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Samenvatting Corporate FinanceChapter 10 Capital markets and the Pricing of Risk
10.1 Risk and Return: Insights from 86 years of Investor History
Standard & Poor’s 500 (S&P500): A portfolio, constructed by Standard and Poor’s,
comprising 90 U.S. stocks up to 1957 and 500 U.S. stocks after that. The firms
represented are leaders in their respective industries and are among the largest
firms, in terms of market value, traded on U.S. markets.
Small stocks: A portfolio, updated quarterly, of U.S. stocks traded on the NYSE
with market capitalization in the bottom 20%.
World portfolio: A portfolio of international stocks from all of the world’s major
stock markets in North America, Europe and Asia.
Corporate bonds: A portfolio of long-term, AAA-rated U.S. corporate bonds with
maturities of approximately 20 years.
Treasury bills: An investment in one-month U.S. treasury bills.
10.2 Common Measures of Risk and Return
When an investment is risky, there are different return it may earn. Each possible return
has some likelihood of occurring. We summarize this information with a probability
distribution, which assigns a probability, PR , that each possible return, R, will occur.
Expected return=E [ R ] =∑ PR∗R
(10.1) R
Variance=Var ( R )=E [ ( R−E [ R ] ) ]=∑ P R∗( R−E [ R ] )
2 2
(10.2) R
standard deviation=√ Var (R)
If the return is risk-free and never deviates from its mean, the variance is zero. The
variance is a measure of how “spread out” the distribution of the return is. In finance, we
refer to the standard deviation of a return as its volatility.
10.3 Historical Returns of Stocks and Bonds
The realized return is the return that actually occurs over a particular time period.
¿t +1+ P t+1 ¿ P −Pt
(10.4) Rt +1= −1= t+1 + t +1
Pt Pt Pt
(10.5) 1+ Rannual=( 1+ R Q 1 )( 1+ R Q 2 )( 1+ R Q3 ) ( 1+ RQ 4 )
When we plot the probability distribution in a histogram using historical data, we refer to
it as the empirical distribution of the returns. The average annual return of a security:
T
1 1
(10.6) Ŕ= ( R + R +…+ RT )= T ∑ Rt
T 1 2 t=1
T
1 2
(10.7) Var ( R )= ∑
T −1 t=1
( Rt − Ŕ )
The standard error is the standard deviation of the estimated value of the mean of the
actual distribution around its true value.
SD (individual risk )
(10.8) SD ( Average of independent , indentical risk )=
√ Number of observations
(10.9) 95 confidence interval=historical average return ±(2∗Standard error )
10.4 The Historical Trade-off between Risk and Return
, The excess return is the difference between the average return for the investment and
the average return for Treasury bills, a risk-free investment, and measures the average
risk premium investors earned for bearing the risk of the investment.
10.5 Common versus Independent Risk
We call risk that is perfectly correlated common risk. We call risks that share no
correlation independent risks. The averaging out of independent risks in a large
portfolio is called diversification.
10.6 Diversification in Stock Portfolios
Independent risks are diversified in large portfolio, whereas common risks are not.
Fluctuations of a stock’s return that are due to firm-specific news are independent risks.
This type of risk is also referred to as firm-specific, idiosyncratic, unique or
diversifiable risk.
Fluctuations of a stock’s return that are due to market-wide news represent common risk.
This type of risk is also called systematic, undiversifiable, or market risk.
The risk premium for diversifiable risk is zero, so investors are not compensated for
holding firm-specific risk. The risk premium of a security is determined by its systematic
risk and does not depend on its diversifiable risk.
10.7 Measuring Systematic Risk
To determine how sensitive a stock is to systematic risk, we can look at the average
change in its return for each 1% change in the return of a portfolio that fluctuate solely
due to systematic risk.
Thus, the first step to measuring systematic risk is finding a portfolio that contains only
systematic risk. Changes in the price of this portfolio will correspond to systematic shocks
to the economy. We call such a portfolio an efficient portfolio.
An efficient portfolio should be a large portfolio. Thus, a natural candidate for an efficient
portfolio is the market portfolio, which is a portfolio of all stock and securities traded in
the capital market. Because it is difficult to find data for the returns of many bonds and
small stocks, it is common in practice to use the S&P500 portfolio as an approximation
for the market portfolio.
The Beta (β) of a security is the expected % change in its return given a 1% change in
the return of the market portfolio. Beta measures the sensitivity of a security to market-
wide risk factors. Stocks in cyclical industries, in which revenues and profits vary greatly
over the business cycle, are likely to be more sensitive to systematic risk and have betas
that exceed 1, whereas stocks of non-cyclical firms tend to have betas that are less than
1.
10.8 Beta and the Cost of Capital
For risky investments, cost of capital correspond to the risk-free interest rate, plus an
appropriate risk premium
(10.10) market risk premium = E( Rmkt ¿−r f
Estimating the cost of capital of an investment from its beta:
(10.11) r I =r f + βi x ( E ( Rmkt )−r f )
Equation 10.11 is often referred to as the capital asset pricing model (CAPM), the
most important method for estimating the cost of capital that is used in practice.
Chapter 11 Optimal Portfolio Choice and the Capital Asset Pricing Model
11.1 The Expected Return of a Portfolio
We can describe a portfolio by its portfolio weights, the fraction of the total investment
in the portfolio held in each individual investment in the portfolio:
value of investment i
(11.1) x i=
total value of the portfolio
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