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# Investment Management FINA 4320

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This 91 page Class Notes was uploaded by Miss Quentin Grady on Saturday September 19, 2015. The Class Notes belongs to FINA 4320 at University of Houston taught by Alexei Boulatov in Fall. Since its upload, it has received 42 views. For similar materials see /class/208192/fina-4320-university-of-houston in Finance at University of Houston.

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Date Created: 09/19/15

Class 28 Review 2 1 Fixed Income Securities quotU m Bond Pricing Cr I1 1rt ParValue T P T B W Price of the bond interest or coupon payments number of periods to maturity semiannual discount rate or the semiannual yield to maturity Price of 8 10yr With yield at 6 1 20 1 40 gtlt 1000 gtlt PB 103t 10320 PB 2 1148 77 Coupon 41000 40 Semiannual Discount Rate 3 Semiannual Maturity 10 years or 20 periods Par Value 1000 Yield to Maturity YTM Discount rate that make the PV of all CF equal to price Example 8 coupon 30yr bond is selling 127676 60 40 1000 t 60 t11l 1r 127676 2 40 x Annuityr601000 gtlt PVfactor r60 r3 ZeroCoupon Bonds Shortterm US Tbills less than 1 yr Longer term created from Tbcnds Price of zero F P T T 1 YTM Example zero F1000 T 30yrs YTM r 10 Price today 5731 Treasury STRIPS Separate Trading of Registered Interest and Principal of Securities Forward Rates 101204 Yield Curve 1ym2 1y5 M 1 1310 1042103 10501 Using a 5yr and lOyr rates Longer term rate y10 4 Shorter term rate y5 3 Fiveyear forward rate in ve years 501 Duration Calculation The duration is a measure at the sensitivity 0f bend price td changes in interest rates To define duration let 3 be the yield to I39TiEittli39ity en the bend under eensid eratien and let 1quot E 13 then duratien is defined by Che nge P dPl quot39P ti lug P I E I 00 hsnge 1 di in ii lug i a That is duration is the yield elasticity at price Duration zero coupon bond in For Zero Coupon Bonds Ft 3 so rin P I Y 1i i t D e at p y That is for Zeros Duration Maturity a REH iEi T IUEh price yield curve for long dated zeros was steeper than it was for zeros with shorter maturities u Longer duration means greater once sensitivity to interest rate fluctuations Duration coupon bond Wt CE 1yt Price T D ZtXWt 11 CF z Cash Flow for period t 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 matching How can you eerreet the I nismstch I Need te duration matchquot that is make DAgsetS Assets DLiabthiES s Liabilitieg Effectively Duration of Equity O Example matching With Zeroes 1 Suppose that you have a a liability orquot 100 million a due in 5 years Suppose further that you Wish to invest today to protect against interest rate variability and that you i can invest in 3 year zero i2ouoon bonds in or year zero muoon bonds and that the term structure is currently flat at 5 Question how much should you invest in each bond today Example matching with Zeroes 11 Well the present value of the liability is ii iii e 2 Ti 7353 Lilliquot New let de ate the fraction of the pertfelle s value you invest in the tl lree year zere ceupeh hehtl then u I must satisfy 31 I TH Iii I u St I is 50 lie LLB 7535 Little is irweeted in each hand II Equity valuation Equity valuation example Stock ABC lyr holding period Expected dividend per share E D1 4 Current price per share P0 48 Expected yearend price P1 52 Required rate of return Suppose rf 6 ErM rf 5 ABC 12 Then r 6 12gtlt5 12 Intrinsic Value IV ED1EPl 452 lr 112 50 gt 48 V0 Conclusion Stock is currently underpriced Buy it Dividend Discount Models General Model V0220 Dr z1 1 7 t 0 V0 Value of Stock Dt Dividend r required return Do we ignore capital gains No they are incorporated into expected future dividends No Growth Model D V0 I Stocks that have earnings and dividends that are expected to remain constant Preferred Stock N0 Growth Model Example D V0 2 I D D1 500 r15 V0 500 15 3333 Constant Growth Model D0 1g D1 r g r g g constant perpetual growth rate Constant Growth Model Example I Do1g r g Ann dividend D0 300 g 8 r 15 D1 3gtlt108 324 V0 324 15 08 4629 V0 Constant Growth Model Example 11 Do1 g 7 8 E1 500 earnings b 40 plowbaok ratio reinvested lb 60 payout ratio dividends r 15 D1 300 g 8 VO 300 15 08 4286 V0 Estimating Dividend Growth Rates gROEXb g growth rate in dividends ROE Return on Equity for the rm b plowbaok or retention percentage rate 1 dividend payout percentage rate Partitioning Value Growth and No Growth Components E1 7quot V0 PVGO D01gE1 r g r PVGO Present Value of Growth Opportunities E1 Earnings Per Share for period 1 PVGO Partitioning Value Example 0 ROE20 d60 b40 E15OO D13OO r 15 g20gtlt40080r8 Partitioning Value Example V0 2 3 1508 NGVo 5 3333 15 4286 PVGO 4286 3333 952 Vo value with growth NGVo no growth component value PVGO Present Value of Growth Opportunities PE Ratio No expected growth PO E1 r P021 E1 r E1 expected earnings for next year E1 is equal to D1 under no growth r required rate of return PE Ratio With Constant Growth D1 E11 b rg rbXROE P0 1 E1 r bXROE m 1 PVGO Elr P0 PE capitalized 1 growthassets in place Numerical Example N0 Growth EO250 g0 r125 PO Dr 250125 2000 PE Mquot 1125 8 Numerical Example With Growth b60 ROE 15 1b40 gb x ROEO6gtlt159 E1 2501g250 x 109 273 D1 273 16 109 r125 g9 P0 109125 09 3114 PE3114273 114 PE1 60125O9 114 Class 28 Review 2 1 Fixed Income Securities Bond Pricing ParValue T PB C T HP I1 1rt PB Price of the bond C interest or coupon payments T number of periods to maturity r semiannual discount rate or the semiannual yield to maturity Price of 8 10yr With yield at 6 1 20 1 p 40 gtlt 2 1000 gtlt B 2 103t 10320 PB 2 1148 77 Coupon 41000 40 Semiannual Discount Rate 3 Semiannual Maturity 10 years or 20 periods Par Value 1000 Yield to Maturity YTM Discount rate that make the PV of all CF equal to price Example 8 coupon 30yr bond is selling 127676 60 40 1000 t 60 t11l 1r 127676 2 40 x Annuityr601000 gtlt PVfactor r60 r3 ZeroCoupon Bonds Shortterm US Tbills less than 1 yr Longer term created from Tbcnds Price of zero F P T T 1 YTM Example zero F1000 T 30yrs YTM r 10 Price today 5731 Treasury STRIPS Separate Trading of Registered Interest and Principal of Securities Forward Rates 101204 Yield Curve 1ym2 1y5 M 1 1310 1042103 10501 Using a 5yr and lOyr rates Longer term rate y10 4 Shorter term rate y5 3 Fiveyear forward rate in ve years 501 Duration Calculation up The duration is a measu re ef the sensitivity of band price to CI IHHQES in interest rates Te tietihe duratieh let 3 be the yield to i i iatLli iW on the bond under cerisid eratieh and let iquot E 1 3 then duratieh is defined by 00 Change P ESPquot39P ti lug P D A Change Trquot it i ci lug 0 That is duratieh is the yield elasticity of price Duration zero coupon bond For Zere Coupen Bonth PL Y se tPllquotP d3quot e i lit71 P dt e That is fer Zeres Duration 2 Maturity Remember price yield curve fer long dated zeres was steeper than it was fer zeros with shorter I i39iBILJFitiGS Lenger duration means greater price sensitivity to interest rate fluetnatiens Duration coupon bond Wt CE 1yt Price T D ZtXWt Z21 CF z Cash Flow for period t 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 matching How can you jrrect the I39nismatcm i Need to duration I39Tl tcl lquot that THElke D Agsetg 332 ASSEKS I D Liabil lties 3f Liabilities Effectively Duration of Equity O Example matching With Zeroes 1 Suppose that yeu have u a liability at 100 million l due in 5 years Suppese t39urtl39ier that you wish to invest tetiay to protect against interest rate variability and that you n can invest in 3 year zere coupen bends in er 7 year zere ceupen hands ancl that the term structure is currently flat at 5 Questien how much sheuici you invest in each bend traciay Example matching with Zeroes 11 Well the present value 01 the liability is liill Ll is 1 3f 35 New let 3 denote the fractieh of the pertfelie s value you invest in the three year zere ceupeh bend theh 3 must satisfy 111quot Til Ii D in se is 50 lilquoti1 ltj T5535 iilie is ll iVESIECi in each band II Equity valuation Equity valuation example Stock ABC lyr holding period Expected dividend per share E D1 4 Current price per share P0 48 Expected yearend price P1 52 Required rate of return Suppose rf 6 ErM rf 5 ABC 12 Then r 6 12gtlt5 12 Intrinsic Value IV ED1EPl 452 lr 112 V0 50gt48 Conclusion Stock is currently underpriced Buy it Dividend Discount Models General Model V0220 Dr z1 1 7 t 0 V0 Value of Stock Dt Dividend r required return Do we ignore capital gains No they are incorporated into expected future dividends No Growth Model D V0 I Stocks that have earnings and dividends that are expected to remain constant Preferred Stock N0 Growth Model Example D V0 2 I D D1 500 r15 V0 500 15 3333 Constant Growth Model D0 1g D1 r g r g g constant perpetual growth rate Constant Growth Model Example I Do1g r g Ann dividend D0 300 g 8 r 15 D1 3gtlt108 324 V0 324 15 08 4629 V0 Constant Growth Model Example 11 Do1 g 7 8 E1 500 earnings b 40 plowbaok ratio reinvested lb 60 payout ratio dividends r 15 D1 300 g 8 VO 300 15 08 4286 V0 Estimating Dividend Growth Rates gROEXb g growth rate in dividends ROE Return on Equity for the rm b plowbaok or retention percentage rate 1 dividend payout percentage rate Partitioning Value Growth and No Growth Components E1 r D01gE1 r g r PVGO Present Value of Growth Opportunities E1 Earnings Per Share for period 1 V0 PVGO PVGO Partitioning Value Example 0 ROE20 d60 b40 E15OO D13OO r 15 g20gtlt40080r8 Partitioning Value Example V0 2 3 1508 NGVo 5 3333 15 4286 PVGO 4286 3333 952 Vo value with growth NGVo no growth component value PVGO Present Value of Growth Opportunities PE Ratio No expected growth P0 E1 r P021 E1 r E1 expected earnings for next year E1 is equal to D1 under no growth r required rate of return PE Ratio With Constant Growth D1 E11 b rg rbXROE P0 1 E1 r bXROE m 1 PVGO Elr P0 PE capitalized 1 growthassets in place Numerical Example N0 Growth EO250 g0 r125 PO Dr 250125 2000 PE Mquot 1125 8 Numerical Example With Growth b60 ROE 15 1b40 gb x ROEO6gtlt159 E1 2501g250 x 109 273 D1 273 16 109 r125 g9 P0 109125 09 3114 PE3114273 114 PE1 60125O9 114 III Derivative Securities Option quotes Example 65134300 155499 0154125 5507110 91ng APHREEr Ii AMP31 Apm M A rES Jag WAVE li MA 3391 045am 01 54125 ESE 1m infill 0504315 HAVE g 61 WAVES ALI L325 3915quot ALI Gil AUG ES MU Jim 11151325 11 51 035 yi yla E w j 01 542125 02 4145 1154 MI 31 I ll 15 015 925 1313 1 1161 quot3413 v181 Example comments XYZ option class May 30 series many EX XYZ May 30 Call Strike price 30share Premium 2 How much do we pay Most options sell 100 shares pay at least 200 Expiration date typically 3 Friday of the month Example call option payoffs Suppose the stock price now is 29 We think it will go up buy call 2share Total pay 200 100 shares Suppose the stock price expiration is 35 Option value 3530 5 Pro t per share 52 3 Total pro t 3100 300 Payoffs and Pro ts on Options at Expiration Calls Notation Stock Price ST Exercise Price X Payoff to Call Holder ST X if ST gtX 0 if ST g X Pro t to Call Holder Payoff Purchase Price Payoffs and Pro ts on Options at Expiration Calls Payoff to Call Writer ST X if ST gtX 0 if ST g X Pro t to Call Writer Payoff Premium Profit Profiles for Calls Profit Call Holder Call Writer Stock Price Payoffs and Pro ts at Expiration Puts Payoffs to Put Holder 0 if ST 3 X X ST if ST lt X Pro t to Put Holder Payoff Premium Profit Profiles for Puts Profits Put Writer Put Holder Stock Price Payoff of Long Call amp Short Put Payoff Combined lt2 Long Call Leveraged Equity Stock Price Short Put Arbitrage amp Put Call Parity Since the payoff on a combination of a long call and a short put are equivalent to leveraged equity the prices must be equal CPSO Xl rfT If the prices are not equal arbitrage will be possible Protective Put long stock long put SltX SgtX Stock S S Put X S O Total X S Protective Put pro ts SltX SgtX Pro ts X SOP S SOP Protective ATM Put insurance Pro ts Stock Protective put Option Strategies Spreads A combination of two or more call options or put options on the same asset with differing exercise prices or times to expiration Vertical or money spread Same maturity Different exercise price Horizontal or time spread Different maturity dates Sample questions I You purchase one IBM July 120 put contract for a premium of 5 You hold the option until the expiration date when IBM stock sells for 123 per share You will realize a on the investment A 300 pro t B 200 loss C 500 loss D 200 pro t Answer C Sample questions 11 You purchase one IBM July 120 call contract for a premium of 5 The stock has a 2 for 1 split prior to the expiration date You hold the option until the expiration date when IBM stock sells for 64 per share You will realize a on the investment A 300 pro t B 500 loss C 1000 loss D 5600 loss Answer A Class 16 Bonds review Bonds Fixed Income Securities Fixed stream of CF as opposed to Equity May have features of other types Other types Equity Valuation based on real assets Derivatives Valuation based on other nancial assets Bond Characteristics Face or par value payment maturity Tbond sold in denominations of 1000 par value Coupon rate interest Typically semiannually Zerocoupon Bond Compounding and valuation Essentially the PV of CF stream will discuss later Accrued interest amp quoted prices Annual coupon Days since last coupon Accrued Interest 2 Days separating coupons Example Tbond 1000 par 8 coupon rate Quoted price 990 What is the invoice price 40 days after the last coupon payment Coupon payment 1000gtlt8gtlt05 40 semiannual Accrued interest 40gtlt40182 879 Invoice price 990 879 99879 Purchase days 40 0 I 182 days 364 days t yrs t12 yrs t1yrs Types of Bonds 1 Treasury bonds amp notes There used to be a call provision for Tbonds Corporate bonds Various provisions derivatives features Normally Issued par coupon discount rate Preferred Stock Has features of both equity and bond Speci ed stream of dividends like bond Dividends are not guaranteed like stock Preferred pay bondholders pref stock then stockholders Types of Bonds 11 Municipal bonds local governments Mortgage passthrough agencies Fannie May Freddie Mac Federal agency debt lntemational bonds Foreign bonds German rm sells dollardenominated bonds in the US Issued by foreign companies Denominated in domestic currency Eurobonds Eurodollars Euroyens Eurosterlings Eurodollar denominated sold outside the US Provisions of Bonds Call provision Issuer may repurchase call price amp call period Convertible provision Bondholder may exchange bond for shares optionally conversion ratio Put provision putable bonds Bondholder may choose to extend the bond s life Floating rate bonds Interest rates are tied to some market rates Example Tbill rate 2 credit conditions 2 Innovations in the Bond Market Reverse oaters coupon falls when interest rises Assetbacked bonds Mortgagebacked securities passthrough Catastrophe CAT bonds Essentially insurance against disasters Indexed bonds payments are tied to indices TIPS Treasury In ation Protected Securities Par value is tied to general level of prices Interest Real riskfree rate VS nominal one quotU m Bond Pricing C ParValue T I1 1rT P T B W Price of the bond interest or coupon payments number of periods to maturity semiannual discount rate or the semiannual yield to maturity Price of 8 10yr With yield at 6 1 20 1 40 gtlt 1000 gtlt PB 103t 10320 PB 2 1148 77 Coupon 41000 40 Semiannual Discount Rate 3 Semiannual Maturity 10 years or 20 periods Par Value 1000 Bond Prices and Yields Prices and Yields required rates of return have an inverse relationship When yields get very high the value of the bond will be very low When yields approach zero the value of the bond approaches the sum of the cash ows Prices and Coupon Rates Price Yield

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