Calculate variability of the stocks, Analyzing and Researching about Riskiest Stock, and the choice among these stocks

1. Title of Case: BETA MANAGEMENT COMPANY
Submission date: 04/26/2016
CERTIFICATION OF AUTHORSHIP: I certify that I am the author of this report and that
any assistance I received in its preparation is fully acknowledged and disclosed in the paper. I
have also cited any sources from which I used data, ideas or words; either quoted directly or
paraphrased I also certify that this paper was prepared by me (my team) specifically for this
course.
Team member Last name, First name/ ID/ Sign
Team member 1 Bui, Thao / 009969505
Team member 2 Vo, Huynh / 009535240
Team member 3 Catig, Justin / 008460569
Team member 4 Sorony, Hiep / 009754277
Team member 5 Bakhtiari, Nima / 008487921
Table of Contents
Executive Summary.........................................................................................................................1
Assignment Questions
1................................................................................................................................................2
2................................................................................................................................................3
3................................................................................................................................................4
4................................................................................................................................................5

2. 1
Executive Summary
Beta Management Company run by market strategist Sarah Wolfe, founder and CEO, is a
small investment management company based in Boston. The company was founded in 1988,
and by 1991, Beta Management had $25 million in assets and an increasing clientele base of
high-net-worth individual clients. The company’s goals were aimed at enhancing returns for
clients, while reducing risk through market timing. Based on the small size of client accounts,
Ms. Wolfe’s ability to easily maintain and adjust market exposure was based on keeping the
majority of the company’s funds in no-load, low-expense index funds. The rest of the money was
in money market instruments. By keeping the company funds in no-load, low-expense index
funds, Beta Management was able to adjust the level of market exposure between 50%-99% of
company funds, which allowed Ms. Wolfe to attempt timing the market. After researching
alternative index funds, Ms. Wolfe chose to exclusively use Vanguard’s Index 500 Trust based
on the low expense ratio and overall success when it came to closely matching the return on the
S&P 500 Index.
As of January 1991, Beta Management had 79.2% of its assets invested in Vanguard, and
within six months, the company had doubled. However, the fact that Beta Management only
used an index mutual fund and didn’t choose any of its own stocks caused some potential clients
to look elsewhere for business. Since Ms. Wolfe didn’t want to compete with larger firms, she
chose to focus on smaller stocks. She also wanted to increase the amount of the company’s assets
that were in equities in 1991, as she believed the market would be promising that year.
Ms. Wolfe chose to look at two small NYSE-listed companies with stock prices that had
gone down unreasonably low over the past two years. The first was California R.E.I.T., a real
estate investment trust. California R.E.I.T. made equity and mortgage investments in Arizona,
California, and Washington, in income-producing properties. The stock price of the company
had been negatively impacted by two factors: an earthquake in 1989, and the drop in California
real estate values. While Ms. Wolfe believed that the stocks were of good value, she also realized
that the company’s stock was very unstable. California R.E.I.T.’s stock price closed at $2 ¼ per
share on January 4, 1991.
The second company Ms. Wolfe looked at was Brown Group, Inc., a branded footwear
manufacturer and retailer ranked as one of the largest in the footwear market. In 1989, the
company began a massive restructuring program and earnings dropped. As a result, the stock
price dropped in 1989 and 1990. However, despite this the company earnings still stayed positive
and ready for an upswing. Ms. Wolfe had knowledge of the company’s products, and knew that
they would sell during the current recession. Additionally, she realized that the company had
steady cash flow and earnings, which she liked. The potential problems she identified were that
the stock price was variable, and it was sensitive to movements in the market. As of January 4,
1991, the price was $24.

3. 2
Assignment Questions
1. We use the standard deviation to calculate the variability. Both California REIT and Brown
Group in both years are more variable than The Vanguard Index 500 as we can see in the sheet.
In 1989 and 1990, California REIT is riskiest because its stock has highest standard deviation,
which is 9.2307% compared to Brown Group is 8.1667%. However, Vanguard is only 4.6063%;
it shows that the standard deviation of both individual stocks is double of the standard deviation
of the market. Therefore, Ms Wolfe sees that REIT is an extremely volatile stock. Brown has
lower risk, so Brown is better for the investment.
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%
Standard Deviation 4.606344 9.230736 8.166771
Beta Value 0.147351 1.163350
Alpha Value -0.024279 -0.019538

4. 3
2. The individual stock does not have big effect on the variability on the portfolio. As we can see
in the spreadsheet, 99% of Vanguard and 1% of California REIT has a standard deviation of
4.567 and 99% of Vanguard and 1% of Brown has standard deviation of 4.614. The variability of
Brown is greater than REIT because Brown has higher covariance. Therefore, Brown stock is
more risky. It explains that when the Vanguard moves, Brown also moves with it. The portfolio
with 1% of Brown is the riskiest even Brown was less risky stock which taken alone. California
REIT stock has lower risk than the Brown Group because of diversification of stock in portfolio.
Also, in this case, REIT and Vanguard have low correlation, if either REIT or Vanguard
decreases, the other does not have to decrease. This makes sense because the relatively higher
volatility found in REIT is balanced out. Since Brown and Vanguard are highly correlated, the
variability in that portfolio is greater than the first portfolio.
Month
99% Vanguard /
1% CA REIT
99% Vanguard /
1% Brown Group
1989 January 6.96% 7.34%
February -2.48% -2.44%
March 2.32% 2.23%
April 5.11% 5.15%
May 3.98% 3.99%
June -0.68% -0.59%
July 9.03% 8.94%
August 1.75% 1.84%
September -0.29% -0.38%
October -2.46% -2.39%
November 1.87% 1.89%
December 2.31% 2.34%
1990 January -6.71% -6.80%
February 1.31% 1.33%
March 2.68% 2.60%
April -2.48% -2.48%
May 9.59% 9.72%
June -0.64% -0.65%
July -0.28% -0.29%
August -8.94% -9.09%
September -4.97% -4.86%
October -0.41% -0.53%
November 6.39% 6.55%
December 2.67% 2.61%
Standard Deviation 4.567995 4.614280
Covariance 2.996289 23.655903
Beta Value 0.991474 1.001633
Alpha Value -0.000243 -0.000195

5. 4
3. Beta ( is “a measure of volatility, or systematic risk, of a security in comparison to the
market as a whole.” The lower the beta, the less risky it is to the market or the return on
investment is less sensitive to the market’s movement. Conversely, a higher beta value indicates
greater risk. Below, the linear regression of the investment returns of Brown Group has a beta of
1.16 while California REIT has 0.15. Therefore, Brown Group is a riskier asset than California
REIT. In part 2, if Ms. Wolfe decides to invest 99% in the Vanguard Index 500 and add another
stock, Brown Group would have a beta of 1.00 while California REIT of 0.99. In both cases,
Brown Group remains the riskier investment option.
y = 0.1474x - 0.0243
R² = 0.0054
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
-10% -5% 0% 5% 10% 15%
CalforniaREITROI
Vanguard ROI
ROI Vanguard-Cal REIT

6. 5
4. In determining the appropriate investment choice with the sole purpose of minimizing
portfolio risk, Ms. Wolfe would need to find the investment that can provide the moderate return
for every unit of risk added to the investment. Using the CAPM (Capital Asset Pricing Model),
“a model that describes the relationship between risk and expected return and is used in the
pricing of risky securities”, and the following assumptions, the expected return of California
REIT and Brown Group are:
rS = rRF + (rM-rRF) β
β = Beta of the security
rRF = Risk free rate
rM = Expected market return
California REIT
rS = rRF + (rM-rRF) β
= 0.01 + (0.011025-0.01)*0.15
= 0.01015
= 1.0 %
Brown Group
rS = rRF + (rM-rRF) β
= 0.01 + (0.011025-0.01)*1.16
= 0.011189
= 1.1 %
y = 1.1633x - 0.0195
R² = 0.4306
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
-10% -5% 0% 5% 10% 15%
BrownGroupROI
Vanguard ROI
ROI Vanguard-Brown Group

7. 6
*Assume the risk free rate is 1%. The assume risk free rate must be below that of the
expected return rate. CAPM assumes a rational investor because one would not risk their
money for a return lower than a risk free asset that yields higher return.
According to the risk/return tradeoff, investments with more risk can expect higher return rate.
Conversely, lower risk securities will yield less returns. From the above calculation, Brown
Group is a riskier investment because it has a higher expected return rate than California REIT.
Therefore, to minimize investment risk, Ms. Wolfe should invest in California REIT.