PTMBA2013 Managerial Finance Beta Case

Managerial Finance

Case: Beta Management

Beta Management company Key facts

• Small investment management company

• Located in a Boston suburb

Location

• Ms. Wolfe founded the company in 1988

• She is the current CEO

Founder and CEO

• 1989: Performance under market returns

• 1990: Good performance despite down market

Past performance

• $25 million in assets from high-net-worth clients due to investment success

Assets

2

Beta Management company Strategy

• Beta Management uses the market

timing principle to maximize returns

while reducing risks for clients via

indexing.

• Market exposure is adjusted between

50% and 99% of equity.

• Most of the money is invested in no-

load, low expense index funds.

• Current exposure level is 79.2%.

• The rest is invested in money market

instruments.

Money

market

instruments

3

Beta Management company Outlook

Size of assets

doubled

Reaction of potential clients

Anticipation for 1991 to be a good

year

Increase the proportion of

assets in equities by

adding stocks

Thanks to the good performance of the

past years, Beta Management has

doubled the size of the assets

Beta has lost potential clients wondering about

why Beta was only using index funds

Ms. Wolfe anticipates 1991 to be a good year for stocks and that the market was still a

good value

She decided to increase the

proportion of Beta‘s assets in equities by purchasing one of the two stocks: California REIT or Brown Group, Inc.

4

Beta Management company Strategy

• Where is she adding “value” before the change in strategy?

• Maximize return while keeping risks under control

• Main focus on affordable Vanguard index delivering similar

return as S&P 500 Index

• Time the market

• Why do you think she is following her existing strategy?

• Because of a lack of time and the small volume of assets

under management, she decides to follow the index strategy

5

Beta Management company Strategy Change

6

Change in

Strategy

Pressure from the potential clients

Prospection of

institutional clients Need for

Growth in managed

Equity

1. Calculate the variability of the stock returns of California REIT and Brown group during the past 2 years. How variable are they compared with Vanguard Index 500 Trust?

• Using the investment return Data (Table

1) we calculate the standard deviation

of the index and of the two stocks.

Year Month Vanguard

Index 500 Trust

California REIT

Brown Group

1989 January 7,32% -28,26% 9,16%

February -2,47% -3,03% 0,73%

March 2,26% 8,75% -0,29%

April 5,18% -1,47% 2,21%

May 4,04% -1,49% -1,08%

June -0,59% -9,09% -0,65%

July 9,01% 10,67% 2,22%

August 1,86% -9,38% 0,00%

September -0,40% 10,34% 1,88%

October -2,34% -14,38% -7,55%

November 2,04% -14,81% -12,84%

December 2,38% -4,35% -1,70%

1990 January -6,72% -5,45% -15,21%

February 1,27% 5,00% 7,61%

March 2,61% 9,52% 1,11%

April -2,50% -0,87% -0,51%

May 9,69% 0,00% 12,71%

June -0,69% 4,55% 3,32%

July -0,32% 3,48% 3,17%

August -9,03% 0,00% -14,72%

September -4,89% -13,04% -1,91%

October -0,41% 0,00% -12,50%

November 6,44% 1,50% 17,26%

December 2,72% -2,56% -8,53%

The variability is calculated using the

standard deviation. In both years and in

total both stocks are more variable than the

Vanguard index.

Vanguard Index 500 Trust

California REIT

Brown Group

1989 mean 2,36% -4,71% -0,66%

standard deviation 3,59% 11,52% 5,39% 1990 mean -0,15% 0,18% -0,68%

standard deviation 5,30% 5,70% 10,51%

Total mean 1,10% -2,27% -0,67% standard deviation 4,61% 9,23% 8,17%

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1. Which stock appears to be riskiest?

Conclusion: The stock with the highest standard deviation (variability) over

1989 and 1990 is the riskiest. In this case California REIT is the riskiest

stock.

Interesting is that in 1990 Brown Group was more risky than California REIT.

Vanguard Index 500 Trust

California REIT

Brown Group

1989 mean 2,36% -4,71% -0,66%

standard deviation 3,59% 11,52% 5,39%

1990 mean -0,15% 0,18% -0,68%

standard deviation 5,30% 5,70% 10,51%

Total mean 1,10% -2,27% -0,67%

standard deviation 4,61% 9,23% 8,17%

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2. Suppose Beta’s position had been 99% of equity funds invested in the index fund, and 1% in the individual stock. Calculate the variability of this portfolio using each stock.

• To find the risk of a portfolio, one must know the degree to which the

stocks’ returns move together. This degree is the covariance.

• The covariance is calculated as the expected product of the deviations of

two returns from their means

• The covariance between Returns Ri and Rj

• Estimate of the Covariance from Historical Data

• If the covariance is positive, the two returns tend to move together.

• If the covariance is negative, the two returns tend to move in opposite

directions.

( , ) [( [ ]) ( [ ])] i j i i j jCov R R E R E R R E R

, ,

1( , ) ( ) ( )

1

i j i t i j t jt

Cov R R R R R RT

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2. Suppose Beta’s position had been 99% of equity funds invested in the index fund, and 1% in the individual stock. Calculate the variability of this portfolio using each stock.

• There are the results of the covariance for the three investments

• Then, we calculate the variability of the portfolio combinations

Covariance between … and … Vanguard Index

500 Trust

California

REIT

Brown

Group

Vanguard Index 500 Trust 2,996 23,656

California REIT 2,996 11,839

Brown Group 23,656 11,839

99 % of Vanguard with 1% of Vanguard Index

500 Trust

California

REIT

Brown

Group

Variance 21,218 20,864 21,271

Standard deviation 4,606 4,568 4,612

Now the portfolio with 1% of Brown Group is the riskest although Brown was

the less risky stock taken alone. The riskiest stock alone California REIT

decreases the risk of the portfolio. Why is that?...

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2. How does each stock affect the variability of the equity investment, and which stock is riskiest? Explain how this makes sense in view of your answer to the first question

• The formula to calculate the variance of a two security portfolio is:

• The riskiest stock makes in this case the portfolio less risky and the less

risky stock makes the portfolio more risky.

• The amount of risk that is eliminated in a portfolio depends on the

degree with which stocks face common risks and their prices move

together. The less correlated the index and the stock are, the lower the

risk (hedging). Because the covariance between Vanguard and

California REIT (2.996) is much lower than the covariance between

Vanguard and Brown Group (23.656), the fact that California REIT alone

is riskier than Brown Group becomes secondary in the formula.

2 2

1 1 2 2 1 2 1 2( ) ( ) ( ) 2 ( , ) PVar R x Var R x Var R x x Cov R R

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3. Perform a regression of each stock’s monthly returns on the Index returns to compute the “beta” of each stock.

y = 1.1633x - 1.9538 R² = 0.4306

-20

-10

0

10

20

-10 -5 0 5 10

Return on the Vanguard Index

Brown Group

y = 0.1474x - 2.4279 R² = 0.0054

-30

-20

-10

0

10

20

-10 -5 0 5 10

Return on the Vanguard Index

California REIT

The sensitivity to systematic risk (Beta, the

slope) is the expected percent change in the

excess return of a security for a 1% change in

the excess return of the market portfolio

= 1.16

An investment in Brown ( =1.16) should

add risk to a = 1 portfolio

= 0.14

An investment in C-REIT( =0.14) should

decrease risk in a = 1 portfolio

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3. How does this relate to the situation described in the above question?

• If we assume she has invested 99% in the Vanguard Index 500

and now decides to add another stock, then the standard

deviation changes:

Std Dev now: 0.99 * 4.606 = 4.560

(1% invested in riskfree asset, Std = 0)

Invest 1 % in Portfolio Std Original Std Change

California REIT 4.568 4.560 + 0.008

Brown Group 4.614 4.560 + 0.054

Vanguard Index 500 4.606 4.560 + 0.046

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4. How might the expected return for each stock relate to its riskiness?

• She would (probably) like the investment that is expected to provide the

most excess return per unit of risk added by the investment.

• Such a risk return relation should equilibrate across investments. If this

would not be the case, we would not invest as we have no compensation

for risk.

046.0008.0

RRRR FMFC

RRRR FMFC

046.0

008.0

=0.17, which is almost exactly

the Beta for C REIT

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• Since market risk cannot be diversified

and Brown Group has the higher beta

(higher sensitivity to systematic risk),

they should offer a factor 1.02 (1.16 –

0.14) higher risk premium than

California REIT. Investors can expect a

superior return rate coming from Brown

group, when taking the Vanguard Index

as the market portfolio.

4. How might the expected return for each stock relate to its riskiness?

• The range 100% until 82 % of

Vanguard is an efficient portfolio.

• Adding more than 18% of C-REIT in

increases the volatility while

decreasing the expected return.

• It makes no sense to add Brown to

Vanguard. The more you add Brown

into the portfolio, the more the

investor is worse off: the return

decreases and the volatility

increases

15

-0,700

-0,200

0,300

0,800

1,300

4,000 5,000 6,000 7,000 8,000

Van, Brown

-2,300

-1,800

-1,300

-0,800

-0,300

0,200

0,700

1,200

4,000 5,000 6,000 7,000 8,000 9,000

Van, CREIT