Measuring market (systematic) risk for individual securities
Market risk, which is relevant for stocks held in well-diversified
portfolios, is defined as the contribution of a security to the overall
riskiness of the portfolio.
 measured by a stock’s beta (β) coefficient. For stock i:
βi = (ρi,M σi) / σM
Where βi indicates beta for stock i, ρi,M is the correlation coef between
stock i and the market, σi is the standard deviation of stock i and σM is
the standard deviation of the overall market.
How is β interpreted?
 If β = 1.0, stock has average risk.
 If β > 1.0, stock is riskier than average.
 If β < 1.0, stock is less risky than average.
Note: Most stocks have betas in the range of 0.5 to 1.5.
How are betas calculated?
 Run a regression with returns on the stock in question plotted on
the Y axis and returns on the market portfolio plotted on the X
axis.
 The slope of the regression line, which measures relative volatility,
is defined as the stock’s beta coefficient, or β.
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Note: In addition to measuring a stock’s contribution of risk to a
portfolio, beta also measures the stock’s volatility relative to the
market.
Calculating Beta in Practice
 Many analysts use the S&P 500 to find the market return.
 Analysts typically use four or five years’ of monthly returns to
establish the regression line.
 Some analysts use 52 weeks of weekly returns.
Other Web Sites for Beta
 Go to http://finance.yahoo.com
 Enter the ticker symbol for a “Stock Quote”, such as IBM or Dell,
then click GO.
 When the quote comes up, select Key Statistics from panel on left.
Now that we know how to find the β for a stock, what can we do with it?
1. Find the portfolio beta
2. Use β in the CAPM model to estimate the required return of each
security
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The Security Market Line (SML) is part of the Capital Asset Pricing
Model (CAPM).
Recall CAPM defines the relationship between systematic risk and
return:
SML: ri = rRF + (RPM) βi
Where ri is the required return on security i
rRF is the risk free rate
RPM = (rM - rRF)
 Assume rRF = 8%; rM = 15%.
 RPM = (rM - rRF) = 15% - 8% = 7%.
Find Required Rates of Return:
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Expected versus Required Returns (%)
Exp.
Req.
r
r
Alta
17.4
17.0
Undervalued
Market
15.0
15.0
Fairly valued
Am. F.
13.8
12.8
Undervalued
T-bills
8.0
8.0
Fairly valued
Repo
1.7
2.0
Overvalued
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SML: ri = rRF + (RPM) βi
ri = 8% + (7%) βi
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2 Stock Portfolio (Find Portfolio Beta, βP)
A. Calculate beta for a portfolio with 50% Alta and 50% Repo
Formula:
N
βP = Σ wi βi
i=1
B. Calculate the required return on this 2 stock portfolio
Required Return on the Alta/Repo Portfolio?
Formula:
N
rP = Σ wi ri
i=1
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Impact of Inflation Change on SML
Recall: SML: ri = rRF + (rM - rRF) βi
Where (rM - rRF)= RPM
Note: rRF = r* + IP
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Impact of Risk Aversion Change
Has the CAPM been completely confirmed or refuted?
- No. The statistical tests have problems that make empirical
verification or rejection virtually impossible.
- Investors’ required returns are based on future risk, but betas are
calculated with historical data.
- Investors may be concerned about both stand-alone and market
risk.
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