This document discusses a case study on beta management. It provides objectives of gaining skills in calculating risk/return measures, understanding concepts like total risk and diversifiable/undiversifiable risk. It examines investment strategies for a portfolio containing a Vanguard S&P 500 index fund with potential additions of individual stocks like California REIT and Brown Group. It analyzes the risks, expected returns and economic impact of these choices using metrics like standard deviation, beta and changes to dollar volatility. The conclusion is that the Brown stock increases portfolio risk more than the REIT due to its higher covariance with the market.

1. Case: Beta
Management

2. The Objectives
 1. To gain practice in calculating risk
and return measures on stocks and
portfolios, including estimation of beta
for stocks by simple regressions.
 2. To understand concepts of total risk,
portfolio risk, diversifiable and
undiversifiable risk, and how these
relate to the beta.
 3. To gain an appreciation of the
relation between risk and return, and
the CAPM.
 4. To allow an introductory discussion of
investment strategies.

3. The Issues
 1. The Strategy
 2. The Choices
 3. The Risks
 4. The Port Folio Risks
 5. The Return

4. The Strategy
 Ms.Wolfe Keeps majority of funds in no
load, low-expense index funds. She
preferably use vanguard’s Index 500
Trust due to its extremely low expense
ratio and its success at closely matching
the return of the S&P 500 index.
 She make money for its client by
investing in index fund even in down
market year.
 Company loses potential new clients
because She only use index mutual fund
and use none of its own stocks.

5.  Company decided to purchase individual
stock to make the equity portfolio.
 Focus on smaller stocks are made to
invest.
 She focus on two stocks :California REIT
and Brown group.
 Both stocks are NYSE listed and stock
price are bad over past two year.
 Both stocks are volatile stocks.
The Choices

6. Some Information of REITS
(REIT, WWW.reit.com)
 REIT: Real Estate Investment Trust.
 A REIT invests in income-producing property,
and may also invest in loans on property.
 There are about 300 REITs, with about 2/3
traded on an exchange, and with assets over
$300 B.
 Cumulative returns from 1/1/99 to 3/3/2003:
◦ REIT=40.67%, S&P500 = -32.09%.
 Volatility over 1/1/99 to 3/3/2003.
◦ REIT = 11.71%, S&P = 22.16%.
 Correlation between returns over 1/1/99 to
3/3/200: 0.2843.
 REIT Index beta from daily data = 0.15.

7. Some Information of Brown Shoe
WWW.Brownshoe.com
 Brown Shoe Company is a $2.6 billion,
global footwear company whose shoes are
worn by people of all ages, from all walks
of life.

8. -30
-25
-20
-15
-10
-5
0
5
10
15
20
Van- Index
Calif-REIT
Brown
Investment Return Data

9. The Risks
 The total risk: The standard deviation of
each stocks.
 Vanguard =15.96%
 REIT = 32%
 Brown=28.30%
 The individual stocks have almost
double the variability of the Vanguard
Index 500.
 So the individual stocks are riskier.
 REIT is more riskier than Brown based
on Standard Deviation.

10. Portfolio risk
 The portfolio : 99% Vanguard + 1%
Stock.
 St.dev of Portfolio(99%
vangauard,1%Brown)
Brown= 16%.
 St.dev of
Portfolio(99%vangauard,1%REIT)
REIT= 15.83%
 The Beta :
REIT=0.141
Brown=1.11

11. Portfolio risk
 Comparing these portfolios, we see that
the Brown stock adds more variability to
the portfolio. Thus, Brown is riskier.
This answer differs from that in individual
stock because a large part of the
portfolio's risk is related to the
covariance between the individual stock
and Vanguard. Since the covariance
between Brown's stock and Vanguard is
almost 8 times that between REIT and
Vanguard, the portfolio that includes
Brown is riskier.

12. Economic Significance
 Consider the dollar impact on existing portfolio
when the new asset is added.
 Investment in vanguard =79.2% of $25 M
=0.792*25
=$19.8M
 Current investment = $19.8 M in index fund of
volatility, with volatility of 15.96%. (Stdev
(vanguard)= 15.96%)
In terms of dollars, the volatility =
0.1596*19.8
= $3.16 M.
=$3,160,000

13. If additional $200 K is invested in Brown, the new dollar
volatility is 0.16x20=$3.2M,
Dollars at risk increase by $40,000 (3,200,000-3,160,000).
If additional $200 K is invested in the California REIT,
the new dollar volatility is 0.1582x20=$3.164M,
Dollars at risk increase by $4000(3,164,000-3,160,000).
If additional $200 K is invested in index itself,
the new dollar volatility is 0.1596x20=$3.192M,
Dollars at risk increase by $32,000.(3,192,000-3,160,000)
Approximate beta of Brown = 40,000/32000=1.25 (From
regression, beta = 1.11).
Approximate beta of California REIT =
4000/32,000=0.125(From regression, beta = 0.141).

14. The Expected Returns
 Expected rate: (CAPM), on annual rate
basis
 REIT=8%
 Brown=14.87%
 Lower the beta, stock will be less sensitive
to market movements. The higher beta
stock(Brown) is riskier.
 CAPM of Brown group is high. The Brown
Group stock should have a higher expected
return. The riskiness of a stock should be
measured by its covariance with the
market, rather than its own variance.

15. The (Required) Returns
 When adding a small amount of a new
asset to a diversified portfolio.
 Covariance between the new asset and
the portfolio, matters more to the total
risk of the final portfolio.
 Individual risks can be diversified away
in a portfolio. But the market risk has
to be held by investors.

16. Short Notes

17. Beta Value Calculations of the shares
The Beta value of a stock describes the
risk of a single stock with respect to
the risk of the overall market. Beta is
defined by the following equation
Where rs are the return on the stock and
rb is the return on a benchmark index.

18. Advantages of investing in Volatile
shares
Maximum return is obtained in volatile
shares in short period of time.

19. Indexed funds
 An index fund or index tracker is
a collective investment fund (usually
a mutual fund or exchange traded
fund) that aims to replicate the
movements of an index of a specific
financial market, or a set of rules of
ownership that are held constant,
regardless of market conditions.
 As of 2007, index funds made up over
11% of equity mutual fund assets in
the US.

20.  Tracking can be achieved by trying to hold
all of the securities in the index, in the
same proportions as the index. Other
methods include statistically sampling the
market and holding "representative"
securities. Many index funds rely on a
computer model with little or no human
input in the decision as to which securities
are purchased or sold and are thus
subject to a form of passive management.

21. THANKS