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# Class Note for FINA 4320 with Professor Boulatov at UH

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This 30 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 24 views.

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Date Created: 02/06/15

Class 2021 Managing Bond Portfolios Managing Fixed Income Securities Basic Strategies Active strategy Trade on interest rate predictions Trade on market inef ciencies Passive strategy Control risk Balance risk and return Bond Pricing Relationships Inverse relationship between price and yield An increase in a bond s yield to maturity results in a smaller price decline than the gain associated with a decrease in yield Longterm bonds tend to be more price sensitive than shortterrn bonds Pricing Relationships Zeroes Some Prices of Zeros Nornmlized to 1 at 5 2 Price Interest Hats Bond Pricing Relationships cont As maturity increases price sensitivity increases at a decreasing rate Price sensitivity is inversely related to a bond s coupon rate Price sensitivity is inversely related to the yield to maturity at which the bond is selling Pricing Relationship Coupons Prices of 10 year Coupon Bonds Normalized to 1 at 5 148 Price 53973 Coupon 25 Coupon 3 50 Coupon 04 I I G Interest Rate Duration A measure of the effective maturity of a bond The weighted average of the times until each payment is received with the weights proportional to the present value of the payment Duration is shorter than maturity for all bonds except zero coupon bonds Duration is equal to maturity for zero coupon bonds Duration Calculation The duration is a ii iEE iSLIi E of the sensitivity of bond price to changes in interest rates To iefil ie duration let 3 be the yield to maturity en the bend under ceheid eratien and let E 13 then duretien i5 defined by Change P SR P d tug P D E if 1U g Change c That is duration is the yield elasticity enquot price Duration zero coupon bond Fer Zerd Couan Bonds PM 3 so P d n l P39 P 13 n That is far Zeros Duration Maturity a Ren39ienitjer price yield curve fer long dated zerds was steeper than it was tdr zerds witl39i shorter maturities u Lenger duration nieans greater price sensitivity td interest rate TlLICtLIEitiDHS Duration coupon bond t Wt CE 1y Price CF z Cash Flow for period t Duration Examples Same tiuretierie et bQi idS with rtiaturitiee et 10 years Yield CDLJDDH Price Duretieri D wf39e Principle 5 5 mm 811 510 5 10 13365 726 5110 1U 10 1GB ere 473 10 15 130 62in 473 n The tiLiret ien at e perpetuity 1 if D 3 Duration Calculation 8 Time Payment PV of CF Weight C1 X Bond years 10 C4 1 80 72727 0765 0765 2 80 66116 0690 1392 3 1080 811420 8539 25617 Sum 950263 10000 27774 DurationPrice Relationship Price Change is proportional to duration and not to maturity APP D X A1y 1y D modi ed duration D D 1y APP D x Ay Duration Properties a Duration l iiE EiSLil39ES the sensitivity ptquot pend prlee te el39tanges in interest rates measures this in units gtquot the sensitivity of zeros with the given time to maturity in Ceuppn bend duratldn is less than maturity value weighted average duratidh of the cash tlpws wltl lput principal duration doesn t depend en ceupeh rate average time of CDLlDOl l gash fldws is the same Duration is less fer larger lean rates er as the yield curve rises in path cases the weighted cash flaws CDI39TWE spener Uses of Duration Summary measure of length or effective maturity for a portfolio Immunization of interest rate risk passive management Net worth immunization Target date immunization Measure of price sensitivity for changes in interest rate Immunization Basic Ideas Two sources of risk in Bonds Price risk Reinvestment rate risk The two risks may offset each other Example coupon bond interest rate rises Value of bond decreases discount rate rises BUT The reinvestment rate on coupons also increases Result If duration equals the portfolio horizon the 2 risks exactly cancel other immunization Immunization Rebalancing Interest rate amp durations Change Rebalanoing Changing compositions of immunized portfolios Purpose Match the durations of assets and liabilities Uses of Duration Immunization Problem How de you insulate a bank39s pertfelid from interest rate i i Lietuatiens Banksquot assets have leng duratiens niainlv leng term leans Banks liabilities have short duratidns mainly shortterm demand denesits When interest rates increase the value at the assets decreases more than the value at the liabilities A bank s tatal worth could be wiped eut Duration matching How can you eerreet the I39hismatch i Need te duration matchquot that make I Could buy Dedicated Zerth long dated discount bends used just to increase partt olie duration cert make it wer k but it r r iight net be the best uee of bank capital Example matching With Zeroes I SL1 DDDSE that yeti have a liability 0rquot 100 millimi a due in 5 years Suppdee further that you wish to invest today to rardteet against interest rate variability and that yeti n can invest in 3 year zere eoupen bends mar 7 year ZEl tliCDLIDOH bends and that the term structure is currently flat at 5 Questidn how much should Emu inveat in each bend teddy Example matching with Zeroes 11 Well the present value of the liability is ll iii 3 T535 1115quot Now let x tienete the fr actien ef the portfolie s value you invest in the tl iree year zere ceupen bend then i r I39TiLIST satisfy 31 I TH Till I a so I is 50 ie its s 7535 iii1e is irwested in each mm Example matching with Zeroes III The strategy yields the fallen ring cash aws Year Frem 3 year zere Frerh 7 year zero 1 D O 2 J D 3 segue gtlt 111153 4535 0 4 J U 5 D U E U U 7 0 same 1 ms 5512 hate that the strategy times not require any rebalahcihg at least up to year three this is because 5113 r 31 t s p n Things are met so easy with camper bends Changing yields Convexity letquots leek at what I ll 10061053 te values it yields Change Yield Liability 3 Year Zeres 7 year Zeres l et39al r39r ll ll39l fquot 1 l r 4535 l39ll l rillquot 5513331 l r quot 4 8219 4032 4189 002 5 7836 3918 3018 0 6 7473 3666 002 u if rates go up a if rates ge tlewr l Yeu de sllghtly better than rrlatcl39llrrg perfectly VVhy Corwexity Pricing Error from ConveXity Price Pricing Error from C0nvexity Duration Yield Correction for ConveXity Modify the pricing equation AP P ConveXity is Equal to 1 CF 92 0 Pxoyfplayf Where CFt is the cash ow interest andor principal at time t D x Ay yz gtlt Convexity gtlt A302 Active Bond Management I Portfolio rebalancing activities Characterized as Swaps Substitution swap Exchange a bond for nearly identical substitute Ex identical bonds different coupons Intermarket swap Exchange bonds from different sectors of the market Ex Tbond and a corporate bond yield spread exceeds the historical one bet yields converge corporate outperforms Tbond Active Bond Management 11 More Swaps Rate anticipation swap Exchange of bonds with different maturities Ex Bet interest falls exchange for longer duration bonds Pure yield pickup Exchange for longer duration higher yield bonds Tax swap Exploit tax advantages Ex exchange for bond with a suitable capital losses realization Horizon Analysis Form of interest rate forecasting Return evaluation Select investment period Predict YTM at the end of the period Calculate the bond price Add the coupon income earned Obtain the total return over the holding period HPR Contingent Immunization Active management return above min acceptable Immunization return below min acceptable EX Manager 2yr horizon 10m portfolio min 2yr cumulative return 10 nal value of portfolio 11m current interest rate 10 Immunization initiates at trigger point V 111101 For t O trigger V 909m Manager can loose smth Interest Rate Swaps Contract trade cash ows of securities Wo trading securities Interest rate swap basic characteristics One party pays xed and receives variable Other party pays variable and receives xed Principal is notional Growth in market Started in 1980 Estimated over 60 trillion today Hedging applications

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