Fixed Income

If a Treasury bond has an annual modified duration of 10.27 and an annual convexity of 143, which of the following is closest to the estimated percentage price change in the bond for a 125 basis point increase in interest rates? A) -11.72%. B) -13.96%. C) -9.33%.

A) -11.72% The estimated percentage price change = the duration effect plus the convexity effect. The formula is: [-duration × (ΔYTM)] + ½[convexity × (ΔYTM)2]. Therefore, the estimated percentage price change is: [-(10.27)(0.0125)] + [(½)(143)(0.0125)2] = -0.128375 + 0.011172 = -0.117203 = -11.72%.

Consider a bond selling for $1,150. This bond has 28 years to maturity, pays a 12% annual coupon, and is callable in 8 years for $1,100. The yield to maturity is closest to: A) 10.34%. B) 10.55%. C) 9.26%.

A) 10.34%. N = 28; PMT = 120; PV = -1,150; FV = 1,000; CPT I/Y = 10.3432.

What is the semiannual-pay bond equivalent yield on an annual-pay bond with a yield to maturity of 12.51%? A) 12.14%. B) 12.00%. C) 12.51%.

A) 12.14%. The semiannual-pay bond equivalent yield of an annual-pay bond = 2 × [(1 + yield to maturity on the annual-pay bond)^0.5 - 1] = 12.14%.

The Macaulay duration in years of a 4-year annual pay, 6% coupon bond with a par value of $100 and yielding 7% is closest to: A) 3.67 years. B) 3.99 years. C) 3.35 years.

A) 3.67 years.

An option-free 5-year 6% annual-pay bond is selling $979.22 per $1,000 of par value and has a Macaulay duration of 4.4587. The bond's modified duration is closest to: A) 4.187. B) 4.206. C) 4.246.

A) 4.187.

Assume that the current price of an annual-pay bond is 102.50 per 100 of face value. If its YTM increases by 0.5% the value of the bond decreases to 100 and if its YTM decreases by 0.5% the price of the bond increases to 105.5. What is the approximate modified duration of the bond? A) 5.37. B) 5.48. C) 5.50.

A) 5.37. (105.5 - 100) / (2 * 102.50 * (0.005)

An analyst collects the following information regarding spot rates: 1-year rate = 4%. 2-year rate = 5%. 3-year rate = 6%. 4-year rate = 7%. The 2-year forward rate two years from today is closest to: A) 9.04%. B) 8.03%. C) 7.02%.

A) 9.04%. (1.07)^4 / (1.05)^2 -1

Assuming bond yields are greater than zero, which of the following statements about zero-coupon bonds is least accurate? A) A zero coupon bond may sell at a premium to par when interest rates decline. B) All interest is earned at maturity. C) The lower the price, the greater the return for a given maturity.

A) A zero coupon bond may sell at a premium to par when interest rates decline. Zero coupon bonds always sell below their par value, or at a discount prior to maturity. The amount of the discount may change as interest rates change, but a zero coupon bond will always be priced less than par if it has a positive yield.

Which of the following issues is most accurately described as a eurobond? A) Brazilian firm's U.S. dollar-denominated bonds sold to investors in Canada. B) European Union firm's Japanese yen-denominated bonds sold to investors in Japan. C) South Korean firm's euro-denominated bonds sold to investors in the European Union.

A) Brazilian firm's U.S. dollar-denominated bonds sold to investors in Canada. Eurobonds are denominated in a currency other than that of the countries in which they are issued. The name "eurobond" does not imply that a bond is sold in Europe or by a European issuer, or denominated in the euro currency. A U.S. dollar-denominated bond sold to investors outside the United States is called a "eurodollar bond."

Which of the following is least likely a form of internal credit enhancement for a bond issue? A) Covering the bond issue via a surety bond. B) Including a tranche system to identify priority of claims. C) Structuring the asset pool such that it has an excess spread.

A) Covering the bond issue via a surety bond. A surety bond is issued by a third party and hence is an external form of credit enhancement.

Fixed income classifications by issuer most likely include: A) Financial sector bonds. B) Floating-rate bonds. C) Money market securities.

A) Financial sector bonds.

Which of the following statements regarding repurchase agreements is most accurate? A) Greater demand for the underlying security results in a lower repo margin. B) Higher credit rating of the underlying collateral results in a higher repo rate. C) Lower credit rating of the underlying collateral results in a lower repo margin.

A) Greater demand for the underlying security results in a lower repo margin. Other things equal, the repo margin (percent difference between the market value of the collateral and the loan amount) is lower if the collateral is in greater demand. The repo margin and repo rate (the annualized percent difference between the sale price and repurchase price of the collateral) are inversely related to the credit quality of the collateral.

For a given change in yields, the difference between the actual change in a bond's price and that predicted using duration alone will be greater for: A) a bond with greater convexity. B) a bond with less convexity. C) a short-term bond.

A) a bond with greater convexity. Duration is a linear measure of the relationship between a bond's price and yield. The true relationship is not linear as measured by the convexity. When convexity is higher, duration will be less accurate in predicting a bond's price for a given change in interest rates. Short-term bonds generally have low convexity.

The primary motivation for investing in the support tranche of a planned amortization class CMO, compared to investing in another tranche, is that the support tranche offers: A) a higher interest rate. B) more protection against contraction risk. C) more protection against extension risk.

A) a higher interest rate.

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) a nonparallel shift in the yield curve. C) the market values of the bonds.

A) a linear approximation of the actual price-yield function for the portfolio. 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.

Loss severity is most accurately defined as the: A) amount a bondholder will lose if the issuer defaults. B) percentage of a bond's value a bondholder will receive if the issuer defaults. C) probability that a bond issuer will default.

A) amount a bondholder will lose if the issuer defaults. Loss severity is the money amount or percentage of a bond's value a bondholder will lose if the issuer defaults. *The percentage of a bond's value a bondholder will receive if the issuer defaults is the recovery rate.*

An investor buys a bond that has a Macaulay duration of 3.0 and a yield to maturity of 4.5%. The investor plans to sell the bond after three years. If the yield curve has a parallel downward shift of 100 basis points immediately after the investor buys the bond, her annualized horizon return is most likely to be: A) approximately 4.5%. B) greater than 4.5%. C) less than 4.5%.

A) approximately 4.5%. With Macaulay duration equal to the investment horizon, market price risk and reinvestment risk approximately offset and the annualized horizon return should be close to the yield to maturity at purchase.

Negative convexity is most likely to be observed in: A) callable bonds. B) government bonds. C) zero coupon bonds.

A) callable bonds.

The interest rate on excess reserves borrowed by one bank from another bank is most accurately described as a(n): A) central bank funds rate. B) interbank lending rate. C) reserve swap rate.

A) central bank funds rate. Required reserves are deposits with a country's central bank. Banks that deposit more than the required amount with the central bank are said to have excess reserves and may lend these to other banks. This lending is said to take place in the central bank funds market and the interest rates on such loans are known as central bank funds rates.

A synthetic collateralized debt obligation (CDO) is backed by a pool of: A) credit default swaps. B) leveraged bank loans. C) other CDOs.

A) credit default swaps. A synthetic CDO is backed by a pool of credit default swaps. Collateralized loan obligations (CLOs) are backed by a pool of leveraged bank loans. CDOs backed by a pool of other CDOs are an example of structured finance CDOs.

An asset-backed security with a senior/subordinated structure is said to have: A) credit tranching. B) prepayment tranching. C) time tranching.

A) credit tranching. A senior/subordinated structure in an ABS establishes credit tranching, in which risk of losses due to defaults on the underlying loans is redistributed among different classes of ABS holders. Time tranching redistributes prepayment risk among different classes of ABS holders.

An increase in net income is most likely to decrease a borrower's: A) debt-to-EBITDA ratio. B) FFO-to-debt ratio. C) operating margin.

A) debt-to-EBITDA ratio. An increase in net income is likely a result from increases in earnings before interest, taxes, depreciation and amortization (EBITDA) and operating income. An increase in net income is also likely to result in an increase in funds from operations (FFO). The only ratio listed that has earnings or operating cash flow in the denominator is the debt-to-EBITDA ratio. As the denominator increases, the ratio will decrease.

Jayce Arnold, a CFA candidate, 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) decrease by $124, price will increase by $149. B) decrease by $149, price will increase by $124. C) increase by $149, price will decrease by $124.

A) decrease by $124, price will increase by $149. 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.

Compared to corporate bonds with the same credit ratings, municipal general obligation (GO) bonds typically have less credit risk because: A) default rates on GOs are typically lower for same credit ratings. B) GOs are not affected by economic downturns. C) governments can print money to repay debt.

A) default rates on GOs are typically lower for same credit ratings. Municipal bonds usually have lower default rates than corporate bonds of the same credit ratings. GO bonds' creditworthiness is affected by economic downturns. Sovereigns can print money to repay debt, but municipalities cannot.

The appropriate measure of interest rate sensitivity for bonds with an embedded option is: A) effective duration. B) Macaulay duration. C) modified duration.

A) effective duration. Effective duration is appropriate for bonds with embedded options because their future cash flows are affected by the level and path of interest rates.

If the yield curve is downward-sloping, the no-arbitrage value of a bond calculated using spot rates will be: A) equal to the market price of the bond. B) greater than the market price of the bond. C) less than the market price of the bond.

A) equal to the market price of the bond. The value of a bond calculated using appropriate spot rates is its no-arbitrage value. If no arbitrage opportunities are present, this value is equal to the market price of a bond.

Which of the following securities is least likely classified as a eurobond? A bond that is denominated in: A) euros and issued in Germany. B) euros and issued in the United States. C) U.S. dollars and issued in Japan.

A) euros and issued in Germany. Bonds denominated in the currency of the country or region where they are issued are domestic bonds. Eurobonds are denominated in a currency other than those of the countries in which they are sold.

Which of the following statements best describes the concept of negative convexity in bond prices? As interest rates: A) fall, the bond's price increases at a decreasing rate. B) fall, the bond's price increases at an increasing rate. C) rise, the bond's price decreases at a decreasing rate.

A) fall, the bond's price increases at a decreasing rate. Negative convexity occurs with bonds that have prepayment/call features. As interest rates fall, the borrower/issuer is more likely to repay/call the bond, which causes the bond's price to approach a maximum. As such, the bond's price increases at a decreasing rate as interest rates decrease. *Convexity is a measure of the curvature of the price-yield relation. The more curved it is, the greater the convexity adjustment.

An investor who buys bonds that have a Macaulay duration less than his investment horizon: A) has a negative duration gap. B)is minimizing reinvestment risk. C)will benefit from decreasing interest rates.

A) has a negative duration gap. A duration gap is a difference between a bond's Macaulay duration and the bondholder's investment horizon. If Macaulay duration is less than the investment horizon, the bondholder is said to have a negative duration gap and is more exposed to downside risk from decreasing interest rates (reinvestment risk) than from increasing interest rates (market price risk).

A mortgage is most attractive to a lender if the loan: A) has a prepayment penalty. B) is convertible from fixed-rate to adjustable-rate. C)Is non-recourse.

A) has a prepayment penalty. Prepayment penalties are attractive to a lender because borrowers are most likely to prepay when interest rates have decreased (i.e., when the lender will earn a lower return by reinvesting prepaid principal). Recourse loans are more favorable to the lender than non-recourse loans because with a non-recourse loan the lender can only reclaim the collateral in the event of default, while recourse gives the lender a claim against the borrower's other assets. The conversion option in a convertible mortgage is held by the borrower and is therefore attractive to a borrower rather than a lender.

For a callable bond, the option-adjusted spread (OAS): A) is less than the zero-volatility spread. B) is greater than the zero-volatility spread. C) can be greater than or equal to the zero-volatility spread.

A) is less than the zero-volatility spread. For a callable bond, the OAS is less than the zero-volatility spread because of the extra yield required to compensate the bondholder for the call option. (Module 55.1, LOS 55.b)

If a callable bond has an option-adjusted spread (OAS) of 75 basis points, this most likelysuggests: A) the bond has a zero-volatility spread greater than 75 basis points. B) the 75 basis points represent the investor's compensation for credit risk, liquidity risk, and volatility risk. C) the implied cost of the call option is the bond's nominal spread minus 75 basis points.

A) the bond has a zero-volatility spread greater than 75 basis points. For a bond with an embedded call option, the OAS is less than its zero-volatility spread by the option cost. Therefore, the zero-volatility spread is greater than the OAS for callable bonds. If the embedded call option has any value to the issuer, a callable bond with an OAS of 75 basis points will have a Z-spread that is greater than 75 basis points.

Today an investor purchases a $1,000 face value, 10%, 20-year, semi-annual bond at a discount for $900. He wants to sell the bond in 6 years when he estimates the yields will be 9%. What is the estimate of the future price? A) $946. B) $1,079. C) $1,152.

B) $1,079. n 6 years, there will be 14 years (20 - 6), or 14 × 2 = 28 semi-annual periods remaining of the bond's life So, N = (20 - 6)(2) = 28; PMT = (1,000 × 0.10) / 2 = 50; I/Y = 9/2 = 4.5; FV = 1,000; CPT → PV = 1,079. Note: Calculate the PV (we are interested in the PV 6 years from now), not the FV.

A bond has a yield to maturity of 7% with a periodicity of 4. The bond has a face value of $100,000 and matures in 13 years. Each coupon payment will be $1,800. The current price of the bond is closest to: A) $101,672. B) $101,698. C) $102,768.

B) $101,698. N = 13 × 4 = 52; FV = 100,000; PMT = 1,800; I/Y = 7 / 4 = 1.75; CPT → PV = 101,698. (Module 54.1, LOS 54.a)

What is the probable change in price of a 30-year semiannual 6.5% coupon, $1000 par value bond yielding 8% if the yield decreases to 7%? A) $106.34. B) $107.31. C) $98.83.

B) $107.31. Price at 8%: is N = 60, FV = $1,000, I = 4%, PMT = $32.50, CPT PV = $830.32 price at 7% is N = 60, FV = $1,000, I = 3.5%, PMT = $32.50, CPT PV = $937.64. Change in price is $937.64 - $830.32 = $107.31.

A bond has a duration of 10.62 and a convexity of 182.92. For a 200 basis point increase in yield, what is the approximate percentage price change of the bond? A) -1.62%. B) -17.58%. C) -24.90%.

B) -17.58%. The estimated price change is: -(duration)(∆YTM) + ½(convexity) × (∆YTM)^2 = -10.62 × 0.02 + (½)(182.92)(0.02^2) = -0.2124 + 0.0366 = -0.1758 or -17.58%.

The approximate modified duration of an option-free 20-year 7% annual-pay par bond based on a 25 basis point change in yield is closest to: A) 5.3. B) 10.6. C) 13.7.

B) 10.6. If the yield on the bond were 7.25%, the price would be 97.402 and would be 102.701 if the yield were 6.75%. The approximate modified duration for this bond based on a 25 basis point change in yield is calculated as: (102.701 - 97.402) / (2 * 100 * 0.0025) = 10.6

A 12% coupon bond with semiannual payments is callable in 5 years. The call price is $1,120. If the bond is selling today for $1,110, what is the yield-to-call? A) 10.25%. B) 10.95%. C) 11.25%.

B) 10.95%. PMT = 60; N = 10; FV = 1,120; PV = -1,110; CPT → I = 5.47546 (5.47546)(2) = 10.95

A 30-year semi-annual coupon bond issued today with market rates at 6.75% pays a 6.75% coupon. If the market yield declines by 30 basis points, the price increases to $1,039.59. If the market yield rises by 30 basis points, the price decreases to $962.77. The bond's approximate modified duration is closest to: A) 1.3%. B) 12.8%. C) 3.9%.

B) 12.8%. Approximate modified duration = (price if yield down − price if yield up) / (2 × initial price × yield change expressed as a decimal). Here, the initial price is par, or $1,000 because we are told the bond was issued today at par. So, the calculation is: (1039.59 − 962.77) / (2 × 1000 × 0.003) = 76.82 / 6.00 = 12.80.

An annual-pay bond is priced at 101.50. If its yield to maturity decreases 100 basis points, its price will increase to 105.90. If its yield to maturity increases 100 basis points, its price will decrease to 97.30. The bond's approximate modified convexity is closest to: A) 0.2. B) 19.7. C) 4.2.

B) 19.7. Approximate modified convexity is calculated as [ V- + V+ - 2V0 ] / [ (V0)(change in YTM)2 ]. [ 105.90 + 97.30 - 2(101.50) ] / [ 101.50(0.01)^2 ] = 19.70.

Consider a floating rate issue that has a coupon rate that is reset on January 1 of each year. The coupon rate is defined as one-year London Interbank Offered Rate (LIBOR) + 125 basis points and the coupons are paid semi-annually. If the one-year LIBOR is 6.5% on January 1, which of the following is the semi-annual coupon payment received by the holder of the issue in that year? A) 3.250%. B) 3.875%. C) 7.750%.

B) 3.875%. This value is computed as follows: Semi-annual coupon = (LIBOR + 125 basis points) / 2 = 3.875% * 125 basis points is 0.0125 but use the percentage value (x100) = 1.25*

Becque Ltd. is a European Union company with the following selected financial information: € billionsYear 1Year 2Year 3Operating income262361503Depreciation & amortization201212256Capital expenditures7897140Cash flow from operations303466361Total debt2,5902,7172,650Dividends707072 Becque's three-year average debt-to-EBITDA ratio is closest to: A) 3.6x. B) 4.6x. C) 7.6x.

B) 4.6x. EBITDA = Operating income + depreciation + amortization Year 1: 262 + 201 = €463 billion Year 2: 361 + 212 = €573 billion Year 3: 503 + 256 = €759 billion Debt/EBITDA ratio: Year 1: 2,590 / 463 = 5.6x Year 2: 2,717 / 573 = 4.7x Year 3: 2,650 / 759 = 3.5x Three-year average = 4.6x.

An international bond investor has gathered the following information on a 10-year, annual-pay U.S. corporate bond: Currently trading at par value Annual coupon of 10% Estimated price if rates increase 50 basis points is 96.99% Estimated price is rates decrease 50 basis points is 103.14% The bond's approximate modified duration is closest to: A) 3.14. B) 6.15. C) 6.58.

B) 6.15.

Assume the following government spot yield curve. One-year rate: 5% Two-year rate: 6% Three-year rate: 7% If a 3-year annual-pay government bond has a coupon of 6%, its yield to maturity is closest to: A) 6.08%. B) 6.92%. C) 7.00%.

B) 6.92%. First determine the current price of the bond: = 6 / 1.05 + 6 / (1.06)^2 + 106 / (1.07)^3 = 5.71 + 5.34 + 86.53 = 97.58 Then compute the yield of the bond: N = 3; PMT = 6; FV = 100; PV = -97.58; CPT → I/Y = 6.92%

An investor purchases a 4-year, 6%, semiannual-pay Treasury note for $9,485. The security has a par value of $10,000. To realize a total return equal to 7.515% (its yield to maturity), all payments must be reinvested at a return of: A) more than 7.515%. B) 7.515%. C) less than 7.515%.

B) 7.515%. The reinvestment assumption that is embedded in any present value-based yield measure implies that all coupons and principal payments must be reinvested at the specific rate of return, in this case, the yield to maturity. Thus, to obtain a 7.515% total dollar return, the investor must reinvest all the coupons at a 7.515% rate of return. Total dollar return is made up of three sources, coupons, principal, and reinvestment income. (Module 58.1, LOS 58.a)

A local bank offers an account that pays 8%, compounded quarterly, for any deposits of $10,000 or more that are left in the account for a period of 5 years. The effective annual rate of interest on this account is: A) 4.65%. B) 8.24%. C) 9.01%.

B) 8.24%. (1 + periodic rate)m - 1 = (1.02)^4 - 1 = 8.24%.

On Monday, the yield curve is upward sloping with yields of 3%, 4%, and 5.5% on 1-year, 5-year, and 10-year government bonds, respectively. The following day, the yield curve experiences an upward parallel shift equal to 50 basis points. Other things equal, which of the following noncallable 6% coupon bonds is likely to experience the smallest percent change in price as a result of the yield curve shift? A) Zero coupon government bond maturing in five years. B) Par value government bond maturing in five years. C) Par value government bond maturing in ten years.

B) Par value government bond maturing in five years. The bond with the least percentage price change will be the bond with the lowest interest rate risk. Higher coupons or shorter maturities decrease interest rate risk. The coupon paying bond with only five years to maturity will have the lowest interest rate risk. (Module 59.1, LOS 59.b)

Which of the following statements regarding zero-coupon bonds and spot interest rates is CORRECT? A) If the yield to maturity on a 2-year zero coupon bond is 6%, then the 2-year spot rate is 3%. B) Price appreciation creates all of the zero-coupon bond's return. C) Spot interest rates will never vary across the term structure.

B) Price appreciation creates all of the zero-coupon bond's return. Zero-coupon bonds are quite special. Because zero-coupon bonds have no coupons (all of the bond's return comes from price appreciation), investors have no uncertainty about the rate at which coupons will be invested. Spot rates are defined as interest rates used to discount a single cash flow to be received in the future. If the yield to maturity on a 2-year zero is 6%, we can say that the 2-year spot rate is 6%.

Jorge Fullen is evaluating a 7%, 10-year bond that is callable at par in 5 years. Coupon payments can be reinvested at an annual rate of 7%, and the current price of the bond is $1,065.00 per $1,000 of face value. The bond pays interest semiannually. Should Fullen consider the yield to first call (YTC) or the yield to maturity (YTM) in making his purchase decision? A) YTM, since YTM is greater than YTC. B) YTC, since YTC is less than YTM. C) YTC, since YTC is greater than YTM.

B) YTC, since YTC is less than YTM. The bond is trading at a premium, and if the bond is called at par that premium would be amortized over a shorter period, resulting in a lower return. The lower return is the more conservative number, so the YTC should be used. You could use your financial calculator to solve for YTC assuming 10 semiannual coupon payments of $35 (FV = 1,000; PMT = 35; PV = -1,065; N = 10; solve for i = 2.75; × 2 to get annual YTC = 5.5%). Calculation of YTM would use the same inputs except N = 20, to get YTM = 6.12% (Module 55.1, LOS 55.a)

Assuming the issuer does not default, can capital gains or losses be a component of the holding period return on a zero-coupon bond that is sold prior to maturity? A) No, because amortization of the discount is interest income. B) Yes, because the bond's yield to maturity may have changed. C) Yes, because the purchase price is less than the bond's value at maturity.

B) Yes, because the bond's yield to maturity may have changed. Prior to maturity, a zero-coupon bond's price may be different than its constant-yield price trajectory and the bondholder may realize a capital gain or loss by selling the bond. For a zero-coupon bond that is held to maturity, the increase from the purchase price to face value at maturity is interest income.

Annual Macaulay duration is least accurately interpreted as the: A) investment horizon at which a bond's market price risk and reinvestment risk exactly offset. B) approximate percentage change in a bond's value for a 1% change in its yield to maturity. C) weighted average number of years until a bond's cash flows are scheduled to be paid.

B) approximate percentage change in a bond's value for a 1% change in its yield to maturity. Modified duration is the approximate percentage change in a bond's value for a 1% change in its YTM. Macaulay duration is the weighted average number of periods until a bond's cash flows are scheduled to be paid and represents the investment horizon at which a bond's market price risk and reinvestment risk exactly offset. (Module 58.1, LOS 58.c)

A 10-year, 5% bond is issued at a price to yield 5.2%. Three months after issuance, the yield on this bond has decreased by 100 basis points. The price of this bond at issuance and three months later is: A) above par at issuance, but below par three months later. B) below par at issuance, but above par three months later. C) below par at issuance, and below par three months later.

B) below par at issuance, but above par three months later. A bond issued at a yield higher than its coupon will be priced below par, or at a discount. Three months later, the yield has declined to 4.2% and the bond will trade at a premium to par, reflecting the fact that the coupon is now higher than the yield. (Module 54.1, LOS 54.b)

Key rate duration is best described as a measure of price sensitivity to a: A) change in a bond's cash flows. B) change in yield at a single maturity. C) parallel shift in the benchmark yield curve.

B) change in yield at a single maturity. Key rate duration is the price sensitivity of a bond or portfolio to a change in the interest rate at one specific maturity on the yield curve.

PRC International just completed a $234 million floating rate convertible bond offering. As stated in the indenture, the interest rate on the bond is the lesser of 90-day LIBOR or 10%. The indenture also requires PRC to retire $5.6 million per year with the option to retire as much as $10 million. Which of the following embedded options is most likely to benefit the investor? The: A) 10% cap on the floating interest rate. B) conversion option on the convertible bonds. C) sinking fund provision for principal repayment.

B) conversion option on the convertible bonds. The conversion privilege is an option granted to the bondholder. The cap benefits the issuer. A sinking fund is not an embedded option; it is an obligation of the issuer.

A disadvantage of G-spreads and I-spreads is that they are theoretically correct only if the spot yield curve is: A) downward sloping. B) flat. C) upward sloping.

B) flat. G-spreads and I-spreads are only correct when the spot yield curve is flat (yields are about the same across maturities).

An annual-pay, 4% coupon, 10-year bond has a yield to maturity of 5.2%. If the price of this bond is unchanged two years later, its yield to maturity at that time is: A) 5.2%. B) greater than 5.2%. C) less than 5.2%.

B) greater than 5.2%. This bond is priced at a discount to par value because its 4% coupon is less than its 5.2% yield to maturity. As the bond gets closer to maturity, the discount will amortize toward par value, which means its price will increase if its yield remains unchanged. For its price to remain unchanged, its yield would have to increase. Price with 10 years to maturity: N = 10; I/Y = 5.2; PMT = 40; FV = 1,000; CPT PV = -908.23 Yield with 8 years to maturity: N = 8; PMT = 40; FV = 1,000; PV = -908.23; CPT I/Y = 5.446% (Module 54.1, LOS 54.b)

Structural subordination means that a parent company's debt: A) has a higher priority of claims to a subsidiary's cash flows than the subsidiary's debt. B) has a lower priority of claims to a subsidiary's cash flows than the subsidiary's debt. C) ranks pari passu with a subsidiary's debt with respect to the subsidiary's cash flows.

B) has a lower priority of claims to a subsidiary's cash flows than the subsidiary's debt. Structural subordination means that cash flows from a subsidiary are used to pay the subsidiary's debt before they may be paid to the parent company to service its debt. As a result, parent company debt is effectively subordinate to the subsidiary's debt.

An investor purchases a fixed coupon bond with a Macaulay duration of 5.3. The bond's yield to maturity decreases before the first coupon payment. If the YTM then remains constant and the investor sells the bond after three years, the realized yield will be: A) equal to the YTM at the date of purchase. B) higher than the YTM at the date of purchase. C) lower than the YTM at the date of purchase.

B) higher than the YTM at the date of purchase. If the investment horizon is shorter than the Macaulay duration, the price impact of a decrease in YTM dominates the loss of reinvestment income and the realized yield will be higher than the YTM at purchase.

A mortgage-backed security has a pass-through rate of 4.3%. The average interest rate on its underlying pool of mortgages is 4.5%. The difference between these rates is most likely due to: A) faster-than-expected prepayments. B) issuance and servicing costs. C) slower-than-expected prepayments.

B) issuance and servicing costs. Pass-through (i.e., coupon) rates on an MBS are less than the average interest rate on its underlying pool of mortgages because some of the cash flows from the mortgages are used to pay issuance costs and fees to the servicer of the mortgages.

Features specified in a bond indenture least likely include the bond's: A) coupon rate and maturity date. B) issuer and rating. C) par value and currency.

B) issuer and rating. Bond ratings are assigned by third-party credit rating agencies and may change during the life of a bond. Features that are specified in the indenture for a fixed income security include its issuer, maturity date, par value, coupon rate and frequency, and currency.

Positive Convexity If interest rates decrease by 50 basis points, a 10-year, 6% coupon, option-free bond will increase in price by $36. If instead interest rates increase by 50 basis points, this bond's price will decrease by: A) $36. B) less than $36. C) more than $36.

B) less than $36. The bond described will have positive convexity. Because of convexity, the bond's price will decrease less as a result of a given increase in interest rates than it will increase as a result of an equivalent decrease in interest rates.(Module 60.1, LOS 60.a)

A sequential-pay CMO has two tranches. Principal is paid to Tranche S until it is paid off, after which principal is paid to Tranche R. Compared to Tranche R, Tranche S has: A) less contraction risk and more extension risk. B) more contraction risk and less extension risk. C) more contraction risk and more extension risk.

B) more contraction risk and less extension risk. In a sequential-pay CMO the short tranche, which receives principal payments and prepayments first, has more contraction risk, while the tranche that receives principal payments and prepayments last has more extension risk.

A step-up coupon bond is structured such that its coupon rate increases: A) if the issuer's credit rating decreases. B) on a predetermined schedule. C) if a reference interest rate increases.

B) on a predetermined schedule. Step-up coupon bonds feature a coupon rate that increases on a predetermined schedule. Credit linked coupon bonds have a coupon rate that changes inversely with the issuer's credit rating. Floating-rate notes have coupon rates that are based on a reference interest rate. (Module 50.1, LOS 50.a)

An investor has an investment horizon of 4 years, and a Macaulay duration for one of her million-dollar bond investments of 3.5 years. The investor's exposure to interest rates is best reflected as: A) minimal, due to the relatively close duration and horizon. B) reinvestment risk due to decreasing interest rates. C) price risk due to increasing interest rates.

B) reinvestment risk due to decreasing interest rates. When the investment horizon exceeds the Macaulay duration (as it does here), there is a negative duration gap that exposes the investors to reinvestment risk; this risk occurs when the cash flows received from an investment must be subsequently invested in a lower interest rate environment. Price risk due to increasing interest rates is a risk when there is a positive duration gap (Macaulay duration exceeds investment horizon). Even though the horizon and duration are within 0.5 years, the risk is not minimal, especially given that 0.5 years is an eighth of the total investment horizon. In another scenario, you might conclude that a duration gap of 0.5 years is relatively close if the investment horizon was much longer. (Module 58.1, LOS 58.c)

An analyst has calculated a Macaulay duration of 2.12 for a three-year corporate bond. For this bond, 2.12 represents: A) when the investor recovers his principal. B) the average time until the receipt of the bond's cash flows. C) the sensitivity of the bond's price to changes in interest rates.

B) the average time until the receipt of the bond's cash flows. The Macaulay duration is the average time until the receipt of the cash flows of the bond. The investor will recover his principal (in a typical scenario) at the end of the bond's life, when it matures (here, that is three years). Duration is a measure of bond price sensitivity to interest rate changes, but that is not the interpretation of the Macaulay duration specifically. (Module 58.1, LOS 58.c)

Asset-backed securities (ABS) may have a higher credit rating than the seller's corporate bonds because: A) the seller's ABS are senior to its corporate bonds. B) they are issued by a special purpose entity. C) ABS are investment grade while corporate bonds may be speculative grade.

B) they are issued by a special purpose entity. The SPE in a securitization is bankruptcy-remote from the seller, which means the seller's creditors do not have a claim against the pool of assets underlying an ABS. As a result, the ABS may have a higher credit rating than the seller's corporate bonds. (Module 65.1, LOS 65.b)

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: Effective Duration - effective duration is used for bonds with embedded options (callable) - effective duration considers expected cash flow changes may occur Bond M: Modified Duration or Effective Duration - modified duration assumes that all the cash flows on the bond will not change

An investor gathered the following information about two 7% annual-pay, option-free bonds: Bond R has 4 years to maturity and is priced to yield 6% Bond S has 7 years to maturity and is priced to yield 6% Both bonds have a par value of $1,000. Given a 50 basis point parallel upward shift in interest rates, what is the value of the two-bond portfolio? A) $2,086. B) $2,030. C) $2,044.

C) $2,044. Given the shift in interest rates, Bond R has a new value of $1,017 (N = 4; PMT = 70; FV = 1,000; I/Y = 6.50%; CPT → PV = 1,017). Bond S's new value is $1,027 (N = 7; PMT = 70; FV = 1,000; I/Y = 6.50%; CPT → PV = 1,027). After the increase in interest rates, the new value of the two-bond portfolio is $2,044 (1,017 + 1,027). (Module 54.1, LOS 54.a)

For a given bond, the duration is 8 and the convexity is 100. For a 60 basis point decrease in yield, what is the approximate percentage price change of the bond? A) 2.52%. B) 4.62%. C) 4.98%.

C) 4.98%. The estimated price change is -(duration)(∆YTM) + (½)(convexity) × (∆YTM)2 = -8 × (-0.006) + (½)(100) × (-0.0062) = +0.0498 or 4.98%.

What is the equivalent annual-pay yield for a bond with a semiannual-bond basis yield of 5.6%? A) 5.52%. B) 5.60%. C) 5.68%.

C) 5.68%. The annual-pay yield is computed as follows: Annual-pay yield = [(1 + 0.056 / 2)^2 - 1 = 5.68%

An analyst gathered the following information about a 15-year bond: 10% semiannual coupon. Modified duration of 7.6 years. If the market yield rises 75 basis points, the bond's approximate price change is a: A) 5.4% decrease. B) 5.4% increase. C) 5.7% decrease.

C) 5.7% decrease. ΔP/P = −DΔi ΔP/P = −7.6(+0.0075)= −0.057, or −5.7%.

An investor buys a pure-discount note that matures in 146 days for $971. The bond-equivalent yield is closest to: A) 1.2%. B) 3.0%. C) 7.5%.

C) 7.5%. The equivalent add-on return the investor earns for the 146-day holding period is $1,000 / $971 - 1 = 0.0299 = 2.99%. The bond-equivalent yield is (365 / 146) × 2.99% = 7.47%.

In a Macaulay duration calculation, the weights calculated for each future cash flow are: A) assigned greater value for earlier cash flows. B) valued equally. C) assigned greater value for later cash flows.

C) assigned greater value for later cash flows. In the Macaulay duration calculation, once the proportion of total PV for each individual PV are determined, they are each multiplied by the length of time until they are received. So, for example, in an annual pay bond calculation, the weighting for the Year 1 cash flow is multiplied by 1, the weighting for the Year 2 cash flow is multiplied by 2, and so on. The highest value is assigned to the last cash flow received—which, in a coupon-paying bond, is typically the final interest payment and the principal payment. (Module 58.1, LOS 58.c)

One notable difference between an issuer credit rating and an issue credit rating is that an: A) issue credit rating applies to the issuer's senior unsecured debt. B) issue credit rating is always notched below the issuer rating. C) issuer credit rating reflects the borrower's overall creditworthiness.

C) issuer credit rating reflects the borrower's overall creditworthiness.

Total cash flows to investors in an ABS issue are: A) equal to the total interest and principal payments from the underlying asset pool if only one class of ABS has been issued from the trust. B) equal to the total interest and principal payments from the underlying asset pool. C) less than the total interest and principal payments from the underlying asset pool.

C) less than the total interest and principal payments from the underlying asset pool. Cash flows from the underlying asset pool are used to pay fees to the servicer as well as payments to the ABS investors. Thus payments to investors are less than the total cash flows from the pool of assets.

If the coupon payments are reinvested at the coupon rate during the life of a bond, then the yield to maturity: A) is greater than the realized yield. B) is less than the realized yield. C) may be greater or less than the realized yield.

C) may be greater or less than the realized yield. For the realized yield to equal the YTM, coupon reinvestments must occur at that YTM. Whether reinvesting the coupons at the coupon rate will result in a realized yield higher or lower than the YTM depends on whether the bond is at a discount (coupon < YTM) or a premium (coupon > YTM).

Strategic default by a mortgage borrower is most likely if the loan is: A) non-amortizing. B) non-conforming. C) non-recourse.

C) non-recourse. If a mortgage is a non-recourse loan, the lender has no claim against the borrower's assets other than the collateral for the loan. If the value of the collateral has decreased significantly below the remaining principal on a non-recourse loan, the borrower has an incentive to engage in "strategic default" and surrender the collateral to the lender.

Securitization least likely benefits the financial system by: A) increasing liquidity for mortgages and other loans. B) increasing the amount banks are able to lend. C) removing liabilities from bank balance sheets.

C) removing liabilities from bank balance sheets. By enabling banks to raise cash by selling their existing loans and mortgages (which are balance sheet assets for banks), securitization increases the amount banks are able to lend.

An interpolated spread (I-spread) for a bond is a yield spread relative to: A) benchmark spot rates. B) risk-free bond yields. C) swap rates.

C) swap rates. Spreads relative to swap rates are referred to as Interpolated or I-spreads.

The bonds of Grinder Corp. trade at a G-spread of 150 basis points above comparable maturity U.S. Treasury securities. The option adjusted spread (OAS) on the Grinder bonds is 75 basis points. Using this information, and assuming that the Treasury yield curve is flat: A) the zero-volatility spread is 225 basis points. B) the zero-volatility spread is 75 basis points. C) the option cost is 75 basis points.

C) the option cost is 75 basis points. The option cost is the difference between the zero volatility spread and the OAS, or 150 − 75 = 75 bp. With a flat yield curve, the G-spread and zero volatility spread will be the same.(Module 55.1, LOS 55.b)

For large changes in yield, which of the following statements about using duration to estimate price changes is most accurate? Duration alone: A) overestimates the increase in price for decreases in yield. B) overestimates the increase in price for increases in yield. C) underestimates the increase in price for decreases in yield.

C) underestimates the increase in price for decreases in yield. For large changes in yield, duration underestimates the increase in price when yield decreases and overestimates the decrease in price when yield increases. This is because duration is a linear estimate that does not account for the convexity (curvature) in the price/yield relationship.

The interbank funds market is most accurately described as: A) banks' borrowing of reserves from the central bank. B) trading of negotiable certificates of deposit. C) unsecured short-term loans from one bank to another.

C) unsecured short-term loans from one bank to another.

McClintock 8% coupon bonds maturing in 10 years are currently trading at 97.55. These bonds are option-free and pay coupons semiannually. The McClintock bonds have a: A) current yield less than 8.0%. B) true yield greater than the street convention. C) yield to maturity greater than 8.0%.

C) yield to maturity greater than 8.0%. A bond trading at a discount will have a YTM greater than its coupon. The current yield is 8 / 97.55 = 8.2%. True yield is adjusted for payments delayed by weekends and holidays and is equal to or slightly less than the yield on a street convention basis.

Which of the following is most likely to be the money duration of newly issued 360-day eurocommercial paper? A) 360 days. B) 4.3%. C) €25 million.

C) €25 million. Money duration is expressed in currency units.

An investor gathers the following information about a 2-year, annual-pay bond: Par value of $1,000 Coupon of 4% 1-year spot interest rate is 2% 2-year spot interest rate is 5% Using the above spot rates, the current price of the bond is closest to:

The coupon payment of the bond is $40 (0.04 × 1,000). The bond price = 40/(1.02) + 1,040/(1.05)^2 = $982.53.

Suppose that the six-month spot rate is equal to 7% and the two-year spot rate is 6%. The one-and a half-year forward rate starting six months from now has to: be less than 6%. be more than 6%. lie between 6% and 7%.

be less than 6%.

When interest rates increase, the modified duration of a 30-year bond selling at a discount: decreases. does not change. increases.

decreases. 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.