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# Inv AnlyPortfolio Mgmt FNAN 411

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This 21 page Class Notes was uploaded by Garrison Osinski on Monday September 28, 2015. The Class Notes belongs to FNAN 411 at George Mason University taught by Christof Stahel in Fall. Since its upload, it has received 13 views. For similar materials see /class/214995/fnan-411-george-mason-university in Finance at George Mason University.

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Date Created: 09/28/15

EDDIE KANE MARCUS Index Model Chapter8 Advantages of the Single Factor or Index Model Reduces number of inputs for diversification Markowitz 72 expected returns n variances nn I2 covariances For 100 assets we have 1001004950 5150 parameters 0 Analysis can easily be specialized Macro analysis Security analysis Consistent approach across analysts Single Factor Model w rizE r1 Bimei Two sources of return uncertainty m is an unanticipated shock in a single common macroeconomic factor that is affecting all returns 3 is the sensitivity of the return r to m e is a firmspecific surprise affecting only the return on stock 139 If the factor is the SampP500 the model becomes the SingleIndex Model Single Factor Model The factor model suggests that the following assumptions make sense 1 Em0 EelO 2 CoveiAO CovueiejVO 81 Risk in the single factor model 2 o 31631 o e 1 Total risk Systematic risk Firmspeci c risk B C 2 limilmiiir Cov rim 3il3jom pm Single Index Model Single Index Model stated in Excess Returns RiZOLiBiRMei R the excess return over the risk free rate R r rf B is the sensitivity to the variations in the market index excess return Oil is the securities expected excess return when the market excess return is zero Expected Return Beta Relationship E R oci3iE RM Single Index Model 0 Implications Number of parameters n Betas n Alphas n variances of the assets 1 risk premium of the index 1 variance of the index For 100 assets we have 10010010011 302 parameters Consistent covariance matrix across all assets Possibility of specialization for subset of assets or index However dichotomy of risk is restrictive 0 Extensions A K Multiindex models riE r1 X k1Bikmkei Diversification in the Single Index Model Let us look at an equally weighted portfolio P o c szer Rizlfwx ociBiRMei szn ocin BiRMn el szocpBpRMep Risk of portfolio P o z ioijoz epaQ o z fpij because Illlllllllllllllllll 2 a 1an llff 2 a lit 2 a 6 6p 6 el G 61 H H H The Variance of a Portfolio with Risk Coefficient Beta in the SingleFactor Economy Diversifiable Risk Bf of l Systematic Risk Excess Returns Estimating the Single Index Model Excess Returns on HP and SampP 500 April 01 March 06 4000 SampP 500 HP 3000 2000 1000 0000 AAA lvv AAAVQVAWAVW WWW W 2000 3000 4000 E S 8 8 8 8 3 8 8 8 MonthYear Scatter Diagram of HP SampP 500 and Security Characteristic Line SCL for HP U39I Excess Return HP A Excess Returns SampP 500 Regression Statistics for the SCL of Hewlett Packa rd Regression Statistics Multiple R 7238 R square 5239 Adjusted R square 5157 Standard error 0767 Observations 60 ANOVA df SS MS Regression 1 3752 3752 Residual 58 3410 0059 Total 59 7162 Coefficients Standard Error tStat pValue Intercept 00086 0099 08719 3868 SampP 500 20348 2547 79888 0000 Excess Returns on other assets Mammy Rates 9 Month Rates 4 Montth Rates 36 x 5ampP 500 HP W WW w W m 71 4 i 7 7 Mar01 MarDZ Mama Mm 04 Mar 05 M3706 MumhYear 3 2 Aw 1 7 SampP 500 A A A ln AA Aux3 ww 3907 V VVW v W V TARGET 71 s2 iIMar l Mar02 Mar03 ManOd Mar05 Mar b MonthYear 3 J I 5w sou 7 BF 039 SHELL Mar02 Mar04 Mar hVear Mar03 MarDS Mon 06 Optimal Risky Portfolio Input list Estimates of risk premium and volatility of the SampP 500 Estimates of asset Alphas Betas and volatilities 60 months Maximizing the Sharpe ratio results in the optimal risky portfolio w max Sp 2 such that w sums to 1 W Efficient Frontiers with the Index Model and Full Risk Premium Covariance Matrix 14 12 10 08 06 4 Efficient frontier full covariance 3904 Efficient frontier index model 02 A SampP 500 00 I u u I I I I 00 05 10 15 20 25 30 35 Standard Deviation 40 Comparison of Portfolios from the Single Index and FullCovariance Models Global Minimum Variance Portfolio Optimal Portfolio FullCovariance FullCovariance Model Index Model Model Index Model Mean 0371 0354 0677 0649 SD 1089 1052 1471 1423 Sharpe ratio 3409 3370 4605 4558 Portfolio Weights SampP 500 88 83 75 83 HP 11 17 10 07 DELL O1 05 04 06 WMT 23 14 03 05 TARGET 18 08 10 06 BP 22 20 25 13 SHELL 02 12 12 03 Industry Implementation of the Index Model 39 Returns instead Of EXCESS returns rizaibirMei b c b c rifociBi rMf el rizocirf13i BirMei b c aizocirf13i biz i Adjusting Beta Beta tends to move towards 1 over time Sampling error 0 Predicting Beta 3 a V B t 2 co 61 B t1 62 other predicting varlables Industry implementation of the Model 200412 Resid Number Ticker Close Std Std Error Adjusted of Symbol Security Nam Price Beta Alpha RSqr Devn Beta Alpha eta Observ HTBK HERITAGE COMM CORP 19020 023 072 001 686 019 089 049 60 HPC HERCULES INC 14850 078 7009 007 1213 034 157 085 60 HFWA HERITAGE FINL CORP WASH 22120 009 169 001 427 012 055 040 60 HRLY HERLEY INDS INC 20340 004 166 002 1037 029 134 031 60 HT HERSHA HOSPITALITY TR PRIORITY A SHS 11450 046 167 012 562 016 073 064 60 HSY HERSHEY FOODS CORP 55540 021 1166 0100 7172 021 100 020 60 HSKA HESKA CORP 1169 187 388 006 3126 086 404 158 60 HF39O HEWLETT PACKARD CO 20970 176 7045 040 1005 028 130 150 60 HXL HEXCEL CORP NEW 14500 085 4108 002 21163 060 280 090 60 HIFN HIFN INC 9220 233 088 021 2055 057 266 188 60 HIBB HIBBETT SPORTING GOODS 26610 103 405 011 1303 036 168 102 60 HIB HIBERNIA CORP CLASS A 29510 059 208 014 653 018 084 073 60 HICK A HICKOK INC CLASS A 7500 029 235 001 19121 053 248 053 60 HTCO HICKORY TECH CORP 10690 013 002 lt001 1074 030 139 042 60 HSVL Y HIGHVELD STL amp VANADIUM ADR 8200 034 264 000 1442 040 186 056 60 HIW HIGHWOODS PROPERTIES IN 27700 010 045 001 570 016 074 040 60 TA I l E 83 Merrill Lynch Pierce Fenner 8 Smith Inc Market sensitivity statistics 39Based on SampP 500 index using straight regression ML Adjustment 3 23B 131 adjusted sample Active Portfolio Management and the Index Model TreynorBlack Model Security analysis uncovers mispriced assets 05172 0 for i e A g ln 0 PM combines two portfolios to create optimal risky portfolio 1 Active portfolio with weight wA consisting of mispriced assets that is adjusted frequently 2 Passive portfolio equals the index with weight WM Trade off between efficient diversification and performance improvement Active Portfolio Management and the Index Model Intuition of trade off assume BA 1 Expected return of the portfolio quot l5 U D C l5 U l5 U wA ocAE RM 1wA E RM E RM oncA The position inA is creating additional exposure to the index Hence the passive index position has to be reduced by that same amount Volatility of the portfolio V quotquot a 2 2 2 Var wAeARM GMWAG eA Volatility increases because of nonoptimal diversification Maximizing Sharpe Ratio results in optimal weight forA 0261 ElRM 2 GM maXSwA gt wj Expected Return and Standard Deviation Active Portfolio Management and the Index Model Sharpe Ratio Sharpe Ratio 89 Q 5 390 a a 0 9 N V o9 e9 e lt19 9 05 e5 6 6 07 c 9 o q Q39 o awhq t bxb c aqueqyxb ozbq 5 n 395 5 V gt pQ 8Q9Q V9b QQ QQBQQ Olt 9Q9Q9 WA Expecledkemrn SmndanlDeialion SharpeRalio Active Portfolio Management and the Index Model Sharpe ratio improvement using optimal F weights wA forA S S 4 G Erp Tf CML A active M market passive

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