Financial Markets - Investments, Solution for Beta Management Company Solutions. May not be 100 % accurate, but identifies an important point in case study.

1. Case Study
Beta Management Company
Raman
Dhiman
INDIAN
INSTITUTE
OF
MANAGEMENT
(IIM),
SHILLONG
For
any
queries
pl
contact:
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 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:
• 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
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
Intercept
X
Variable
1
-­‐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%
-­‐2.427871621
1.977939832
-­‐1.227474962
0.232616969
-­‐6.529867769
1.674124527
-­‐6.529867769
1.674124527
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.

5. 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.

6. 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

7. 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

8. Thank You …