Download PowerPoint-Präsentation

Risk, Return,
and CAPM
Professor Dr. Rainer Stachuletz
Corporate Finance
Berlin School of Economics and Law
Berlin, 04.01.2006
Fußzeile
1
Expected Returns
Decisions must be based on expected returns
Methods used to estimate expected return
Historical approach
Probabilistic approach
Risk-based approach
Berlin, 04.01.2006
Fußzeile
2
Historical Approach for
Estimating Expected Returns
Assume that distribution of expected returns will be similar to
historical distribution of returns.
Using 1900-2003 annual returns, the average risk premium for
U.S. stocks relative to Treasury bills is 7.6%. Treasury bills
currently offer a 2% yield to maturity
Expected return on U.S. stocks: 7.6% + 2% =
9.6%
Can historical approach be used to estimate the
expected return of an individual stock?
Berlin, 04.01.2006
Fußzeile
3
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%
Limitations of
historical
approach for
individual
stocks
Berlin, 04.01.2006
May reflect GM’s past more than its future
Many stocks have a long history to
forecast expected return
Fußzeile
4
Probabilistic Approach for
Estimating Expected Returns
Identify all possible outcomes of returns and assign a
probability to each possible outcome:
For example, assign probabilities for possible states of economy:
boom, expansion, recession and project the returns of GM stock
for the three states
Outcome
Probability
GM Return
Recession
20%
-30%
Expansion
70%
15%
Boom
10%
55%
GM Expected Return = 0.20(-30%) + 0.70(15%)
+0.10(55%) = 10%
Berlin, 04.01.2006
Fußzeile
5
Risk-Based Approach for
Estimating Expected Returns
1. Measure the risk of the asset
2. Use the risk measure to estimate the expected
return
1. Measure the risk of the asset
• Systematic risks simultaneously affect many different assets
• Investors can diversify away the unsystematic risk
• Market rewards only the systematic risk: only systematic risk
should be related to the expected return
How can we capture the systematic risk
component of a stock’s volatility?
Berlin, 04.01.2006
Fußzeile
6
Risk-Based Approach for
Estimating Expected Returns



Collect data on a stock’s returns and returns on a market
index
Plot the points on a scatter plot graph
- Y–axis measures stock’s return
- X-axis measures market’s return
Plot a line (using linear regression) through the points
Slope of line equals beta, the sensitivity of a stock’s
returns relative to changes in overall market returns
Beta is a measure of systematic risk for a particular
security.
Berlin, 04.01.2006
Fußzeile
7
Scatter Plot for Returns
on Sharper Image and S&P 500
30%
Slope = Beta = 1.44
20%
10%
0%
-30%
-20%
-10%
0%
10%
20%
30%
-10%
-20%
-30%
S&P 500 weekly returns
Berlin, 04.01.2006
Fußzeile
8
Scatter Plot for Returns
ConAgra and S&P 500
15%
10%
5%
Beta = 0.11
0%
-15%
-10%
-5%
0%
5%
10%
15%
-5%
-10%
-15%
S&P 500 weekly returns
Berlin, 04.01.2006
Fußzeile
9
Risk-Based Approach for
Estimating Expected Returns
Capital
Average
Market Line
Return
Individual
Stock A:
rM
cov A ,M
CAPM
Rf
Slope CML:
r
M
 rf

 M2
s2 M
Berlin, 04.01.2006
Risk
Fußzeile
10
The Security Market Line
E(RP)
SML
A - Undervalued
•
•A
RM
•
RF
B
•
•
Slope = E(Rm) - RF = Market
Risk Premium
• B - Overvalued
•
 =1.0
Berlin, 04.01.2006
i
Fußzeile
11
Risk-Based Approach for
Estimating Expected Returns
2. Use the risk measure to estimate the expected
return:
• Plot beta against expected return for two assets:
- A risk-free asset that pays 4% with certainty,
with zero systematic risk and
- An “average stock”, with beta equal to 1, with
an expected return of 10%.
• Draw a straight line connecting the two points.
• Investors holding a stock with beta of 0.5 or 1.5, for
example, can find the expected return on the line.
Beta measures systematic risk and links the risk and
expected return of an asset.
Berlin, 04.01.2006
Fußzeile
12
Risk and Expected Returns
Security Market Line
18%
•
14%
•
10%
•
4%
•
Expected returns
•
•
ß = 1.5
“average”
stock
Risk-free asset
•
0.2
•
0.4
•
0.6
•
0.8
•
1
•
1.2
•
1.4
•
1.6
•
1.8
•
2
Beta
What is the expected return for stock with beta = 1.5 ?
Berlin, 04.01.2006
Fußzeile
13
Estimating the Risk Free Rate
UK INTEREST RATES
Feb 17
Treasury Bills
OverNight
One
month
Three
months
43/4 – 411/16
425/32-423/32
7 days
notice
Two prices are quoted,
quoted,
Two
for
one
sellingare
forprices
one
for
selling
one forTake
middle
theone
buying.
middle
the
Take
buying.
value
value
Extract of UK interest rate data from the Financial Times (17 February, 2005)
14
Six
months
One
Year
The Steps Towards the Estimation of
Beta Using Ordinary Least Squares Regression
15
The Security Market Line
16
Arbitrage Drivers and the
Linearity of the Security Market Line
17
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
Expected return of a portfolio with N securities
E(Rp) = w1E(R1)+ w2E(R2)+…+wnE(Rn)
• w1, w2 , … , wn : portfolio weights
• E(R1), E(R2), …, E(RN): expected returns of securities
Berlin, 04.01.2006
Fußzeile
18
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
E (Rp) = w1 E (R1)+ w2 E (R2)+…+wn E (Rn)
E (Rp) = (0.125) (10%) + (0.25) (12%) + (0.125)
(8%) + (0.5) (14%) = 12.25%
Berlin, 04.01.2006
Fußzeile
19
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
Berlin, 04.01.2006
Fußzeile
20
Security Market Line
Portfolio composed of the following two assets:
• An asset that pays a risk-free return Rf, , and
• A market portfolio that contains some of every risky
asset in the market.
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
Berlin, 04.01.2006
Fußzeile
21
The Security Market Line
Plots relationship between expected return and
betas
 In equilibrium, all assets lie on this line.
• If
• If
-
Berlin, 04.01.2006
individual stock or portfolio lies above the line:
Expected return is too high.
Investors bid up price until expected return falls.
individual stock or portfolio lies below SML:
Expected return is too low.
Investors sell stock driving down price until expected
return rises.
Fußzeile
22
Efficient Markets
Efficient market hypothesis (EMH): in an efficient market,
prices rapidly incorporate all relevant information
Financial markets much larger, more competitive, more
transparent, more homogeneous than product markets
Much harder to create value through financial activities
Changes in asset price respond only to new information. This
implies that asset prices move almost randomly.
Berlin, 04.01.2006
Fußzeile
23
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.
Berlin, 04.01.2006
Fußzeile
24
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 stock’s beta, the risk-free rate and
the market premium.
Berlin, 04.01.2006
Fußzeile
25