L7: Risk and return trade off and capital budgeting
1. MEASURING MARKET RISK
A. Only “macro” events affect the value of the market portfolio, or a portfolio of all
assets in the economy.
B. A broad market base, for ex. the OMX SPI is often used as a proxy for the market
portfolio.
C. Firm specific or unique risk are averaged out or diversified away when
considering the market portfolio.
D. A measure of a stock’s risk relative to the risk of the market portfolio is called the
stock’s beta, and is expressed as the Greek letter, .
Measuring Beta
1. Investors with diversified portfolios are not concerned about the specific or
unique risk of a stock, only the impact of the stock on the risk of the entire
portfolio.
2. The relative risk of the stock compared to the portfolio risk or beta is the
relevant risk to consider when a new stock is added to the portfolio.
3. Beta is the slope of the regression line of the individual stock returns relative
to the market portfolio returns. If the slope indicates a change in historical
stock returns similar to the market (-1 to +1), the beta has a value of 1. If the
variation in the stock return, given a 1 percent variation in the market returns,
is less than the market variation, the beta is less than 1 and the stock is noted
as a “defensive” stock. If the slope of the line through the points found by
plotting the stock’s returns relative to a 1 percent change in the market
portfolio is greater than 1, the beta has a value greater than 1.
4. Any stock’s return is comprised of two parts. The first is explained by the
macro events in the market or the market rate of return. The second part of the
return is related to the specific or unique risk of the stock relative to the
market rate of return, or the stock beta.
Portfolio Betas
A. Diversification decreases the variability from unique risk but not from market risk.
B. The beta of a portfolio is an average of the betas of the securities in the portfolio,
weighted by the investment in each security.
C. A large portfolio of diversified stocks would approximate the market index and
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have a portfolio beta around one. An index mutual fund is a “market portfolio” of
stocks with a beta close to the value of one.
2.
RISK AND RETURN
A. U.S. Treasury bills have very low risk and a beta of zero, or no relationship with
the variations of the market portfolio of stocks, which has a beta of 1.0.
B. The difference between the return on the market and the T-bill rate is called the
market risk premium, or the risk premium demanded by investors to hold the
market portfolio rather than T-bills.
C. Over the past century, the market risk premium has averaged 7.6 percent per year;
the market, 11.6%; and T-bills, 4.0% (From Chapter 11). See Figure 12.4(a).
D. The expected rate of return on any portfolio combining T-bills and the market
portfolio lies on a straight line between T-bills and the market portfolio.
security market line
(SML)
Market Risk Premium = rm - rf = 10% - 3% = 7%
E. Beta measures risk of the stock relative to the market. The expected risk premium
on an individual stock is the stock return less the risk-free rate or equivalently,
beta times the market risk premium:
Risk Premium on any asset = r - rf = β*(rm - rf)
The above formula relating the expected return as the sum of the risk-free rate plus
the risk premium is called the capital asset pricing model (CAPM). The rate of
return on an individual stock is dependent upon the risk-free rate and the risk
premium, which is related to the market risk premium and the risk of the stock
relative to the market risk premium, its beta.
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How the CAPM Works
A. The CAPM assumes well-diversified investors; market risk is the only relevant
risk.
B. The expected return on a portfolio is equal to the risk-free interest rate plus the
expected portfolio risk premium.
The Security Market Line
A. A plot of expected rates of return of varied risk (beta) portfolios is called the
security market line.
B. According to the CAPM, expected rates of return for all securities and all
portfolios lie on this line.
C. The required risk premium for any investment is given by the security market line.
D. A stock with a given beta that is expected to earn a return higher than that on the
security market line will be purchased by investors, bidding up the stock price and
lowering the expected rate of return to the security market line. Investors keep
expected returns on the security market line.
E. The security market line is the risk-return trade-off of investors.
F. The CAPM states that the expected risk premium on an investment should be
proportional to its beta.
Good to know:
The CAPM explains the risk-return trade-off well in the period 1931 to 2006, though
the security market line tends to understate low beta returns which means lower
beta portfolios have historically a higher return than what security market line
dictates.
Value stocks are those with high ratios of book value to market value. Growth stocks
are those with low ratios of book to market. Since 1926 the average annual
difference between returns on value and growth stocks has been 5.3%.
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