Module 7 - Chapter 11 Risk and Return - Biz Finance
What the CAPM shows is that the expected return for a particular asset depends on three things:
-The pure time value of money. As measured by the risk-free rate, Rf, this is the reward for merely waiting for your money, without taking any risk. -The reward for bearing systematic risk. As measured by the market risk premium, [E(RM) − Rf], this component is the reward the market offers for bearing an average amount of systematic risk in addition to waiting. -The amount of systematic risk. As measured by βi, this is the amount of systematic risk present in a particular asset, relative to an average asset.
unsystematic risk
A risk that affects at most a small number of assets. Also unique or asset-specific risk.
systematic risk
A risk that influences a large number of assets. Also market risk.
beta coefficient
Amount of systematic risk present in a particular risky asset relative to that in an average risky asset. -an average asset has a beta of 1.0 relative to itself. An asset with a beta of .50, therefore, has half as much systematic risk as an average asset; an asset with a beta of 2.0 has twice as much. -beta of .82, should expect to earn less, on average, than an investor who buys stock in Apple, with a beta of 1.27
What about systematic risk? Can it also be eliminated by diversification? The answer is no because, by definition, a systematic risk affects almost all assets to some degree.
As a result, no matter how many assets we put into a portfolio, the systematic risk doesn't go away. Thus, for obvious reasons, the terms systematic risk and nondiversifiable risk are used interchangeably.
the standard deviation of the annual return on a portfolio of 500 large common stocks has historically been about 20 percent per year. Does this mean that the standard deviation of the annual return on a typical stock in that group of 500 is about 20 percent?
As you might suspect by now, the answer is no. This is an extremely important observation.
capital asset pricing model (CAPM)
Equation of the security market line showing the relationship between expected return and beta.
Systematic risk is also called nondiversifiable risk or market risk. Unsystematic risk is also called diversifiable risk, unique risk, or asset-specific risk.
For a well-diversified portfolio, the unsystematic risk is negligible. For such a portfolio, essentially all of the risk is systematic.
portfolio
Group of assets such as stocks and bonds held by an investor.
we see that the standard deviation for a "portfolio" of one security is about 49 percent. What this means is that, if you randomly selected a single NYSE stock and put all your money into it, your standard deviation of return would typically be a substantial 49 percent per year.
If you were to randomly select two stocks and invest half your money in each, your standard deviation would be about 37 percent on average, and so on.
portfolio weight
Percentage of a portfolio's total value in a particular asset.
security market line (SML)
Positively sloped straight line displaying the relationship between expected return and beta.
states of the economy
Recession and boom
expected return
Return on a risky asset expected in the future.
market risk premium
Slope of the security market line; the difference between the expected return on a market portfolio and the risk-free rate.
principle of diversification
Spreading an investment across a number of assets will eliminate some, but not all, of the risk.
The second point is equally important: There is a minimum level of risk that cannot be eliminated by diversifying. This minimum level is labeled "nondiversifiable risk".
Taken together, these two points are another important lesson from capital market history: Diversification reduces risk, but only up to a point. Put another way: Some risk is diversifiable and some is not.
systematic risk principle
The expected return on a risky asset depends only on that asset's systematic risk. -Because unsystematic risk can be eliminated at virtually no cost (by diversifying), there is no reward for bearing it. Put another way: The market does not reward risks that are borne unnecessarily. -The expected return on an asset depends only on that asset's systematic risk. -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.
The return on any stock traded in a financial market is composed of two parts. First, the normal, or expected, return from the stock is the part of the return that shareholders in the market predict or expect. This return depends on the information shareholders have that bears on the stock, and it is based on the market's understanding today of the important factors that will influence the stock in the coming year.
The second part of the return on the stock is the uncertain, or risky, part. This is the portion that comes from unexpected information revealed within the year.
A common way of saying that an announcement isn't news is to say that the market has already "discounted" the announcement.
The use of the word discount here is different from the use of the term in computing present values, but the spirit is the same.
It is possible for the percentage invested in Asset X to exceed 100 percent.
The way this can happen is for the investor to borrow at the risk-free rate
The Fundamental Result The situation we have described for Assets A and B cannot persist in a well-organized, active market because investors would be attracted to Asset A and away from Asset B. As a result, Asset A's price would rise and Asset B's price would fall. Because prices and returns move in opposite directions, the result would be that A's expected return would decline and B's would rise.
This buying and selling would continue until the two assets plotted on exactly the same line, which means they would offer the same reward for bearing risk. -The reward-to-risk ratio must be the same for all the assets in the market.
For example, going back to Flyers, suppose the government announces that the actual GDP increase during the year has been 1.5 percent. Now shareholders have learned something, namely, that the increase is one percentage point higher than they had forecast.
This difference between the actual result and the forecast, one percentage point in this example, is sometimes called the innovation or the surprise.
In any given year, the unexpected return will be positive or negative, but, through time, the average value of U will be zero.
This means that, on average, the actual return equals the expected return.
The principle of diversification has an important implication:
To a diversified investor, only systematic risk matters.
Total Risk = Stand-alone Risk
Total risk = Systematic risk + Unsystematic risk -The standard deviation of returns is a measure of total risk •For well-diversified portfolios, unsystematic risk is very small ÆTotal risk for a diversified portfolio is essentially equivalent to the systematic risk
The arguments we have presented apply to active, competitive, well-functioning markets. The financial markets, such as the NYSE, best meet these criteria. Other markets, such as real asset markets, may or may not. For this reason, these concepts are most useful in examining financial markets.
We thus focus on such markets here. However, as we discuss in a later section, the information about risk and return gleaned from financial markets is crucial in evaluating the investments that a corporation makes in real assets.
alpha The excess return an asset earns based on the level of risk taken.
When an asset plots on the SML, it earns exactly the return it should earn based on its level of risk, or beta. A positive alpha means that the asset (or portfolio) has earned a return in excess of what it should earn based on its beta. Of course, an asset can have a negative alpha, which is less than desirable.
The line, which we use to describe the relationship between systematic risk and expected return in financial markets, is usually called the
security market line
Unsystematic risk is essentially eliminated by diversification,
so a relatively large portfolio has almost no unsystematic risk.
risk premium
the difference between the return on a risky investment and that on a risk-free investment
Unsystematic Risk
•= Diversifiable risk •Risk factors that affect a limited number of assets •Risk that can be eliminated by combining assets into portfolios •"Unique risk" •"Asset-specific risk" •Examples: labor strikes, part shortages, etc.
Announcements, News and Efficient markets
•Announcements and news contain both expected and surprise components •The surprise component affects stock prices •Efficient markets result from investors trading on unexpected news -The easier it is to trade on surprises, the more efficient markets should be •Efficient markets involve random price changes because we cannot predict surprises
Portfolio Conclusions
•As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio - sp falls very slowly after about 40 stocks are included -The lower limit for sp ≈ 20% = sM. ÆForming well-diversified portfolios can eliminate about half the risk of owning a single stock.
The Principle of Diversification
•Diversification can substantially reduce risk without an equivalent reduction in expected returns -Reduces the variability of returns -Caused by the offset of worse-than-expected returns from one asset by better-than-expected returns from another •Minimum level of risk that cannot be diversified away = systematic portion
Systematic Risk
•Factors that affect a large number of assets •"Non-diversifiable risk" •"Market risk" •Examples: changes in GDP, inflation, interest rates, etc.
Interpretation of beta
•If b = 1.0, stock has average risk •If b > 1.0, stock is riskier than average •If b < 1.0, stock is less risky than average •Most stocks have betas in the range of 0.5 to 1.5 •Beta of the market = 1.0 •Beta of a T-Bill (risk-free rate) = 0
Market Equilibrium
•In equilibrium, all assets and portfolios must have the same reward-to-risk ratio •Each ratio must equal the reward-to-risk ratio for the market
Portfolios
•Portfolio = collection of assets •An asset's risk and return impact how the asset affects the risk and return of the portfolio •The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets
Portfolio Risk Variance & Standard Deviation
•Portfolio standard deviation is NOT a weighted average of the standard deviation of the component securities' risk -If it were, there would be no benefit to diversification.
Beta and the Risk Premium
•Risk premium = E(R ) - Rf •The higher the beta, the greater the risk premium should be •Can we define the relationship between the risk premium and beta so that we can estimate the expected return? -YES!
Market Risk for Individual Securities
•The contribution of a security to the overall riskiness of a portfolio •Relevant for stocks held in well-diversified portfolios •Measured by a stock's beta coefficient, bj •Measures the stock's volatility relative to the market
Security Market Line
•The security market line (SML) is the representation of market equilibrium •The slope of the SML = reward-to-risk ratio (E(RM) - Rf) / bM •Slope = E(RM) - Rf = market risk premium -Since b of the market is always 1.0
Systematic Risk Principle
•There is a reward for bearing risk •There is no reward for bearing risk unnecessarily • •The expected return (market required return) on an asset depends only on that asset's systematic or market risk.
Returns
•Total Return = Expected return + unexpected return R = E(R) + U •Unexpected return (U) = Systematic portion (m) + Unsystematic portion (ε) •Total Return = Expected return E(R) + Systematic portion m + Unsystematic portion ε = E(R) + m + ε