Reading 53- Introduction to Fixed-Income Valuation
(implied) forward rate p. 425
Forward rates can be defined as the way the market is feeling about the future movements of interest rates. They do this by extrapolating from the risk-free theoretical spot rate. For example, it is possible to calculate the one-year forward rate one year from now. 2y5y= five year yield two years into the future
yield spread: bond YTM differ due to different
-credit risk -liquidity risk -tax status -periodicity (annual, semiannual, quarterly, etc.)
Which of the following statements about duration is NOT correct A) Effective duration is the exact change in price due to a 100 basis point change in rates. B) For a specific bond, the effective duration formula results in a value of 8.80%. For a 50 basis point change in yield, the approximate change in price of the bond would be 4.40%. C) The numerator of the effective duration formula assumes that market rates increase and decrease by the same number of basis points.
A Effective duration is an approximation because the duration calculation ignores the curvature in the price/yield graph.
A non-callable bond with 10 years remaining maturity has an annual coupon of 5.5% and a $1,000 par value. The current yield to maturity on the bond is 4.7%. Which of the following is closest to the estimated price change of the bond using duration if rates rise by 75 basis points? A) -$61.10. B) -$47.34. C) -$5.68.
A First, compute the current price of the bond as: FV = 1,000; PMT = 55; N = 10; I/Y = 4.7; CPT → PV = -1,062.68. Then compute the price of the bond if rates rise by 75 basis points to 5.45% as: FV = 1,000; PMT = 55; N = 10; I/Y = 5.45; CPT → PV = -1,003.78. Then compute the price of the bond if rates fall by 75 basis points to 3.95% as: FV = 1,000; PMT = 55; N = 10; I/Y = 3.95; CPT → PV = -1,126.03. The formula for effective duration is: (V--V+) / (2V0Δy). Therefore, effective duration is: ($1,126.03 - $1,003.78) / (2 × $1,062.68 × 0.0075) = 7.67. The formula for the percentage price change is then: -(duration)(Δy). Therefore, the estimated percentage price change using duration is: -(7.67)(0.75%) = -5.75%. The estimated price change is then: (-0.0575)($1,062.68) = -$61.10
Negative convexity for a callable bond is most likely to be important when the: A) price of the bond approaches the call price. B) bond is first issued. C) market interest rate rises above the bond's coupon rate.
A Negative convexity illustrates how the relationship between the price of a bond and market yields changes as the bond price rises and approaches the call price. The convex curve that we generally see for non-callable bonds bends backward to become concave (i.e., exhibit negative convexity) as the bond approaches the call price.
Consider an annual coupon bond with the following characteristics: Face value of $100 Time to maturity of 12 years Coupon rate of 6.50% Issued at par Call price of 101.75 (assume the bond price will not exceed this price) For a 75 basis point change in interest rates, the bond's duration is: A) 5.09 years. B) 8.79 years. C) 8.17 years.
A Since the bond has an embedded option, we will use the formula for effective duration. (This formula is the same as the formula for modified duration, except that the "upper price bound" is replaced by the call price.) Thus, we only need to calculate the price if the yield increases 75 basis points, or 0.75%. Price if yield increases 0.75%: FV = 100; I/Y = 6.50 + 0.75 = 7.25; N = 12; PMT = 6.5; CPT → PV = 94.12The formula for effective duration is Where: V- = call price/price ceiling V+ = estimated price if yield increases by a given amount, Dy V0 = initial observed bond price Dy = change in required yield, in decimal form Here, effective duration = (101.75 - 94.12) / (2 × 100 × 0.0075) = 7.63 / 1.5 = 5.09 years.
How does the price-yield relationship for a putable bond compare to the same relationship for an option-free bond? The price-yield relationship is: A) more convex at some yields for the putable bond than for the option-free bond. B) the same for both bond types. C) more convex for a putable bond than for an option-free bond.
A Since the holder of a putable has an incentive to exercise his put option if yields are high and the bond price is depressed, this puts a lower limit on the price of the bond when interest rates are high. The lower limit introduces a higher convexity of the putable bond compared to an option-free bond when yields are high.
Which of the following statements on spreads is NOT correct? A) The Z-spread may be used for bonds that contain call options. B) The Z-spread will equal the nominal spread if the term structure of interest rates is flat. C) The option-adjusted spread (OAS) is the difference between the Z-spread and the option cost.
A The Z-spread is used for risky bonds that do NOT contain call options in an attempt to improve on the shortcomings of the nominal spread. The other statements are correct.
When calculating duration, which of the following bonds would an investor least likely use effective duration on rather than modified duration? A) Option-free bond. B) Callable bond. C) Convertible bond.
A The duration computation remains the same. The only difference between modified and effective duration is that effective duration is used for bonds with embedded options. Modified duration assumes that all the cash flows on the bond will not change, while effective duration considers expected cash flow changes that may occur with embedded options.
Consider a bond with a duration of 5.61 and a convexity of 21.92. Which of the following is closest to the estimated percentage price change in the bond for a 75 basis point decrease in interest rates? A) 4.33%. B) 4.21%. C) 4.12%.
A The estimated percentage price change is equal to the duration effect plus the convexity effect. The formula is: [-duration × (Δy)] + [convexity × (Δy)2]. Therefore, the estimated percentage price change is: [-(5.61)(-0.0075)] + [(21.92)(-0.0075)2] = 0.042075 + 0.001233 = 0.043308 = 4.33%.
Given the following spot and forward rates, how much should an investor pay for each $100 of a 3-year, annual zero-coupon bond? One-year spot rate is 3.75% The 1-year forward rate 1 year from today is 9.50% The 1-year forward rate 2 years from today is 15.80% The investor should pay approximately: A) $76. B) $44. C) $83.
A The yield to maturity on an N-year zero coupon bond is equivalent to the N-year spot rate. Thus, to determine the present value of the zero-coupon bond, we need to calculate the 3-year spot rate. Using the formula: (1 + Z3)3 = (1 + 1f0)(1 + 1f1)(1 + 1f2) where Z = spot rate and nfm = the n year rate m periods from today, (1f0 = the 1 year spot rate now). (1 + Z3)3 = (1.0375) × (1.095) × (1.158) Z3 = 1.3155601/3 − 1 = 0.095730, or 9.57% Then, the value of the zero coupon bond = 100 / (1.09573)3 = 76.01, or approximately $76, or, using a financial calculator, N = 3; I/Y = 9.57; FV = 1,000; PMT = 0; CPT → PV = 76.20 or approximately $76.
If a put feature expires on a bond so that it becomes option-free, then the curve depicting the price and yield relationship of the bond will become: A) less convex. B) more convex. C) inversely convex.
A When the option expires, the prices at the lower end of the curve will become lower. This will make the curve less convex.
A $1,000 face, 10-year, 8.00% semi-annual coupon, option-free bond is issued at par (market rates are thus 8.00%). Given that the bond price decreased 10.03% when market rates increased 150 basis points (bp), which of the following statements is CORRECT? If market yields: A) decrease by 150bp, the bond's price will decrease by more than 10.03%. B) decrease by 150bp, the bond's price will increase by more than 10.03%. C) decrease by 150bp, the bond's price will increase by 10.03%.
B All other choices are false because of positive convexity - bond prices rise faster than they fall. Positive convexity applies to both dollar and percentage price changes. For any given absolute change in yield, the increase in price will be more than the decrease in price for a fixed-coupon, noncallable bond. As yields increase, bond prices fall, and the price curve gets flatter, and changes in yield have a smaller effect on bond prices. As yields decrease, bond prices rise, and the price curve gets steeper, and changes in yield have a larger effect on bond prices. Here, for an absolute 150bp change, the price increase would be more than the price decrease. For a 100bp increase, the price decrease would be less than that for a 150bp increase.
The price value of a basis point (PVBP) of a bond is $0.75. If the yield on the bond goes up by 1 bps, the price of the bond will: A) increase by $0.75. B) decline by $0.75. C) increase or decrease by $0.75.
B Inverse relationships exist between price and yields on bonds. The larger the PVBP, the more volatile the bond's price.
Convexity is important because: A) it measures the volatility of non-callable bonds. B) the slope of the price/yield curve is not linear. C) the slope of the callable bond price/yield curve is backward bending at high interest rates.
B Modified duration is a good approximation of price changes for an option-free bond only for relatively small changes in interest rates. As rate changes grow larger, the curvature of the bond price/yield relationship becomes more prevalent, meaning that a linear estimate of price changes will contain errors. The modified duration estimate is a linear estimate, as it assumes that the change is the same for each basis point change in required yield. The error in the estimate is due to the curvature of the actual price path. This is the degree of convexity. If we can generate a measure of this convexity, we can use this to improve our estimate of bond price changes.
How does the price-yield relationship for a callable bond compare to the same relationship for an option-free bond? The price-yield relationship is: A) concave for the callable bond and convex for an option-free bond. B) concave for low yields for the callable bond and always convex for the option-free bond. C) the same for both bond types.
B Since the issuer of a callable bond has an incentive to call the bond when interest rates are very low in order to get cheaper financing, this puts an upper limit on the bond price for low interest rates and thus introduces the concave relationship between yields and prices
With market interest rates at 6%, an analyst observes a 5-year, 5% coupon, $1,000 par value callable bond selling for $950. At the same time the analyst observes a non-callable bond, identical in all other respects to the callable bond, selling for $980. The analyst should estimate that the value of the call option on the callable bond is closest to: A) $50. B) $30. C) $20.
B The difference in price between the two bonds is the value of the option: $980 − $950 = $30.
In comparing the price volatility of putable bonds to that of option-free bonds, a putable bond will have: A) less price volatility at low yields. B) less price volatility at higher yields. C) more price volatility at higher yields.
B The only true statement is that putable bonds will have less price volatility at higher yields. At higher yields the put becomes more valuable and reduces the decline in price of the putable bond relative to the option-free bond. On the other hand, when yields are low, the put option has little or no value and the putable bond will behave much like an option-free bond. Therefore at low yields a putable bond will not have more price volatility nor will it have less price volatility than a similar option-free bond.
Assume that a straight bond has a duration of 1.89 and a convexity of 15.99. If interest rates decline by 1% what is the total estimated percentage price change of the bond? A) 1.56%. B) 2.05%. C) 1.89%.
B The total percentage price change estimate is computed as follows: Total estimated price change = -1.89 × (-0.01) × 100 + 15.99 × (-0.01)2 × 100 = 2.05%
Assume an option-free 5% coupon bond with annual coupon payments has two years remaining to maturity. A putable bond that is the same in every respect as the option-free bond is priced at 101.76. With the term structure flat at 6% what is the value of the embedded put option? A) 1.76. B) 3.59. C) -3.59.
B The value of the embedded put option of the putable bond is the difference between the price of the putable bond and the price of the option-free bond. The value of the option-free bond is computed as follows: PMT = 5; N = 2; FV = 100; I = 6; CPT → PV = -98.17(ignore sign). The option value = 101.79 − 98.17 = 3.59.
The zero volatility spread (Z-spread) is the spread that: A) is added to the yield to maturity of a similar maturity Treasury bond to equal the yield to maturity of the risky bond. B) is added to each spot rate on the Treasury yield curve that will cause the present value of the bond's cash flows to equal its market price. C) results when the cost of the call option in percent is subtracted from the option adjusted spread.
B The zero volatility spread (Z-spread) is the interest rate that is added to each zero-coupon bond spot rate that will cause the present value of the risky bond's cash flows to equal its market value. The nominal spread is the spread that is added to the YTM of a similar maturity Treasury bond that will then equal the YTM of the risky bond. The zero volatility spread (Z-spread) is the spread that results when the cost of the call option in percent is added to the option adjusted spread.
Consider two bonds, A and B. Both bonds are presently selling at par. Each pays interest of $120 annually. Bond A will mature in 5 years while bond B will mature in 6 years. If the yields to maturity on the two bonds change from 12% to 10%, both bonds will: A) increase in value, but bond A will increase more than bond B. B) increase in value, but bond B will increase more than bond A. C) decrease in value, but bond B will decrease more than bond A.
B There are three features that determine the magnitude of the bond price volatility: 1.The lower the coupon, the greater the bond price volatility. 2.The longer the term to maturity, the greater the price volatility. 3.The lower the initial yield, the greater the price volatility. Since both of these bonds are the same with the exception of the term to maturity, the bond with the longer term to maturity will have a greater price volatility. Since bond value has an inverse relationship with interest rates, when interest rates decrease bond value increases.
add-on rate
Bank CD's, repos, indices such as Libor and Euribor PV= FV/ (1+ days/year*AOR)
Which of the following is most accurate about a bond with positive convexity? A) Positive changes in yield lead to positive changes in price. B) Price increases and decreases at a faster rate than the change in yield. C) Price increases when yields drop are greater than price decreases when yields rise by the same amount.
C A convex price/yield graph has a larger increase in price as yield decreases than the decrease in price when yields increase. This comes from the definition of a convex graph.
Jayce Arnold, a CFA candidate, is studying how the market yield environment affects bond prices. She considers a $1,000 face value, option-free bond issued at par. Which of the following statements about the bond's dollar price behavior is most likely accurate when yields rise and fall by 200 basis points, respectively? Price will: A) increase by $149, price will decrease by $124. B) decrease by $149, price will increase by $124. C) decrease by $124, price will increase by $149.
C As yields increase, bond prices fall, the price curve gets flatter, and changes in yield have a smaller effect on bond prices. As yields decrease, bond prices rise, the price curve gets steeper, and changes in yield have a larger effect on bond prices. Thus, the price increase when interest rates decline must be greater than the price decrease when interest rates rise (for the same basis point change). Remember that this applies to percentage changes as well.
The price value of a basis point (PVBP) for a 7-year, 10% semiannual pay bond with a par value of $1,000 and yield of 6% is closest to: A) $0.92. B) $0.28. C) $0.64.
C PVBP = initial price - price if yield changed by 1 bps. Initial price: Price with change: FV = 1000 FV = 1000 PMT = 50 PMT = 50 N = 14 N = 14 I/Y = 3% I/Y = 3.005 CPT PV = 1225.92 CPT PV = 1225.28 PVBP = 1,225.92 - 1,225.28 = 0.64 PVBP is always the absolute value.
Suppose you have a three-security portfolio containing bonds A, B and C. The effective portfolio duration is 5.9. The market values of bonds A, B and C are $60, $25 and $80, respectively. The durations of bonds A and C are 4.2 and 6.2, respectively. Which of the following amounts is closest to the duration of bond B? A) 7.4. B) 1.4. C) 9.0.
C Plug all the known figures and then solve for the one unknown figure, the duration of bond B. Proof: (60/165 × 4.2) + (25/165 × 9.0) + (80/165 × 6.2) = 5.9
bond price=
PV= PMT/(1+r) + PMT/(1+r)^2 + ... + (PMT+FV)/(1+r)^n
Z-spread p. 430
PV= PMT/(1+z1+Z)^1 + PMT/(1+z2+Z)^2 + ... + (PMT+FV)/(1+zn+Z)^n calculate a constant yield spread over a government spot curve and add it to the spot rate
par curve
a sequence of yields to maturity such that each bond is priced at par value
forward curve
above government spot yield curve graphs the forward rates, breakeven reinvestment rate
There will be a capital gain if a bond is purchased
below its par value
discount rate basis
commercial paper, T-bills, bankers' acceptances quoted on discount rate basis
Bond Selling at Discount
coupon rate < YTM market discount rate (inverse effect)
Bond Selling at Premium
coupon rate > YTM market discount rate (inverse effect)
Bond Selling at Par
coupon rate= YTM market discount rate
Holding maturity & YTM constant, bonds selling at a premium will be more
dependent on reinvestment income than bonds selling at par
spread
difference between yield to maturity (microeconomic factors such as credit risk and quality) and benchmark (macroeconomic factors such as expected rate of inflation) yield spread is the risk premium over the risk-free rate of return
matrix pricing p. 407 example
estimate the YTM required rate of return by investors by averaging out two different required YTMs 1. find r (YTM) of Bond A 2. find r (YTM) of Bond B 3. average (YTM A + YTM B)/2 4. use the average YTM to estimate the price of the illiquid bond
discount margin
estimates average margin over the reference rate that the investor can expect to earn over the life of the security Floating Rate Notes
forward rate
f= (1+z2)^2/(1+z1) - 1
coupon effect: a lower-coupon bond has a _____ % change than a higher-coupon bond
greater (lower coupon bonds have higher price volatility than higher coupon bonds)
constant-yield price trajectory
if issuer doesn't default, price of bond approaches par value as time to maturity approaches zero
yield to maturity
internal rate of return on cash flows such that when future cash flows are discounted at that rate, the sum of the present values equals the price of the bond
I-spread
interpolated spread yield spread of a specific bond over the standard swap rate in that currency (yield spread over LIBOR)
Yield to call assumes that
investor will hold the bond to the assumed call date issuer will call the bond on that date
yield on a discount basis
limitation= based on maturity value investment rather than actual dollar amount invested
Yield to worst p. 412
lowest of the sequence of yields-to-call & yield-to-maturity worst yield out of a possible range. gives investor a conservative estimate of the rate of return
convexity effect: for the same coupon rate & time-to-maturity, the percentage price change is greater when
market discount rate goes down than when it goes up
bond equivalent yield
money market rate stated on a 365-day add-on rate basis
For a given YTM and non-zero coupon rate, the longer the maturity, the
more the bond's total dollar return depends on reinvestment income to realize the yield to maturity at the time of purchase (the greater the reinvestment risk)
For zero-coupon bonds, ____ is dependent on reinvestment income
none of the bond's total dollar return
drawback of the current yield
only considers the coupon interest and no other source for investor's return
There will be a capital gain for a CALLABLE bond if
price at which bond is called is greater than purchase price
Treasury Yield Curve government spot (zero, strip) yield curve
sequence of yields for 0-coupon bonds upward sloping & flattens the longer the maturity longer term bonds usually have higher yields than short-term bonds government bonds have the same currency, credit risk, liquidity, and tax status & no reinvestment risk
maturity effect: a longer-term bond has a greater percentage price change than
shorter-term bond
z spread curve
spread that when added to each spot rate on the yield curve makes the present value of the bonds cash flows equal to the bonds market price - assumes interest rate vol is 0 *It represents a spread to compensate for the non-Treasury security's credit risk, liquidity risk, and any option risk
flat price p. 403
takes into account accrued interest, *bond dealers quote the flat price* PV full (dirty price)= PV flat (clean) + Accrued Interest Accrued Interest= t/T*PMT t/T= fraction of coupon period that has gone by since last payment, or (# days between last coupon date- settlement date)/ # days in coupon period PMT/2 for semiannual coupon actual/actual for government bonds 30/360 for corporate bonds PV full= PV*(1+r)^(t/T)
Which bond will go down in price the least (in % terms)?
the bond with highest coupon rate + shorter time to maturity
Which bond will go up in price the most (in % terms)?
the bond with lowest coupon rate + longer time to maturity
option-adjusted price
value of the embedded call option + flat price of bond
G-spread
yield spread in bps over a government bond
spot rate
yields on maturity on zero-coupon bonds maturing at date of each cash flow one-year spot rate= 2% two-year spot rate= 3% three-year spot rate= 4% price of bond= 5/(1.02)^1 + 5/(1.03)^2 + 5/(1.04)^3
What kind of payment does a zero-coupon bond return?
zero periodic coupon interest payment because investor purchases security BELOW par value and receives full par value at maturity so essentially, this is a lump-sum payment.
Relationships between Bond Price and Bond Characteristics:
1. The bond price is inversely related to the market discount rate. When the market discount rate increases, the bond price decreases (the inverse effect). 2. For the same coupon rate and time-to-maturity, the percentage price change is greater (in absolute value, meaning without regard to the sign of the change) when the market discount rate goes down than when it goes up (the convexity effect). 3. For the same time-to-maturity, a lower-coupon bond has a greater percentage price change than a higher-coupon bond when their market discount rates change by the same amount (the coupon effect). 4. Generally, for the same coupon rate, a longer-term bond has a greater percentage price change than a shorter-term bond when their market discount rates change by the same amount (the maturity effect). lower coupon (more price volatility), longer maturity, YTM decreases
When an investor purchases a fixed income security, he/ she can expect to receive a dollar return from: (3)
1. coupon interest payments 2. capital gain/ loss 3. income from reinvestment of interim (intervening time) cash flows
converting yields for different bond periods p. 409
1. find the YTM annual rate 2.48% 2. for semiannual, multiply YTM in 1) by 2: 2.48%*2= 4.96% 3. set semiannual equal to quarterly period: (1+ (.0496/2)^2= (1+ APR4/4)^4 APR4= 4.93% check: compounding more frequently at a lower annual rate corresponds to compounding less frequently at a higher annual rate
The yield to maturity assumptions: (3)
1. investor holds the bond to maturity 2. issuer makes the promised yield (all coupon & principal payments on scheduled dates) 3. investor is able to reinvest coupon payments at same yield
current yield
=coupon payment/ price of bond $7/ $94.17=7.43% current yield will be greater than coupon rate if bond is sold at a discount. & vice versa
An analyst is evaluating the following two statements about putable bonds: Statement #1: As yields fall, the price of putable bonds will rise less quickly than similar option-free bonds (beyond a critical point) due to the decrease in value of the embedded put option. Statement #2: As yields rise, the price of putable bonds will fall more quickly than similar option-free bonds (beyond a critical point) due to the increase in value of the embedded put option. The analyst should: A) disagree with both statements. B) agree with both statements. C) agree with only one statement.
A Both statements are false. As yields fall, the value of the embedded put option in a putable bond decreases and (beyond a critical point) the putable bond behaves much the same as an option-free bond. As yields rise, the value of the embedded put option increases and (beyond a critical point) the putable bond decreases in value less quickly than a similar option-free bond.
Which of the following is a limitation of the portfolio duration measure? Portfolio duration only considers: A) a linear approximation of the actual price-yield function for the portfolio. B) the market values of the bonds. C) a nonparallel shift in the yield curve.
A Duration is a linear approximation of a nonlinear function. The use of market values has no direct effect on the inherent limitation of the portfolio duration measure. Duration assumes a parallel shift in the yield curve, and this is an additional limitation.
Kwagmyre Investments, Ltd., hold two bonds: a callable bond issued by Mudd Manufacturing Inc. and a putable bond issued by Precarious Builders. Both bonds have option adjusted spreads (OAS) of 135 basis points (bp). Kevin Grisly, a junior analyst at the firm, makes the following statements (each statement is independent). Apparently, Grisly could benefit from a CFA review course, because the only statement that could be accurate is: A) Given a nominal spread for Precarious Builders of 110 bp, the option cost is -25 bp. B) The Z-spread for Mudd's bond is based on the YTM. C) The spread over the spot rates for a Treasury security similar to Mudd's bond is 145 bp.
C The "spread over the spot rates for a Treasury security similar to Mudd's bond" refers to the Z-spread on the bond.For a callable bond, the OAS < Z-spread, so this could be a true statement because 135bp < 145 bp. The other statements are false. The option cost is calculated using the OAS and the Z-spread, not the nominal spread. The static spread (or Z-spread)is the spread over each of the spot rates in a given Treasury term structure, not the spreadover the Treasury's YTM. Following is a more detailed discussion: The option-adjusted spread (OAS) is used when a bond has embedded options. The OAS can be thought of as the difference between the static or Z-spread and the option cost. For the exam, remember the following relationship between the static spread (Z-spread), the OAS, and the embedded option cost: Z Spread - OAS = Option Cost in % terms Remember the following option value relationships: For embedded short calls (e.g. callable bonds): option value > 0 (you receive compensation for writing the option to the issuer), and the OAS < Z-spread. In other words, you require more yield on the callable bond than for an option-free bond. For embedded long puts (e.g. putable bonds): option value < 0 (i.e., you must pay for the option), and the OAS > Z-spread. In other words, you require a lower yield on the putable bond than for an option-free bond.
An investor gathered the following information on two U.S. corporate bonds: Bond J is callable with maturity of 5 years Bond J has a par value of $10,000 Bond M is option-free with a maturity of 5 years Bond M has a par value of $1,000 For each bond, which duration calculation should be applied? Bond J Bond M A) Modified Duration Effective Duration only B) Effective Duration Effective Duration only C) Effective Duration Modified Duration or Effective Duration
C The duration computation remains the same. The only difference between modified and effective duration is that effective duration is used for bonds with embedded options. Modified duration assumes that all the cash flows on the bond will not change, while effective duration considers expected cash flow changes that may occur with embedded options.
A noncallable bond with seven years remaining to maturity is trading at 108.1% of a par value of $1,000 and has an 8.5% coupon. If interest rates rise 50 basis points, the bond's price will fall to 105.3% and if rates fall 50 basis points, the bond's price will rise to 111.0%. Which of the following is closest to the effective duration of the bond? A) 6.12. B) 5.54. C) 5.27.
C The formula for effective duration is: (V- - V+) / (2V0Δy). Therefore, effective duration is: ($1.110 - $1.053) / (2 × $1.081 × 0.005) = 5.27.
When interest rates increase, the duration of a 30-year bond selling at a discount: A) increases. B) does not change. C) decreases.
C The higher the yield on a bond the lower the price volatility (duration) will be. When interest rates increase the price of the bond will decrease and the yield will increase because the current yield = (annual cash coupon payment) / (bond price). As the bond price decreases the yield increases and the price volatility (duration) will decrease.
Which of the following approaches in measuring interest rate risk is most accurate when properly performed? A) Duration approach. B) Duration/convexity approach. C) Full Valuation approach.
C The most accurate approach method for measuring interest rate risk is the so-called full valuation approach. Essentially this boils down to the following four steps: (1) begin with the current market yield and price, (2) estimate hypothetical changes in required yields, (3) recompute bond prices using the new required yields, and (4) compare the resulting price changes. Duration and convexity are summary measures and sacrifice some accuracy.
An analyst has gathered the following information: Bond A is an 11% annual coupon bond currently trading at 106.385 and matures in 3 years. The yield-to-maturity (YTM) for Bond A is 8.50%. The YTM for a Treasury bond that matures in 3-years is 7.65%. 1, 2, and 3-year spot rates are 5.0%, 6.5% and 8.25%, respectively. Which of the following statements regarding spreads on bond A is CORRECT? A) The nominal spread is approximately 25 basis points. B) The Z-spread is approximately 85 basis points. C) The nominal spread is approximately 85 basis points.
C The nominal spread is 8.50% − 7.65% = 0.85%. Note that the Z-spread, calculated by trial and error, is approximately 48 basis points.
In addition to effective duration, analysts often use measures such as Value-at-Risk (VaR) to estimate the price sensitivity of bonds to changes in interest rates because these measures also incorporate the effects of: A) time to maturity. B) embedded options. C) yield volatility.
C The volatility of a bond's yield should be considered along with the bond's effective duration when estimating its price sensitivity to interest rates. Measures of price risk such as VaR account for yield volatility. Effective duration includes the effects of time to maturity and embedded options.
Holding other factors constant, the interest rate risk of a coupon bond is higher when the bond's: A) current yield is higher. B) coupon rate is higher. C) yield to maturity is lower.
C There are three features that determine the magnitude of the bond price volatility: 1.The lower the coupon, the greater the bond price volatility. 2.The longer the term to maturity, the greater the price volatility. 3.The lower the initial yield, the greater the price volatility. In this case the only determinant that will cause a higher interest rate risk is having a low yield to maturity (initial yield). A higher coupon yield and a higher current yield will cause for lower interest rate risk.
If interest rates fall, the: A) value of call option embedded in the callable bond falls. B) callable bond's price rises faster than that of a noncallable but otherwise identical bond. C) callable bond's price rises more slowly than that of a noncallable but otherwise identical bond.
C When a callable bond's yield falls to a certain point, when the yields fall the price will increase at a decreasing rate. Compare this to a noncallable bond where, as the yield falls the price rises at an increasing rate.
option-adjusted spread (OAS)
OAS= Z-spread- option value (in basis points per year)
Z-spread graph & definition
The constant spread that will make the price of a security equal to the present value of its cash flows when added to the yield at each point on the spot rate Treasury curve where a cash flow is received . In other words, each cash flow is discounted at the appropriate Treasury spot rate plus the Z-spread.
