Transcript Chapter 11

Chapter 11
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Measuring Market Risk and beta
Portfolio Betas
CAPM and Expected Return
Security Market Line
Capital Budgeting and Project Risk
Measuring Market Risk
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Market risk: Economy-wide sources of risk that
affect the overall stock market. Also called
“systematic risk.”
Market risk of an individual stock represents part
of its total risk.
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Total risk = market risk + unique risk
Total risk is measured by variance (or Std.Dev.)
For well-diversified investors, only market risk
matters, since unique risk has been eliminated through
diversification.
Total Risk, Unique Risk and
Market Risk
Measuring Market Risk
• Beta: Sensitivity of a stock's return to fluctuations
in returns on the market portfolio.
– Market Portfolio – An ultimate well-diversified
portfolio with all assets (stocks) in the economy. In
practice a broad stock market index, is used to represent
the market.
– In terms of numbers, beta gives the size and sign of
change in the return of an investment when there is one
unit change in return on market portfolio.
• Beta describes the size of an investment’s market
risk relative to that of market portfolio, but it does
not give us the exact size of the market risk.
Measuring Market Risk
More on Beta
• Market portfolio’s beta is 1.0
– A portfolio that replicates a market index has beta of 1.0
• Beta for a riskless investment is zero
– Treasury bills
• Most stocks have betas in the range of 0.5 to 1.5.
– If beta = 1.0, stock has as much market risk as the market
portfolio.
– If beta > 1.0, stock has larger market risk than the market.
– If beta < 1.0, stock has less market risk than the market.
– Most stocks have betas in the range of 0.5 to 1.5.
• Beta can be negative, but very unlikely.
Estimating Beta
• Beta can be estimated using past return data
cov(ri , rm )
betai   i 
var(rm )
• Regression analysis
– Find the fitted line for the plot of a stock’s
returns against market portfolio’s returns.
ri  ˆi  ˆi  rm  
– The slope is the estimate of beta.
Estimating Beta
Portfolio Betas
• Diversification decreases unique risk, but
not market risk.
• The beta of your portfolio will be an
weighted average of the betas of the
securities in the portfolio.
n
 portfolio   i  wi  1  w1   2  w2 
i i
  n  wn
Example: Portfolio beta
Calculate beta for a portfolio with 50% HP and
50% Wal-Mart. Assume beta for HP and Wal-Mart
are 1.29 and 0.61, respectively
Capital Asset Pricing Model
ri  rf
i
Risk premium i
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 i
Market risk premium rm  rf
m
Expected Re turn  ri  rf   i  (rm  rf )
– Expected risk premium on a stock/portfolio is
proportional to its beta.
– Expected return on a security depends on the risk
free rate and an risk premium.
• Difference in expected return across securities arises
from difference in risk premium which can be fully
explained by beta.
Example: CAPM and Expected Return
Assume rf = 8% and rM=15%.
1) How much is the market risk premium?
2) Use CAPM to compute the expected rate of
return on a stock with beta=1.25
Capital Asset Pricing Model
• The CAPM world assumes that stock market is
dominated by well-diversified investors, i.e. every
investor holds an two-asset portfolio consisting of
the market portfolio and/or the risk free asset.
• Investors are concerned with only market risk in
individual stocks.
• An investor’s risk preference determines how
he/she allocates funds between market portfolio
and risk free asset.
Example: Two Fund Separation
Jessica and John both has $10,000 to invest in stock
market and T-bills, but they have very different risk
preference. Jessica believes that life is full of adventures
and she is ready to take risks; while John thinks that
stability builds a peaceful mind and he always tries to
avoid risk. Therefore, Jessica puts 80% of her money in
market portfolio but John only puts 20%. Now assume
market portfolio return is 10% and T-bill rate is 4%. If
CAPM is turn, please answer the following question:
1) What will be Jessica’s and John’s expected return on their
investment?
2) Is Jessica’s investment strategy superior to John’s? (Hint:
Sharpe ratio)
3) What happens when Jessica stead borrow $2,000 and
invest the total of $12,000 in market portfolio?
Security Market Line
Security Market Line
- Plot the expected return against beta according to CAPM.
- We only need two benchmark securities (each with
expected rate of return and beta) to specify the security
market line. (e.g. T-bill and market portfolio)
Over-pricing and Under-pricing
Asset A is under-priced; asset B is over-priced.
CAPM and Investment Projects
• Company cost of capital and project cost of
capital are different.
• We can find a matched company for a
project so that they have similar risk, and
then use the beta for this company to
estimate expected return for the project.
– Pure-play method
Beyond CAPM
• Three factor model
Expected Re turn :
ri  rf  i  (rm  rf )  i  rSML   i  rHML
– Two other risk factors related to firm size and
book to market ratio help explain the difference
in expected return on stocks