%.
B. +0.693%.
C. +1.673%.
B
convexity effect = 1/2 x convexity x ( ΔYTM)^2
= (0.5)(114.6)(0.011)^2 = 0.00693 = 0.693%
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:
A. 19.05%.
B. 22.95%.
C. 24.89%.
B
Total estimated price change = (duration effect + convexity effect)
{[-10.5 x (-0.02)] + [1/2 x 97.3 x (-0.02)2]} x 100 = 21.0% + 1.95% = 22.95%
An investor with an investment horizon of six years buys a bond with a modified duration of 6.0. This investment has:
A. no duration gap.
B. a positive duration gap.
C. a negative duration gap.
B
Duration gap is Macaulay duration minus the investment horizon. Because modified duration equals Macaulay duration / (1 + YTM), Macaulay duration is greater than modified duration for any YTM greater than zero. Therefore, this bond has a Macaulay
Which of the following most accurately describes the relationship between liquidity and yield spreads relative to benchmark government bond rates? All else being equal, bonds with:
A. less liquidity have lower yield spreads.
B. greater liquidity have higher yield spreads.
C. less liquidity have higher yield spreads.
C
The less liquidity a bond has, the higher its yield spread relative to its benchmark. This is because investors require a higher yield to compensate them for giving up liquidity.
An investor buys a 15-year, £800,000, zero-coupon bond with an annual YTM of 7.3%. If she sells the bond after 3 years for £346,333 she will have:
A. a capital gain.
B. a capital loss.
C. neither a capital gain nor loss.
A
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 / 1.073^12 = 343,473.57, so she will have a capital gain relative to the bond's carrying value.
A "buy-and-hold" investor purchases a fixed-rate bond at a discount and holds the security 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
A is correct.
A capital gain is least likely to contribute to the investor's total return. There is no capital gain (or
loss) because the bond is held to maturity. The carrying value of the bond at maturity is par value, the same as the redemption amount. When a fixed-rate bond is held to its maturity, the investor receives the principal payment at maturity. This principal payment is a source of return for the investor. A fixed-rate bond pays periodic coupon payments, and the reinvestment of these coupon payments is a source of return for the investor. The investor's total return is the redemption of principal at maturity and the sum of the reinvested coupons.
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
C is correct.
Because the fixed-rate bond is held to maturity (a ''buy-and-hoId" investor), interest rate risk arises entirely from changes in coupon reinvestment rates. Higher interest rates increase income from reinvestment of coupon payments, and lower rates decrease income from coupon reinvestment. There will not be a capital gain or loss because the bond is held until maturity. The carrying value at the maturity date is par value, the same as the redemption amount. The redemption of principal does not expose the investor to interest rate risk. The risk to a bond's principal is credit risk
An investor purchases a bond at a price above par value. Two years later, the investor sells the bond. The
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.
A is correct.
Capital gains (losses) arise if a bond is sold at a price above (below) its constant-yield price trajectory. A point on the trajectory represents the carrying value of the bond at that time. That is, the capital gain/loss is measured from the bond's carrying value, the point on the constant-yield price trajectory, and not from the original purchase price. The carrying value is the original purchase price plus the amortized amount of
the discount if the bond is purchased at a price below par value. If the bond is purchased at a price above par
value, the carrying value is the original purchase price minus (not plus) the amortized amount of the premium. The amortized amount for each year is the change in the price between two points on the trajectory.
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%. The investor sells the bond after five years. Assume that interest rates remain unchanged at 8% over the five-year holding period.
1. 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.
2. The 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
3. 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%.
4
5
6...... is this really important?
An investor buys a three-year bond with a 5% coupon rate paid annually. The 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.
A
use calc
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.
C is correct
A bond's modified duration cannot be larger than its Macaulay duration. The formula for modified
duration is:
ModDur = MacDur 1 + r
ModDur = MacDur / (1 + r)
where r is the bond's yield-to-maturity per period. A bond's yield-to-maturity has an effective lower bound of 0, and thus the denominator 1 + r term has a lower bound of 1. Therefore, ModDur will typically be less than MacDur.
Effective duration is a measure of curve duration. Modified duration is a measure of yield duration.
An investor buys a 6% annual payment bond with three years to maturity. The bond has a yield-to-maturity of
8% and is currently priced at 94.845806 per 100 of par. The bond's Macaulay duration is closest to:
A. 2.62.
B. 2.78.
C. 2.83.
C
Find mdur from calc and use this formula:
Mod Dur = Mac Dur * (1+YTM / period)
2.62 = Mac Dur * (1+.08 / 1)
The 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
A is correct.
The interest rate risk of a fixed-rate bond with an embedded call option is best measured by effective
duration. A callable bond's future cash flows are uncertain because they are contingent on future interest rates. The issuer's decision to call the bond depends on future interest rates. Therefore, the yield-to-maturity on a callable bond is not well defined. Only effective duration, which takes into consideration the value of the call option, is the appropriate interest rate risk measure. Yield durations like Macaulay and modified durations are not relevant for a callable bond because they assume no changes in cash flows when interest rates change.
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
A is correct.
Key rate duration is used to measure a bond's sensitivity to a shift at one or more maturity segments
of the yield curve which result in a change to yield curve shape. Modified and effective duration measure a
bond's sensitivity to parallel shifts in the entire curve.
A Canadian pension fund manager seeks to measure the sensitivity of her pension liabilities to market interest rate changes. The 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%. The results of the manager's analysis are presented below:
Interest Rate Assumption ===Present Value of Liabilities
6% ======================CAD 510.1 million
7% ======================CAD 455.4 million
8% ======================CAD 373.6 million
The effective duration of the pension fund's liabilities is closest to:
A. 1.49.
B. 14.99.
C. 29.97.
B
(PV-) - (PV+) / (2
curve
PV0) = eff dur
(510.1 - 373.6) / (2
.01
455.4) = 14.99
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. The Macaulay duration of a zero-coupon bond is less than its time-to-maturity.
B is correct.
A bond's yield-to-maturity is inversely related to its Macaulay duration: The higher the yield-to maturity, the low'er its Macaulay duration and the lower the interest rate risk. A higher yield-to-maturity decreases the weighted average of the times to the receipt of cash flow, and thus decreases the Macaulay duration.
A bond's coupon rate is inversely related to its Macaulay duration: The lower the coupon, the greater the weight of the payment of principal at maturity. This results in a higher Macaulay duration. Zero-coupon bonds do not pay periodic coupon payments; therefore, the Macaulay duration of a zero-coupon bond is its time-to-maturity.
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.
A is correct.
The presence of an embedded put option reduces the effective duration of the bond, especially when
rates are rising. If interest rates are low compared with the coupon rate, the value of the put option is low and the impact of the change in the benchmark yield on the bond's price is very similar to the impact on the price of a non-putable bond. But when benchmark interest rates rise, the put option becomes more valuable to the investor. The ability to sell the bond at par value limits the price depreciation as rates rise. The presence of an embedded put option reduces the sensitivity of the bond price to changes in the benchmark yield, assuming no change in credit risk.
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
A ========6 years =====170,000 =========85
B ========10 years ====120,000 =========80
C ========15 years ====100,000 =========100
Coupon =====YTM ======Modified Duration
2.00% =======4.95%===== 5.42
2.40% =======4.99%===== 8.44
5.00% =======5.00%===== 10.38
The bond portfolio's modified duration is closest to:
A. 7.62.
B. 8.08.
C. 8.20.
A
Portfolio dur = D1
weight + D2
weight + ......
5.42
(170k / 390k) + 8.44
(120k / 390k) + 10.38*(100k/390k) = 7.62
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.
A is correct.
A limitation of calculating a bond portfolio's duration as the weighted average of the yield durations of the individual bonds is that this measure implicitly assumes a parallel shift to the yield curve (all rates change by the same amount in the same direction). In reality, interest rate changes frequently result in a steeper or flatter yield curve. This approximation of the "theoretically correct" portfolio duration is more accurate when the yield curve is flatter (less steeply sloped). An advantage of this approach is that it can be used with portfolios that include bonds with embedded options. Bonds with embedded options can be included in the weighted average using the effective durations for these securities.
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 ====Maturity ====Price
A ========6 years =====85
B ========10 years ====80
C ========9 years =====100
Coupon ======YTM ======Modified Duration
2.00% =======4.95%===== 5.42
2.40% =======4.99%===== 8.44
5.00% =======5.00%===== 10.38
A. Bond A
B. Bond B
C. Bond C
B is correct.
Bond B has the greatest money duration per 100 of par value. Money duration (MoneyDur) is calculated as the annual modified duration (AnnModDur) times the full price (PV full ) of the bond including accrued interest. Bond B has the highest money duration per 100 of par value.
MoneyDur = AnnModDur x PV full
MoneyDur ofBond A = 5.42 x 85.00 = 460.70
MoneyDur ofBond B = 8.44 x 80.00 = 675.20
MoneyDur of Bond C = 7.54 x 85.78 = 646.78
A bond with exactly nine years remaining until maturity offers a 3% coupon rate with annual coupons. The bond, with a yield-to-maturity of 5%, is priced at 85.784357 per 100 of par value. The estimated price value of a basis point for the bond is closest to:
A. 0.0086.
B. 0.0648.
C. 0.1295
B
PVBP = ( P V —) — (P V + ) 2
use calc with I/Y=4.99 and get PV = 85.849134
PVBP = (85.849134-85.719638) / 2
The "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
B is correct
Convexity measures the "second order" effect on a bond's percentage price change given a change in yield-to-maturity. Convexity adjusts the percentage price change estimate provided by modified duration to better approximate the true relationship between a bond's price and its yield-to-maturity which is a curved line (convex).
Duration estimates the change in the bond's price along the straight line that is tangent to this curved line ("first
order" effect). Yield volatility measures the magnitude of changes in the yields along the yield curve
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. The bond's approximate convexity is closest to:
A. 0.071.
B. 70.906.
C. 1,144.628
B
ApproxCon = [98.782 + 98.669 - (2 x 98.722)] / (0.001^2 x 98.722) = 70.906
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%.
C
[—AnnModDur x ΔYield] +[0.5 x AnnConvexity x (ΔYield)^2]
[-7.020
(-0.0025)] + [0.5
65.180 * (-0.0025)^2] = 0.017754, or 1.78%
A bond has an annual modified duration of 7.140 and annual convexity of 66.200. The bond's yield-to-maturity is expected to increase by 50 basis points. The expected percentage price change is closest to:
A. —3.40%.
B. -3.49%.
C. -3.57%
B
[—AnnModDur x ΔYield] +[0.5 x AnnConvexity x (ΔYield)^2]
[—7.140
0.005] + [0.5
* 66.200 * (0.005)^2] = -0.034873, or -3.49%
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 fluctuation than long-term bonds.
B is correct
If the term structure of yield volatility is downward-sloping, then short-term bond yields-to-maturity
have greater volatility than for long-term bonds. Therefore, long-term yields are more stable than short-term yields. Higher volatility in short-term rates does not necessarily mean that the level of short-term rates is higher than long-term rates. With a downward-sloping term structure of yield volatility, short-term bonds will not always experience greater price fluctuation than long-term bonds. The estimated percentage change in a bond price depends on the modified duration and convexity as w'ell as on the yield-to-maturity change.
The holding period fora 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.
C is correct
When the holder of a bond experiences a one-time parallel shift in the yield curve, the Macaulay
duration statistic identifies the number of years necessary to hold the bond so that the losses (or gains) from coupon reinvestment offset the gains (or losses) from market price changes. The duration gap is the difference between the Macaulay duration and the investment horizon. Modified duration approximates the percentage price change of a bond given a change in its yield-to-maturity.
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.
C is correct
The duration gap is equal to the bond's Macaulay duration minus the investment horizon. In this
case, the duration gap is positive, and price risk dominates coupon reinvestment risk. The investor risk is to higher rates.
The investor is hedged against interest rate risk if the duration gap is zero; that is, the investor's investment
horizon is equal to the bond's Macaulay duration. The investor is at risk of lower rates only if the duration gap is negative; that is, the investor's investment horizon is greater than the bond's Macaulay duration. In this case,
coupon reinvestment risk dominates market price risk.
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. The investor's investment horizon is eight years. The approximate
modified duration of the bond is 11.470 years. The duration gap at the time of purchase is closest to:
A. -7.842.
B. 3.470.
C. 4.158.
C is correct
The duration gap is closest to 4.158.
The duration gap is a bond's Macaulay duration minus the investment horizon.
The approximate Macaulay duration is the approximate modified duration times one plus the yield-to-maturity. It is 12.158 (= 11.470 x 1.06).
Given an investment horizon of eight years, the duration gap for this bond at purchase is positive: 12.158 —8 = 4.158. When the investment horizon is less than the Macaulay duration of the bond, the duration gap is positive, and price risk dominates coupon reinvestment risk.
A manufacturing company receives a ratings upgrade and the price increases on its fixed-rate bond. The 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.
A is correct.
The price increase was most likely caused by a decrease in the bond's credit spread. The ratings upgrade most likely reflects a lower expected probability of default and/or a greater level of recovery of assets if default occurs. The decrease in credit risk results in a smaller credit spread. The increase in the bond price reflects a decrease in the yield-to-maturity due to a smaller credit spread. The change in the bond price was not due to a change in liquidity risk or an increase in the benchmark rate.
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