Case: Beta Case: Beta ManagementManagement

The ObjectivesThe Objectives1. 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.

The IssuesThe Issues1. The Strategy2. The Choices3. The Risks4. The Port Folio Risks5. The Return

The StrategyThe StrategyMs.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.

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

Some Information of REITSSome Information of REITS(REIT, WWW.reit.com)(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.

Some Information of Brown Shoe Some Information of Brown Shoe WWW.Brownshoe.comWWW.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.

Investment Return DataInvestment Return Data

The RisksThe RisksThe 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.

Portfolio riskPortfolio 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=0.141Brown=1.11

Portfolio riskPortfolio riskComparing 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.

Economic SignificanceEconomic SignificanceConsider 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

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).

The Expected ReturnsThe Expected ReturnsExpected rate: (CAPM), on annual rate basisREIT=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.

The (Required) ReturnsThe (Required) ReturnsWhen 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.

Short NotesShort Notes

Beta Value Calculations of the sharesBeta 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.

Advantages of investing in Volatile Advantages of investing in Volatile sharesshares

Maximum return is obtained in volatile shares in short period of time.

Indexed fundsIndexed fundsAn 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.

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.

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