1. Case Study Beta Management Company RamanDhiman INDIANINSTITUTEOFMANAGEMENT(IIM),SHILLONG Foranyqueriesplcontact:raman.pgpex12@iimshillong.in

2. Company Background Beta Management Company was founded in 1988 Ms. Wolfe considered herself a market strategist, and Beta Management's stated goals were to enhance returns but reduce risks for clients via market timing . She would keep a majority of Beta's funds in no-load, low-expense index funds (with the remainder in money market instruments), adjusting the level of market exposure between 50% and 99% of Beta's funds in an attempt to "time the market."Issue Mrs. Wolfe also decided to increase the proportion of Beta's assets in equities, since she felt the market was still a good value and that 1991 would be a good year. As a first step toward both of these goals, Ms. Wolfe was considering immediately increasing her equity exposure to 80% with the purchase of one of two stocks recommended by her newly hired analyst Both were small NYSE-listed companies whose stock price had eroded over the past two years to levels that seemed unreasonably low She noticed that these stocks both seemed to bounce around in price much more than the market (or the index fund), and she wondered if she was doing the right thing exposing her clients to these new risks 3. Analysis & Way forwardMonthVanguard CaliforniaREIT Index500TrustBrown Group1989-January February March April May June July August September October November December 1090-January February March April May June July August September October November December7.32 -2.47 2.26 5.18 4.04 -0.59 9.01 1.86 -0.4 -2.34 2.04 2.38 -6.72 1.27 2.61 -2.5 9.69 -0.69 -0.32 -9.03 -4.89 -0.41 6.44 2.72-28.26 -3.03 8.75 -1.47 -1.49 -9.09 10.67 -9.38 10.34 -14.38 -14.81 -4.35 -5.45 5 9.52 -0.87 0 4.55 3.48 0 -13.04 0 1.5 -2.569.16 0.73 -0.29 2.21 -1.08 -0.65 2.22 0 1.88 -7.55 -12.84 -1.7 -15.21 7.61 1.11 -0.51 12.71 3.32 3.17 -14.72 -1.91 -12.5 17.26 -8.53Average1.1025-2.265416667-0.67125Covariance & Beta Value Covarianceof BetaValueforCaliforniaRateof CaliforniaREIT 2.996288542 Interestw.r.t.Vanguardrateof 0.14121179 w.r.t.Vanguard interest Covarianceof BetaValueforBrownRateof BrownGroupw.r.t. 23.65590313 Interestw.r.t.Vanguardrateof 1.114876744 Vanguard interestStandard Deviation & Beta Value Stock StdDeviaZon BetaValueVanguard 4.6 California 9.2 0.14121179Brown 8.1 1.114876744First cut analysis: Risk value of California stock & Brown stock is twice that of Vanguard. From the Beta Value, the Brown share is more riskier than California. ** Pl refer further analysis 4. Results of Regression California & Vanguard SUMMARYOUTPUT RegressionSta-s-cs MulZpleR0.07353166RSquare AdjustedR Square Standard Error ObservaZon s0.005406905ANOVA Regression Residual Total Intercept XVariable1-0.039801872 9.412643861 24df 1 22 23 CoecientsSS MS F SignicanceF 10.59617781 10.59617781 0.119598569 0.732755502 1949.153018 88.59786446 1959.749196 StandardErrortStatP-valueLower95%Upper95%Lower95.0%Upper95.0%-2.4278716211.977939832 -1.227474962 0.232616969-6.5298677691.674124527 -6.5298677691.6741245270.1473514330.426080217 0.345830261 0.732755502-0.7362848551.03098772 -0.7362848551.03098772Take away: Since the value of Significance F is more than 0.05, so it means that the Probability that an equation used will not explain the similar relationship between the subject stocks is 27%. Therefore, we do not have a meaningful correlation Moreover the P Value is also more than 0.05, means that the variable X i.e. Vanguard do not really influences Brown. 5. Results of Regression Brown & Vanguard SUMMARYOUTPUT RegressionSta-s-cs MulZpleR 0.656169766 RSquare 0.430558762 AdjustedRSquare 0.40467507 StandardError 6.301260285 ObservaZons 24 ANOVA Regression Residual Total Intercept XVariable1dfSS MS F SignicanceF 1 660.4820765 660.4820765 16.6343639 0.000498022 22 873.529386 39.70588118 23 1534.011463 Coecients StandardError tStat P-value Lower95% Upper95% Lower95.0% Upper95.0% -1.953842984 1.324124645 -1.475573309 0.154228174 -4.699909424 0.792223455-4.699909424 0.792223455 1.163349646 0.285237856 4.078524721 0.000498022 0.571802539 1.754896753 0.571802539 1.754896753In this case the value of significance F is less than 0.05, So the correlation is meaningful. Moreover the P Value is also less than 0.05, means that the variable X i.e. Vanguard really influences Brown. 6. Weighted Average Portfolio Risks WeightedAverageRiskinaporKolioofVanguard&California(PorKolio1) Parameter Weight StdDev(Risk) Average VabguardFund 0.98989899 4.606343688 4.559814964 California 0.01010101 9.230735982 0.093239757 AverageRisk% 4.653054721 WeightedAverageRiskinaporKolioofVanguard&Brown(PorKolio2) Parameter Weight StdDev(Risk) Average VabguardFund 0.98989899 4.606343688 4.559814964 California 0.01010101 8.166771121 0.082492638 AverageRisk% 4.642307602Take Away: From Weighted average calculations, Portfolio 1 is more risky than Portfolio 2 Note: We can not find here the risk through 2X2 matrix, as from regression analysis, the value of Significance F and P Value are more than 0.05. So the correlation between California & Vanguard fund is irrelevant.Weighted Average Portfolio Returns WeightedAverageReturnsinaporKolioofVanguard&California(PorKolio1) Parameter Weight Return Average VabguardFund 0.98989899 1.1025 1.091363636 California 0.01010101 -2.265416667 -0.022882997 AverageReturns% 1.06848064 WeightedAverageReturnsinaporKolioofVanguard&Brown(PorKolio2) Parameter Weight Return Average VabguardFund 0.98989899 1.1025 1.091363636 California 0.01010101 -0.67125 -0.006780303 AverageReturns% 1.084583333Take Away: From Weighted average calculations, Portfolio 2 is giving more returns than Portfolio 1 7. Rate of returns from Capital Asset Pricing ModelR=rf +(rm -rf ) Rf Taken a 6% (RBI Rate of Return). Value may be taken as required. Poreolio Poreolio1 Poreolio2Rf 6 6BetaValue 0.14121179 1.114876744PoreolioReturn R(ReturnfromCAPMmethod) 1.06848064 6.696388674 1.084583333 11.48008373Take away: Portfolio 2 will provide us more return than Portfolio 1 8. Thank You