Risk, Return, and CAPM

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Risk, Return, and CAPM

• Professor XXXXX
• Course Name / Number

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Expected Returns
Decisions must be based on expected returns

• Methods used to estimate expected return

Historical approach
Probabilistic approach
Risk-based approach
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Historical Approach for Estimating Expected
Returns
Assume that distribution of expected returns will
be similar to historical distribution of returns.
Can historical approach be used to estimate the
expected return of an individual stock?
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Historical Approach for Estimating Expected
Returns

• Assume General Motors long-run average return is
  17.0. Treasury bills average return over same
  period was 4.1

GM historical risk premium 17.0 - 4.1
12.9 GM expected return Current Tbill rate
GM historical risk premium 2 12.9 14.9
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Probabilistic Approach for Estimating Expected
Returns
Identify all possible outcomes of returns and
assign a probability to each possible outcome
GM Expected Return 0.20(-30) 0.70(15)
0.10(55) 10
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Risk-Based Approach for Estimating Expected
Returns
1. Measure the risk of the asset 2. Use the risk
measure to estimate the expected return
How can we capture the systematic risk component
of a stocks volatility?
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Risk-Based Approach for Estimating Expected
Returns

• Collect data on a stocks returns and returns on
  a market index
• Plot the points on a scatter plot graph
• Yaxis measures stocks return
• X-axis measures markets return
• Plot a line (using linear regression) through the
  points

Slope of line equals beta, the sensitivity of a
stocks returns relative to changes in overall
market returns
Beta is a measure of systematic risk for a
particular security.
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Scatter Plot for Returns on Sharper Image and SP
500
Sharper Image weekly returns
SP 500 weekly returns
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Scatter Plot for Returns on ConAgra and SP 500
ConAgra weekly returns
SP 500 weekly returns
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Risk-Based Approach for Estimating Expected
Returns
Beta measures systematic risk and links the risk
and expected return of an asset.
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Risk and Expected Returns
Expected returns

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14


10
average stock

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Risk-free asset










1
0.2
0.4
0.6
0.8
2
1.2
1.4
1.6
1.8
Beta
What is the expected return for stock with beta
1.5?
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Portfolio Expected Returns
How does the expected return of a portfolio
relate to the expected returns of the securities
in the portfolio?
The portfolio expected return equals the weighted
average of the portfolio assets expected returns
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Portfolio Expected Returns
Portfolio E(R) Invested Weights
IBM 10 2,500 0.125
GE 12 5,000 0.25
Sears 8 2,500 0.125
Pfizer 14 10,000 0.5
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Portfolio Risk
Portfolio risk is the weighted average of
systematic risk (beta) of the portfolio
constituent securities.
Portfolio Beta Invested Weights
IBM 1.00 2,500 0.125
GE 1.33 5,000 0.25
Sears 0.67 2,500 0.125
Pfizer 1.67 10,000 0.5
ß P (0.125)(1.00) (0.25)(1.33)
(0.125)(0.67) (0.50)(1.67) 1.38
But portfolio volatility is not the same as the
weighted average of all portfolio security
volatilities
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Security Market Line
Portfolio E(R) Beta
Risk-free asset Rf 0
Market portfolio E(Rm) 1
Security market line the line connecting the
risk-free asset and the market portfolio
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Security Market Line and CAPM
The two-asset portfolio lies on security market
line
Given two points (risk-free asset and market
portfolio asset) on the security market line, the
equation of the line
The equation represents the risk and return
relationship predicted by the Capital Asset
Pricing Model (CAPM)
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The Security Market Line
Plots relationship between expected return and
betas

• In equilibrium, all assets lie on this line.
• If individual stock or portfolio lies above the
  line
• Expected return is too high.
• Investors bid up price until expected return
  falls.
• If individual stock or portfolio lies below SML
• Expected return is too low.
• Investors sell stock driving down price until
  expected return rises.

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The Security Market Line
E(RP)
SML
Slope E(Rm) - RF Market Risk Premium


RM
RF

? 1.0
?i
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Efficient Markets
Efficient market hypothesis (EMH) in an
efficient market, prices rapidly incorporate all
relevant information
Changes in asset price respond only to new
information. This implies that asset prices move
almost randomly.
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Efficient Markets
If asset prices unpredictable, then what is the
use of CAPM?
CAPM gives analyst a model to measure the
systematic risk of any asset.
On average, assets with high systematic risk
should earn higher returns than assets with low
systematic risk.
CAPM offers a way to compare risk and return on
investments alternatives.
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Risk, Return, and CAPM
Decisions should be made based on expected
returns. Expected returns can be estimated using
historical, probabilistic, or risk
approaches. Portfolio expected return/beta
equals weighted average of the expected
returns/beta of the assets in the
portfolio. CAPM predicts that the expected
return on a stock depends on the stocks beta,
the risk-free rate and the market premium.