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# Note 6 for FINA 4320 with Professor Boulatov at UH

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This 34 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 30 views.

## Reviews for Note 6 for FINA 4320 with Professor Boulatov at UH

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Date Created: 02/06/15

Class 6 Risk and Return I Rates of Return Single Period HPR Pl P0D1 0 HPR Holding Period Return P1 Ending price P0 Beginning price D1 Dividend during period one Rates of Return Single Period Example Ending Price 24 Beginning Price 20 Dividend 1 HPR242012025 Rates of Return Multiple Period Example Fund starts with lm under management Initial Value 1m Receives additional funds during the year quarterly Cash Flow CF CF can be positive or negative Note next Slide Net flOW represents the new investments attracted by high previous returns Returns Multiple periods p133 Quarter 1 2 3 4 AssetsBeg 10 12 20 8 HPR 10 25 20 25 Assets Before Net Flows 11 15 16 10 Net Flows 01 05 08 00 End Assets 12 20 8 10 HOW to Characterize Returns Average Returns Arithmetic Geometric Dollarweighted Returns Using Arithmetic and Geometric Averaging Arithmetic rar1 r2 r3 rnn ra 10 25 20 25 4 10 or 10 Geometric timeweighted average Why r lt1r1gt lt1r2gt lt1rngt II1 rg 11 125 8 125 14 1 15150 14 1 0829 829 Dollar Weighted Returns corp n Internal Rate of Return IRR the discount rate that results present value of the future cash ows being equal to the investment amount investment has zero value Considers changes in investment Initial Investment is an out ow Ending value is considered as an in ow Additional investment is a negative ow Reduced investment is a positive ow Dollar Weighted Average Quarter 1 2 3 4 CF mil 1 5 8 10 Solving for IR 10 111quot1 511quot2 8113 1011quot4 r 0417 or 417 lt 829 Why Because the returns were high when price was low Quoting Conventions 1 Returns on assets with regular Cash Flows Quoted annually CF may have different structure Mortgages monthly payments Bonds semiannual coupons Therefore Compound Quoting Conventions 11 APR annual percentage rate periods in year X rate for period EAR effective annual rate 1 rate for periodPeriods Peryr 1 Example monthly return 0f1 APR 1 X 12 12 EAR 10112 1 1268 Example Financial Securities 1 The Return is a measure of I iew well a security derferrrls 3 rdss Return H fir H Pr I l 41 Pf Au exer r lele suppose you buy a share at 56 at the end enquot a year it pays 2 dividend and sells fer 55 3 397 4 l Gress Return 114 lid1 5139 1 Example Financial Securities II a Mere Often we wer with net returns 531 F s H Pi i ri I T 3 RH i a We often separate net returns into twe cempenente dii J Pii i Pi f3ri Pii P1 1 J I Pr P1 P1 P5 income yield cash payputs received by the iiwestpr dividende fer Stocks couppn Dayl39l lEEI39itS for bonds capital gain loss Change in security price 3 a in the previpue example the income yield was 4 and the capital gain was 10 quotquot1 quotquot39ji Til i Example Financial Securities III Think carefully about which atquot these variables is known in ad vance 1 T Bills d u ki iewr PHI unkr idwn unless hill matures at t ii 2 T Bdnds d Cdupdn payment kl lDWl l PM again Lmkndwn unless bend matures at 15 1 3 Stacks d dividend u n kn ewn PH unkr idwr i Expected amp Realized Returns up At the start at the period eerne variables are net kliDWli SO we can erin calculate the expected return ma 1 2 E eh i 1 Pl 1 Elm 1 At the end atquot the period we knew what l iEEDDEHECI and can calculate the realizeei return 7 39l39 l J F 31 T u The tare numbers may he very different Multiperiod Returns P E P 1 P 12 1 1 n d 2 time t time t1 tin rt2 Let RHI rsienete the grass return i39rem time t te t 1 RH rgr rgies return trem time t l l to t l 2 Ri3n jji gross return from time t to time t l i2 r it139 Rigi2ji 1 net return trem time t te time t l 2 T Compounding ASSLII39hihg that we reinvest divit39iei39ids then the return over the two peridds is I I l 391 time Pi2i P Cir H Pt i I ffi4er 32 Pi Pi i J Rt i i Rii l RH I ie the familiar CDI39iiDCiLIi idiiig formula 1 PM U i ii393quot11 quoti2i Compounding Example Example you earn 10 in year 1 and 20 in year 2 a 2 year return is rirt1j1n1 1112 r 13 1 32 Wl39iat is the average annual return in the exarriple above Izjeeauee erquot COITIDDLJHCHHQ it is NOT L5H also it is NOT rir 39 what we want is a rate r euch that 3911 i532 1 i r J 33911 i r2139 5 r i1 i ri i H n3 i I l 149 Geometric VS Arithmetic r is the geometric average of 10 and 20 as epgesed te the aritl39ir netlc average which was 15ij geometric average is always less than the arithmetic ave is it better te use geometric er arithmetic average z it s really a cerwentien but it is mere cer lsistent can get large differences in averages esp leng herizen ex 5 years of returns on Dell 199D 90 1991 35 1992 25 1993 40 1995 10 Ariti39lmetic 8 Geen ietric 45 Characteristics of Probability Distributions 1 Mean most likely value 2 Variance or standard deviation 3 Skewness If a distribution is approximately normal the distribution is described by characteristics 1 and 2 Normal Distribution r Symmetric distribution Skewed Distribution Large Negative Returns Possible A Negative Positive Skewed Distribution Large Positive Returns Possible Median Negative r Positive Measuring Mean Scenario or Subjective Returns Subiective returns Er g ps rs Ms prebabittty of a state Ms a return it a state eeeurs t to s states Numerical Example Subjective or Scenario Distributions State Prob of State 5 State 1 1 05 2 2 05 3 4 15 4 2 25 5 1 35 Er 105 205 135 Er 15 Variance as Measure of Risk I Varr E rs E392 Variance 2 p8 rs Equot2 S Standard deviation variance1 2 Variance as Measure of Risk 11 Risk in Risk is uneertainty abeut the future in While ateeks tie better on average irwestere know that in any one year eteeks may tie rnueh averse than bends ie they are more risky a One mnnnen way rat summarizing risk is through standard deviation 0 a measure of dispersion Measuring Variance or Dispersion of Returns Subjective or Scenario Variance 2 p8 rs E392 Standard deviation variance12 Using Our Example Var 105152205 152 135152 Var 01199 SD011991 2 1095 Variance of Returns time series a if mg m are yearly returns first crarnpute tne sarnnie mean is given by we use sample estimates as an appreximatiens fer true ex ante means and variances since we CEiiil iCit see inte the future Sample Statistics time series The sampfe standard deviatten is just the square reet atquot the sample variance Irquot r V J 1926 2002 Average Real Standard Return Deviatidn T Bills 05 43 T Bdnds 17 1d1 Stacks 66 19 Conclusion Risk Premium People demand compensation for risk compare a lottery wl iere yeu will either receive 50000 it39 a celn lands heads and lese 20000 it it lands tails with getting 15000 fer sure mest peepie weuld prefer the sure 15000 both choices offer an expected reward at 15000 but ene at them else has risk which we dislike it the sure thing reward was ehly 10000 yeu might cheese the lottery instead Stacks offer higher average returns than bends because peepie are risk averse dislike risk require higher expected returns to be willing to held riskyr securities Equity Premium Puzzle 1 in feet economists have hati trouble justifying a premium as big as 6 on the basis of risk This is termed the equity prel39nium puzzle 1 In otl ter words examining I39iistoricel returns long term in vestors should hold 100 equity and enjoy the 61 bremiu m on stocks a Possible EXDIEHEHUDHS for the puzzle 1 l tistorical realized returns are not necessarily an indiea tion of future expected returns 2 mismeasurement of risk and return Equity Premium Puzzle 11 3 surviversl tip hiae Guetzmaim and lerleh 1998 cutie examining US market the heat gerturming and surviving market ever the last century When examining the glehal market including emerging equities the Di El i ilUl l l is small 4 catastrophe risk theery 5 private equity returns are lew Meakewitz anti Viaaing Jergenaen 2000 Long Horizon Returns 1 The equity Di ElTliLliT l iaeeemes even mere puzzling when we leek at the risk et steaks ever leng herizens 1 Take seme simple l i39iEEiSLIi ES et risk and see what they shew 1 Minimum and I TIElXiITIUlTl real heleling periecl returns ever 29 year periecl range fer stecks 26 te 107 per year range r er pends 19 te 14 per year suggests the presence of meal l reversien in steck returns after a geee year slightly mere liker that steek market will de peerly anti e iCe versa ie geed years cancel eut bad years

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