CFA Level 1 (2009) - 5

Study Session \6

Cross-Reference to CFA Institute Assigned Reading #66 - Introduction to the Measurement of Interest Rate Risk

I.Portfolio effective duration is the weighted average of the effecrive durations of the portfolio honds.

Numerators in weights are market values (par value x pricc as fH:rccnt oC par). [)cnomin<lror is (olal nLHkcr v,duc of the portfolio.

3.l'hc 6. 'i% and 7% coupon bonds likcly have no cmbedded options. For both of rhese bonds, modified duration and effeClive duration are identical. which would be the case if they had no embedded options. (It is possible that these bonds have options that are so far out of the money that the bond prices act as if there is no embedded option. One example might be a conversion option to cornman stock at $40 per share when the market value of the shares is $2.)

4.The 8% bond is likely callable. It is trading at a premium, its effective duration is less than modified duration, and it exhibits negative convexity. Remember, call price can be above par.

5.The 5.5% bond is likely putable. It is trading at a significam discount, its effective duration is much lower than its modified duration (close to zero in fact), and its convexity is positive but low. Note that a putable bond may trade below par when the put price is below par (also if there is risk that the issuer cannot honor the put). If it were callable, we would expect its modified and effective durations to be closer in val ue because the market price is significantly below likely call prices.

6.Based on the effective duration and effective convexity of the 7% bond, the approximate price change is:

[-8.5 x 0.0025] + [130 x 0.00252] x 950,000 '" -$\9,415.63

7.In order to estimate effective duration, the dealers must use a pricing model for the bonds and choose a specific yield change. Differences in models or the yield change used

can lead to differences in their estimates of effective duration.

8.Effective duration is based on small changes in yield and is appropriate for parallel changes in the yield curve (or equal changes in the yields to maturity for all portfolio bonds). Other types of yield changes will make portfolio dutation an inadequate measure of portfolio imerest rate risk.

A.is roo small.

B.is too large.

C. may be roo small or roo large.

2.Alfred LeBon purchased a semiannual pay, 7%, U.S. Treasury bond with 19 years to maturity for 91.16 the day after it had made a coupon payment. Two years later, the YTM was unchanged when he sold the bond. LeBon's gain when he sold the bond is closest ro:

A.0.483%.

B.0.733%.

C.0.931%.

3.Which statement about the theories of the term structure of interest rates is most accurate?

A.Under the liquidity preference theory, the yield curve will be positively sloped.

B.A yield curve that slopes up and then down (humped) is consistent with the market segmentation theory but not with the pure expectations theory.

C.Evidence that life insurance companies have a strong preference for 30-year bonds supports the market segmentation theory.

4.Which of the following is least likely a common form of external credit enhancement?

A.Portfolio insurance.

B.A corporate guarantee.

C. A letter of credit from a bank.

5.A bond with an embedded put option has a modified duration of7, an effective duration of 6 and a convexity of 62.5. If interest rates rise 25 basis points, the bond's price will change by approximately:

A.1.46%.

B.1.50%.

C.1.54%.

6.Which of the following bonds would be the best one ro own if the yield curve shifts down by 50 basis points at all maturities?

A.4-year 8%, 8% YTM.

B.5-year 8%, 7.5% YTM.

C.5-year 8.5%, 8% YTM.

7.Which of the following provisions would most likeL), decrease the yield to maturity on a debt security?

A.Call option.

B.Conversion option.

C. Cap on a floating-rate security.

Sclf-Test: Fixed Income Investments

8.The price ofa 10-year zero coupon bond with a current YTM of9.4% is 39.91. If lhe YTM increaJes to 9.9%. the price will decrease (0 38.05. If lhe YTM decreases to 8.9%, lhe price will increase to 41.86. The effective duralion is closest to:

A.9.38.

B.9.48.

C. 9.55.

9.The e["[ects of a decrease in interest rale (yield) volarility on the markel yield of a

spot rates arc: I-year = 2%, 2-year = 3%, 3-year = 3.5%, 4-year = 4.5%, the base (risk-free) forward rate for the loan before adding a risk premium is closest to:

A.4.5%.

B.6.0%.

C.9.0%.

12.Compared to mortgage passthrough securities, CMOs created from them most likely have:

A.less prepayment risk.

B.greater average yields.

C.a different claim to the mortgage cash Aows.

13.The arbitrage-free approach to bond valuation most likely:

A.can only be applied to Treasury securities.

B.requires each cash flow to be discounted at a fate specific to its time period.

C.shows that discounting each cash Aow at the yield to maturity must result in the correer value for a bond.

Self-Test: Fixed Income Investments

14.Which of the following statements least accurately describes a form of risk

associated wi th investing in fixed income sccuri ti~s?

A.Credit risk has only two components, default risk and downgrade risk.

B.Other things equal, a bond is more valuable to an investor when it has less liquidity risk.

C.Bonds that are callable, prepayable, or amortizing have more reinvesunent risk than otherwise equivalent bonds without these features.

Self-Test: Fixed Income Investments

SELF-TEST ANSWERS: FIXED INCOME INVESTMENTS -

.'.

1.A Duration is a linear measure, but the relationship between bond price and yield for an oprion-free bond is convex. For a given decrease in yield, the estimated price increase using duration alone will be smaller than the actual price increase.

2.A First, determine the semiannual yield to maturity:

N=38, PMT=3-5, PV= -91.16, FV=100 CPT-7IIY = 3.9534.

Second, retain TVM info and enter:

N = 34 CPT -7 PV = 91.60 fat a gain of (91.60 - 91.16)/91.] 6 = 0.4827%.

3.C The market segmentation theory is based on the idea that different market participants (both borrowers and lenders) have strong preferenCl:s for diflerent segments of the yield curve. If expectations are that ftlture short-term interest rates will be falling enough, then the yield curve could be downward sloping even given that there is an increasing premium for lack of liquidity at longer maturities. A humped yield curve is consistent with expectations that short-term rates will rise over the near (erl11 and then decline.

4.A External credit enhancements are financial guarantees from third parties that generally

support the performance of the bond. Portfolio insurance is not a third party guarantee.

5.A Effective duration must be used with bonds that have embedded options.

~P = (-)(ED)(~y) + (C)(6y)2

6r = (-)(6)(0.0025) + (62.5)(0.0025)2 = -0.015 t 0.00039 =-0.014610% or -1.461%.

6.B The bond with the highest duration will benefit tile most from a decrease in rates. The lower the coupon, lower the yield to maturity, and longer the time to maturity, the higher will be the duration.

7.B A conversion provision is an embedded option that favots the buyer, not the issuer, so buyers will accept a lowe( YTM with a conversion option. Call options and caps favor the issuer and increase the YTM that buyers will require.

8.C Effective duration = (41.86 - 38.05)/(39.91 x 2 x 0.005) = 9.546. Note that the price

changes are based on a 50 basis points change in yield, so 6y = 0.005.

9.B A decrease in yield volatility will decrease the values of embedded options. The security holder is shon the prepaymen t option. The decrease in the value of the prepayment option increases the value of the security, anc! the required yield will decrease. The security holder is long the put option so the value of a putable bond will decrease with a decrease in yield volatility and the required yield will increase.

10. C Since the OAS is less (han the Z-spread for Bond A, the effect of the embedded option is to decrease the required yield, so it must be a call option and not a put option. The OAS is the spread after taking out the effeer of the embedded option. Since the OAS is higher for Bond B, it represents the better value after adjusting for the value of the call in Bond A.

Sdf--Iest: Fixed Income Investments

11. B The forward rate is [1.045"1/1.0.')2]1/2 - 1 = 6.02%, or use the approximation

[4.5(4) - 3(2))/2 = 6.

12.C CMOs arc created to have different claims to the cash flows (principal, scheduled repaymeIlls, prepaymeIlls) than lhose of the underlying mortgage passthrough securities. On average, the yield will likely be lower on the CMO, since the reason lO creale them is to lower overall funding costs. They Gln have more or less prepaymelll risk, but on average will have the same prepaymenl risk as the underlying MRS.

13.B The arbitrage-free valuation approach discounls each cash Row at a discount rate specific to its maturity. For Treasury securities these discount rates arc theoretical Treasury SPOl rates. For non-Treasury securities, these discount rates arc Treasury spot rates plus a spread ro account for liquidity risk, credit risk, and any other relevant risks that differ from those of a Treasury bond of similar maturilY.

14. A Even if a bond does not default and is not downgraded, it still faces credit spread risk as the premium in the market for the bond's credit risk may increase. Lower liquidilY risk (i.e., higher liquidity) is preferred by investors, reduces a bond's required rate of retUJll, and increases ils value, othcr rhings equal. Reinvcstlllent risk is lligllcr for callable, prepayable, or amortizing bonds as all these featllres lead ro a grearer probability of receiving principal repaymenr earlier, which means rhere arc more funds lO be reinvesled over the life of rhe bond.

The following is a review of the Derivative Inve.'tments principles designed to address the learning outcome

statements set forth by CFA Institute®. This topic is also covered in:

DERIVATIVE MARKETS AND

INSTRUMENTS

Study Session 17

EXAM Focus

LOS 67.a: Define a derivative and differentiate between exchange· traded and over-the-counter derivatives.

A derivative is a security that derives its value from the value or return of another asset or seCUrIty.

A physical exchange exists for many options contracts and futures contracts. Exchange-traded derivatives are standardized and backed by a clearinghouse.

Forwards and swaps are custom instruments and are traded/created by dealers in a market with no central location. A dealer market with no central location is referred to as an over-the-counter market. They are largely unregulated markets and each contract is with a counterparty, which may expose the owner of a derivative to default risk (when the counterparty does not honor their commitment).

Some options trade in the over-the-counter market, notably bond options.

LOS 67.b: Define a forward commitment and a contingent claim, and describe the basic characteristics of forward contracts, futures contracts, options (calls and puts), and swaps.

A forward commitment is a legally binding promise to perform some action in the future. Forward commitments include forward contracts, futures contracts, and swaps.

Forward contracts and futures contracts can be written on equities, indexes, bonds, physical assets, or interest rates.

In a forward contract, one party agrees to buy, and the counterparty to sell, a physical asset or a security at a specific price on a specific date in the future. If the future price of the asset increases, the buyer (at the older, lower price) has a gain, and the seller a loss.

Study Session 17

Cross-Reference to CFA Institute Assigned Reading #67 - Derivative Markets and Instruments

A futures contract is a forward contract that is standardiz.ed and exchange-Haded. The main differences with forwards are that fUlllres arc Haded in an aCl'iv~ secondary market,

arc regulated, backed by the clearinghouse, and require a daily settlement of gains and losses.

A swap is a series of fi:Hward contracts. In the simplest swap, one party agrees to pay the short-term (Iloating) Lite of interest on some principal amount, and the counlcrpany agrees ro pay a certain (fixed) rale of interest in return. SwailS of different currencies and equity returns are also COI1l111on.

An option to buy an asset at a particular price is termed a call option. The seller of the option has an obligation to scll the asset at the agreed-upon price, if the call buyer chooses to exercise the right to buy the asset.

An option to sell an asset at a particular price is termed a put option. The seller of the o~1[ion has an obligation to purchase the asset at the agreed-upon price, if the put buyer chooses to exercise the right to sell rhe asset.

Pro/eHor's Note: To remember the.re terms, note that the owner ola Ctll! can "[til! the aHet in" (i.e., buy it); the owner ofa put has the right to "put the asset to" the writer of the put.

A contingent claim is a claim (to a payoff) that depends on a particular event. Options are contingent claims that depend on a stock price at some future date, rather than forward commitments. While forwards, futures, and swaps have payments that are made based on a price or rate outcome whether the movement is up or down, contingent claims onJy require a payment if a certain threshold price is broken (e.g., if the price is above X or the rate is below Y). It takes two options to replicate a future or forward.

LOS 67.c: Discuss the purposes and criticisms of derivative markets.

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The criticism ofderilJ{/tives is that they are "roo risky," especially ro investors with limited knowledge of sometimes complex instruments. Because of the high leverage involved in derivatives payoffs, they are sometimes likened to gambling.

The benefits ofderlTJatives markets are that [hey;

•Provide price information.

•Allow risk to be managed :lnd shifted among market participants.

•Red uce transactions costs.

LOS 67.d: Explain arbitrage and the role it plays in determining prices and promoting market efficiency.

Arbitrage is an important concept in valuing (pricing) derivative securities. In its purest sense, arbitrage is riskless. If a return greater than the risk-free rate can be earned by holding a portfolio of assets that produces a certain (riskless) return, thell an arbitrage 0pportunl[yexlsts.

Study Session 17

Cross-Reference to CFA Institute Assigned Reading #67 - Derivative Markets and Instruments

Arbirrage opportunities arise when assets are mispriced. Trading by arbirrageurs will continue unti'] they affect supply and demand enough to bring asset prices to efficient (no-arbitrage) levels.

There are two arbirrage arguments that arc particularly useful in the study and use of derivatives.

The first is based on the "law of one price." Two securities or portfolios that have identical cash Aows in the future, regardless of future events, should have the same price. If A and B have the identical future payoffs, and A is priced lower than B, buy A and sell

B. You have an immediate profit, and the payoff on A will satisfy the (future) liability of being short on B.

The second type of arbirrage is used where two securities with uncertain returns can be combined in a portfolio that will have a certain payoff. If a portfolio consisting of A and

B has a certain payoff, the portfolio should yield the risk-free rate. If this no-arbirrage condition is violated in that the certain return of A and B together is higher than the risk-free rate, an arbitrage opportunity exists. An arbitrageur could borrow at the

risk-free rate, buy the A + B portfolio, and earn arbitrage profits when the certain payoff occurs. The payoff will be more than is required to pay back the loan at the risk-free rate.

o Professor's Note: W'ewill discuss arbitrage further in our relliew of options.

Srudy Session 17

Cross-Reference to CFA Institute Assigned Reading #67 - Derivative Markets and Instrumellls

lOS (l7.a

A derivative has a value that is "derived" from the value of another assct or interest rate.

Exchange-traded derivatives, notably furures and some options, arc traded in ccntralizl'll locations and are standardized, regulated, and default risk free.

Forwards and swaps are cusromized contracts created by dealers and by financial instirutions. There is vcry limited trading of these conrracts in secondary markets and default (counrerparry) risk must be considered.

lOS ()7.h

A forward commitment is a binding promise ro buy or sell an asset or make a paymenr in the future. Forward contracts, CUlUrrs contracts, and s,",vaps are all forward commItments.

A conringenr claim is an asset that has value only if some furure evenr takes place (e.g., asset price is greater than a specified price). Options are conringent claims.

Forward contracts obligate one parry to buy, and another ro sell, a specific asset at a predetermined price at a specific time in the future.

Swaps contracts are equivalent to a series of forward conrracts on interest rates, currencies, or equity returns.

Futures contracts are much like forward contracts, but are exchange-traded, quite liquid, and require daily settlement of any gains or losses.

A call option gives the holder the right, but not the obligation, to buy an asset at a predetermined price at some time in the future.

A put option gives the holder the right, but not the obligation, to sell an asset at a predetermined price at some time in the future.

LOS 67.c

Derivative markets are criticized for their risky nature. However, many market participants use derivatives ro manage and reduce existing risk exposures.

Derivative securities play an important role in promoting efficienr market prices and reducing transaction costs.

LOS (;}.d

Riskless arbitrage refers to earning more than the risk-free rate of return with no risk, or earning an immediate gain with no possible future liability.