Case Study
Beta Management Company
Raman Dhiman INDIAN INSTITUTE OF MANAGEMENT (IIM), SHILLONG For any queries pl contact: raman.pgpex12@iimshillong.in Company Background
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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."
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Issue
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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
Analysis & Way forward
Month Vanguard California REIT Index 500 Trust Brown Group 1989 -­‐ January February March April May June July August September October November December 1090 -­‐ January February March April May June July August September October November December 7.32
-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
-2.56
9.16
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
-8.53
Average 1.1025 -­‐2.265416667 -­‐0.67125 Covariance & Beta Value
Covariance of Beta Value for California Rate of California REIT 2.996288542 Interest w.r.t. Vanguard rate of 0.14121179 w.r.t. Vanguard interest Covariance of Beta Value for Brown Rate of Brown Group w.r.t. 23.65590313 Interest w.r.t. Vanguard rate of 1.114876744 Vanguard interest Standard Deviation & Beta Value
Stock Std DeviaZon Beta Value Vanguard 4.6 California 9.2 0.14121179 Brown 8.1 1.114876744 First cut analysis:
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Risk value of California stock & Brown stock is twice
that of Vanguard.
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From the Beta Value, the Brown share is more riskier
than California.
** Pl refer further analysis
Results of Regression – California & Vanguard
SUMMARY OUTPUT Regression Sta-s-cs MulZple R 0.07353166 R Square Adjusted R Square Standard Error ObservaZon
s 0.005406905 ANOVA Regression Residual Total -­‐0.039801872 9.412643861 24 df 1 22 23 Coefficients SS MS F Significance F 10.59617781 10.59617781 0.119598569 0.732755502 1949.153018 88.59786446 1959.749196 Standard Error t Stat P-­‐value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -­‐2.427871621 1.977939832 -­‐1.227474962 0.232616969 -­‐6.529867769 1.674124527 -­‐6.529867769 1.674124527 X Variable 1 0.147351433 0.426080217 0.345830261 0.732755502 -­‐0.736284855 1.03098772 -­‐0.736284855 1.03098772 Take 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.
Results of Regression – Brown & Vanguard
SUMMARY OUTPUT Regression Sta-s-cs MulZple R 0.656169766 R Square 0.430558762 Adjusted R Square 0.40467507 Standard Error 6.301260285 ObservaZons 24 ANOVA Regression Residual Total Intercept X Variable 1 df SS MS F Significance F 1 660.4820765 660.4820765 16.6343639 0.000498022 22 873.529386 39.70588118 23 1534.011463 Coefficients Standard Error t Stat P-­‐value Lower 95% Upper 95% Lower 95.0% Upper 95.0% -­‐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 1.754896753 In 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.
Weighted Average Portfolio Risks
Weighted Average Risk in a porKolio of Vanguard & California (PorKolio 1) Parameter Weight Std Dev(Risk) Average Vabguard Fund 0.98989899 4.606343688 4.559814964 California 0.01010101 9.230735982 0.093239757 Average Risk % 4.653054721 Weighted Average Risk in a porKolio of Vanguard & Brown (PorKolio 2) Parameter Weight Std Dev(Risk) Average Vabguard Fund 0.98989899 4.606343688 4.559814964 California 0.01010101 8.166771121 0.082492638 Average Risk % 4.642307602 Take 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
Weighted Average Returns in a porKolio of Vanguard & California (PorKolio1) Parameter Weight Return Average Vabguard Fund 0.98989899 1.1025 1.091363636 California 0.01010101 -­‐2.265416667 -­‐0.022882997 Average Returns % 1.06848064 Weighted Average Returns in a porKolio of Vanguard & Brown (PorKolio 2) Parameter Weight Return Average Vabguard Fund 0.98989899 1.1025 1.091363636 California 0.01010101 -­‐0.67125 -­‐0.006780303 Average Returns % 1.084583333 Take Away: From Weighted average calculations,
Portfolio 2 is giving more returns than Portfolio 1
Rate of returns from Capital Asset Pricing Model
R=rf +β(rm -rf )
Rf – Taken a 6% (RBI Rate of Return). Value may be taken as required.
Poreolio Poreolio 1 Poreolio 2 Rf 6 6 Beta Value 0.14121179 1.114876744 Poreolio Return R (Return from CAPM method) 1.06848064 6.696388674 1.084583333 11.48008373 Take away: Portfolio 2 will provide us more return than Portfolio 1
Thank You …