Chapter 12 – Return, Risk, and the Security Market Line
12.1 – Announcements, Surprises, and Expected Returns
Expected and Unexpected Returns
The return on any stock traded in a financial market is composed of two parts.
o The normal, or expected, part of the return is the return that investors predict or expect.
o The uncertain, or risky, part of the return comes from unexpected information revealed during the year.
R – actual total return in the year
E(R) – expected part of the return
U – unexpected part of the return
o Because of surprises that occur during the year, R differs from the E(R)
o The unexpected return will be positive or negative, but the average value of U will be zero
o On average, the actual return equals the expected return
Total Return = Expected Return + Unexpected Return
Unexpected Return = Total Return - Expected Return
U = R - E(R)
Announcements and News
Firms make periodic announcements about events that may significantly impact the profits of the firm.
o Product development
The impact of an announcement depends on how
much of the announcement representsnew
o When the situation is not as bad as previously
thought, what seems to be bad news is
actually good news.
o When the situation is not as good as
previously thought, what seems to be good
news is actually bad news.
News about the future is what really matters.
o Market participants factor predictions about
the future into the expected part of the stock
Announcement = Expected News + Surprise News
12.2 – Efficient Frontier and Capital Asset Line
Markowitz examined relationship between risk and return of asset prices and developed Efficient Frontier
This theory states that total risk level (standard deviation or variance) is the important factor in rewards of
portfolios and portfolio preference of investors
He claims that investors fin the minimum risk portfolios at every return level and choose these portfolios over the
When investors combine the risk-free asset with efficient frontier, they obtain a line called the CAL (Capital Asset
o The upper part of the parabola is called the efficient frontier
o Markowitz states that every rational investor will chose his or her optimal portfolio on CAL according to his
or her preferred risk level
12.3 – Risk: Systematic and Unsystematic
Systematic and Unsystematic Risk
Systematic risk is risk that influences a large number of assets. Also called market risk.
Unsystematic risk is risk that influences a single company or a small group of companies. Also called unique
risk or firm-specific risk.
Total risk = Systematic risk + Unsystematic risk
Systematic and Unsystematic Components of Return
R – E(R)= U = Systematic portion + Unsystematic portion
= m + e
R – E(R)= m + e
12.4 – Diversification, Systematic Risk, and Unsystematic Risk
Diversification and Unsystematic Risk
In a large portfolio:
Some stocks will go up in value because of positive company-specific events, while
Others will go down in value because of negative company-specific events.
Diversification essentially eliminates unsystematic risk, so a portfolio with many assets generally has almost no
Unsystematic risk is also called diversifiable risk.
Systematic risk is also called non-diversifiable risk.
Diversification and Systematic Risk
12.5 – Systematic Risk and Beta
The Systematic Risk Principle
What determines the size of the risk premium on a risky asset?
The systematic risk principle states:
The expected return on an asset depends only on its systematic risk.
So, no matter how much total risk an asset has, only the systematic portion is relevant in determining the
expected return (and the risk premium) on that asset.
Measuring Systematic Risk
To be compensated for risk, the risk has to be special.
Unsystematic risk is not special.
Systematic risk is special.
The Beta coefficient (b) measures the relative systematic risk of an asset.
Assets with Betas larger than 1.0 have more systematic risk than average.
Assets with Betas smaller than 1.0 have less systematic risk than average.
Because assets with larger betas have greater systematic risks, they will have greater expected returns.
Note that not all Betas are created equally.
The total risk of a portfolio has no simple relation to the total risk of the assets in the portfolio.
Recall the variance of a portfolio equation.
For two assets, you need two variances and the covariance.
For four assets, you need four variances and six covariances.
In contrast, a portfolio Beta can be calculated just like the expected return of a portfolio.
That is, you can multiply each asset’s Beta by its portfolio weight and then add the results to get the portfolio’s
Using Value Line data from Table 12.1, we see
Beta for Starbucks (SBUX) is 1.15
Beta for Yahoo! (YHOO) 0.95
You put half your money into SBUX and half into YHOO.
What is your portfolio Beta?
12.6 – The Security Market Line
Beta and the Risk Premium
Consider a portfolio made up of asset A and a risk-free asset.
For asset AA E(R ) = A6% and b = 1.6.
The risk-freefrate R = 4%. Note that for a risk-free asset, b = 0 by definition. We can calculate some different possible portfolio expected returns and betas by changing the percentages
invested in these two assets.
Note that if the investor borrows at the risk-free rate and invests the proceeds in asset A, the investment in asset A
will exceed 100%.
The Reward-to-Risk Ratio
Notice that all the combinations of portfolio expected returns and betas fall on a straight line.
Slope (Rise over Run):
= E( )A −R f=16%−4% = 7.50%
• What this tells us is that asset A offers a reward-to-risk ratio of 7.50%. In other words, asset A has a risk premium
of 7.50% per “unit” of systematic risk.
The Basic Argument
Recall that for asseA A: E(R ) A 16% and b = 1.6
Suppose there is a second asset, asset B.
For asset B: B(R ) = 12%Aand b = 1.2
Which investment is better, asset A or asset B?
Asset A has a higher expected return
Asset B has a lower systematic risk measure
As before with Asset A, we can calculate some different possible portfolio expected returns and betas by changing
the percentages invested in asset B and the risk-free rate.
% of Portfolio in AsPortfolio Expected Portfolio Beta
0% 4 0.0
25 6 0.3
50 8 0.6
75 10 0.9
100 12 1.2
125 14 1.5
150 16 1.8
The Fundamental Result
The situation we have described for assets A and B cannot persist in a well-organized, active market
Investors will be attracted to asset A (and buy A shares)
Investors will shy away from asset B (and sell B shares)
This buying and selling will make
The price of A shares increase
The price of B shares decrease
This price adjustment continues until the two assets plot on exactly the same line.
That is, until:
E R −R E R −R
( )A f= ( B f
In general …
The reward-to-risk ratio must be the same for all assets in a competitive financial market.
If one asset has twice as much systematic risk as another asset, its risk premium will simply be twice as large.
Because the reward-to-risk ratio must be the same, all assets in the market must plot on the same line. The Security Market Line
E R M)− Rf E R M)− Rf
= E(RM )− Rf
The Security market line (SML) is a graphical representation of the linear relationship
between systematic risk and expected return in financial market