BBB) or Moody’s (Aaa, Aa, A, Baa). Investment grade bonds are generallylegal for purchase by banks; junk bonds are not. Bonds that cross thethreshold from investment grade to junk bonds must be purged from mostinstitutional accounts, creating potential profit opportunities for thediscerning distressed debt investor.The term “junk” is reserved for all bonds with Standard & Poor’s ratingsbelow BBB and/or Moody’s ratings below Baa. Junk bond ratings includeBB, B, CCC, CC, C and D. BB-rated bonds have the lowest degree ofspeculation (among junk bonds) while a D rating is assigned to an issuer indefault of payment. As the investor reaches for higher yield by steppingdown the credit rating spectrum, he is accepting less quality and protectivecharacteristics (i.e., interest coverage) and assuming greater financial risk.Bullet: A regular coupon paying bond with a single repayment of principal(the bullet) on the maturity date.148
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Current yield: Current yield = Annual dollar coupon interest/PriceConvexity: The formula for convexity is rather unwieldy. Remember thatthe price/yield relationship of a bond is inverse and convex. Duration is astraight-line estimate. Conceptually, convexity is the prediction errorbetween the straight-line duration estimate and the convex price/yield curve.The equation for convexity is:Convexity (in years) =1*2*PVCF1 + 2*3*PVCF2 +...N* (N+1)*PVCFN/[(1+YTM/2)^2*k^2*PVTCF]
Where:k = the number of periods (payments) per year, so k = 2 for a semiannual paybond)N = Number of periods until maturity (Years to maturity*k)PVCFT = Present value of the cash flow in period t discounted at the YTMPVTCF = Total present value of the cash flows of the bond where the presentvalue is determined using the bond’s YTM.The approximate percentage price change due to convexity =0.5*Convexity*(Yield change)^2*100The approximate percentage price change based on duration and convexity isadditive:Estimated percentage price change =-Modified duration*Yield change*100change)^2*100
+
0.5*Convexity*(Yield
For option-free bonds, convexity is always positive. Bonds with embeddedoptions that the investor is short (think callable bonds and mortgage-backedsecurities where the investor is short the prepayment option) exhibit negativeconvexity. If bond yields fall far enough, negative convexity limits the upsideprice appreciation relative to an option-free bond. For example, if bondyields fall far enough, then issuers will realize a gain by calling the bondaway from the investors at the lower call price. Similarly, mortgage ownerswill exercise their prepayment option with greater frequency if bond yieldsfall. In a lower interest rate environment, mortgage holders have an incentiveto prepay the higher rate mortgage so that they can refinance at the lower,Visit the Vault Finance Career Channel at http://finance.vault.com — withinsider firm profiles, message boards, the Vault Finance Job Board and more.
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current rate. This prepayment results in an earlier than expected return ofprincipal to the MBS investor, who must also contend with lowerreinvestment rates.Duration: Duration describes of the sensitivity of a bond’s price to a changein yield.Effective annual yield (EAY):EAY = (1+ periodic interest rate)^k – 1Where k is the number of payments per yearFor example, if I have a bond with a 5% semi-annual interest rate, theeffective annual yield is:EAY = (1.05)^2 – 1EAY = 10.25%Although this is the mathematically correct way to annualize a semiannualinterest rate, most market practitioners use the bond-equivalent yield.Effective duration: Effective duration is a duration measure that quantifiesthe price sensitivity of the bond while also allowing for changes in the bond’sexpected cash flows. The methodology for computing effective durationrequires the use of a binomial interest-rate tree.Eurodollar: An American dollar held by a foreign institution outside theU.S., usually a bank in Europe.LIBOR: The London Inter-bank Offer Rate is the rate that is the interest ratethat the largest international banks charge each other for loans usuallydenominated in Eurodollars.Macaulay duration: Macaulay duration measures the price volatility of abond. The concept was first formulated by Frederick Macaulay in 1938.Macualay duration is a weighted average of the bond’s cash flows where theweights are the present value of each cash flow as a percentage of the bond’sfull price.Macaulay Duration = 1*PVCF1 + 2*PVCF2 + 3*PVCF3…+N*PVCFN/(k*PVTCF)Where:The terms are the same as defined under the convexity equation150
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If you don’t totally understand duration, just remember that the longer theduration of the bond, the greater is its percentage price volatility.Marked-to-market: A trader’s profit and loss statement is marked-tomarket. This refers to the daily valuation of the trader’s account to reflectcurrent market prices. The goal of every trader is to make his P&L statementas large and positive as possible. Some times, traders will make moneytrading, but will lose money because a large position goes down. The trader’sexplanation to the boss will go something like this: “I traded pretty well, butthis piece of crap position was marked down $100,000.”Medium term note (MTN): A medium-term note is a program of bondissues for a specified total amount of bonds over a specified period of time.MTNs are usually unsecured, fixed or floating rate, non-callable debtsecurities. MTNs save issuers time and money by allowing them to registera program of issuance rather than a series of separate bond issues.Modified duration: Modified duration measures the sensitivity of thebond’s price to changes in the yield to maturity. It assumes a flat-termstructure of interest rates and that yield changes do not change the bond’scash flow.Modified duration = Macaulay duration / 1 + (YTM/k)Modified duration can then be used to estimate the percentage price change:Percentage price change = -Modified duration*Yield change*100The operative word here is estimate. Duration estimates are linear andsymmetric, but if you’ve taken an elementary finance course, you know thatthe price/yield relationship is not linear and not symmetric. Convexityimproves duration by estimating the curvature of the price/yield relationship.On-the-runs: On-the-runs issues are those bonds most recently issued ineach maturity. Off-the-runs refer to everything else. All else being equal anon-the-run bond will trade at a slightly lower yield than the comparable offthe-run bond. This difference in yield reflects the liquidity premium offeredby trading the most current bond.Option-adjusted spread (OAS): A fixed income security’s implied riskpremium above the risk-less rate. The OAS is the spread above the risk-free
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rate that makes the average present value of the security’s cash flows equal tothe market price of the security. The OAS of a risk-free security is zero.Option-payoff diagram: These diagrams indicate the expected profit of anoption strategy at expiry. Options allow investors to hedge risk in long andshort positions. Combining options can create the desired risk-reward profilefor the options trader. Options strategies that are worth knowing are thebutterfly spread, condor spread, bull and bear spreads, calendar spread,straddle, strangles and portfolio insurance.Prepayment model: Mortgage holders typically have the right to prepay allor part of their mortgage. Therefore, to properly value mortgage-backedsecurities, investors must make some sort of assumption of the prepaymentrate on the underlying mortgage collateral. Two simple prepayment modelsare the Constant Prepayment Rate (CPR) and the Public SecuritiesAssociation (PSA) model. Wall Street is always tinkering with proprietaryeconometric prepayment models which try to better estimate prepaymentrates based on a collection of explanatory variables.Price value of a basis point (PVBP): PVBP is a measure of price volatilityfor a bond. It measures the change in yield for a one basis point change inprice.Primary dealer: A designation awarded by the Federal Reserve tocommercial banks or broker/dealers who meet specific criteria, most notablycapital requirements and participation in Treasury auctions.Redemption classification: Most bonds are bullets, but sometimes bondshave embedded options that alter the structure of a bond such that theprincipal may be repaid prior to maturity. A callable bond gives the issuer theright but not the obligation to redeem a bond at strike prices and dates beforethe bond is scheduled to mature. Putable bonds give the investor the right butnot the obligation to put the bond back to the issuer. A sinking fund bondretires a portion of the principal according to an agreed schedule. A sinkingfund can be thought of as a series of call options that the investor writes to theissuer, except that a sinking fund provision is obligatory rather than just aright. Perpetual bonds pay a coupon to the investor forever. Call options areoften embedded within perpetual bonds to give the issuer an opportunity toreturn this perpetual obligation.
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Yield curve: The yield curve graphically represents the relationship betweenthe yield on bonds of the same credit quality but different maturities. Themost commonly quoted yield curve is the Treasury yield curve, which isassumed to be free of default risk. Other yield curves are quoted as a spreadover the Treasury yield curve.Yield-to-maturity (YTM): The YTM is the interest rate that will make thepresent value of the cash flows of the bond equal to the price of the bond. Themajor shortfall of YTM is that this measure assumes that there is noreinvestment risk, i.e. that coupons can be reinvested at a rate that is equal tothe YTM. Another way of stating this is that the yield curve is flat. This israrely ever the case and YTM is almost always never realized.
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About the AuthorGabriel Kim studied at the Wharton School of the University ofPennsylvania, first as an undergraduate in the Management and Technologydual degree program and then as an MBA. Gabriel managed an equity hedgefund, and traded equities for ING Barings and Lehman Brothers. Gabriel hasbeen passionate about the stock market ever since his first purchase of DellComputer shares during high school.
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