Expected Returns

• Expected returns are based on the probabilities of possible outcomes • In this context, “expected” means average if the Chapter 11 process is repeated many times • The “expected” return does not even have to be a possible return Risk and Return

n E(R) = ∑ pi Ri i=1

Variance and Standard Deviation Portfolios • Variance and standard deviation still • A portfolio is a collection of assets measure the volatility of returns • An asset’s risk and return is important in • Using unequal probabilities for the entire how it affects the risk and return of the range of possibilities portfolio • Weighted average of squared deviations • The risk-return trade-off for a portfolio is measured by the portfolio expected return n 2 2 and standard deviation, just as with σ = ∑pi (Ri −E(R)) i=1 individual assets

Portfolio Expected Returns Portfolio Variance • The expected return of a portfolio is the weighted average of the expected returns for • Compute the portfolio return for each each asset in the portfolio state: m RP = w1R1 + w2R2 + … + wmRm E(RP ) = ∑ w j E(R j ) • Compute the expected portfolio return j=1 using the same formula as for an • You can also find the expected return by individual asset finding the portfolio return in each possible • Compute the portfolio variance and state and computing the expected value as standard deviation using the same we did with individual securities formulas as for an individual asset

1 Expected versus Unexpected Announcements and News Returns • Realized returns are generally not equal to • Announcements and news contain both an expected returns expected component and a surprise component • There is the expected component and the unexpected component • It is the surprise component that affects a stock’s price and therefore its return – At any point in time, the unexpected return can be either positive or negative • This is very obvious when we watch how stock prices move when an unexpected – Over time, the average of the unexpected announcement is made or earnings are component is zero different from anticipated

Efficient Markets Systematic Risk

• Efficient markets are a result of investors • Risk factors that affect a large number of trading on the unexpected portion of assets announcements • Also known as non-diversifiable risk or • The easier it is to trade on surprises, the market risk more efficient markets should be • Includes such things as changes in GDP, • Efficient markets involve random price inflation, interest rates, etc. changes because we cannot predict surprises

Unsystematic Risk Returns

• Risk factors that affect a limited number of • Total Return = expected return + assets unexpected return • Also known as unique risk and asset- • Unexpected return = systematic portion + specific risk unsystematic portion • Includes such things as labor strikes, part • Therefore, total return can be expressed shortages, etc. as follows: • Total Return = expected return + systematic portion + unsystematic portion

2 Diversification Table 11.7

• Portfolio diversification is the investment in several different asset classes or sectors • Diversification is not just holding a lot of assets • For example, if you own 50 internet stocks, you are not diversified • However, if you own 50 stocks that span 20 different industries, then you are diversified

The Principle of Diversification Figure 11.1 • Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns • This reduction in risk arises because worse-than-expected returns from one asset are offset by better-than-expected returns from another • However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion

Diversifiable Risk Total Risk

• The risk that can be eliminated by • Total risk = systematic risk + unsystematic combining assets into a portfolio risk • Often considered the same as • The standard deviation of returns is a unsystematic, unique or asset-specific risk measure of total risk • For well-diversified portfolios, • If we hold only one asset, or assets in the unsystematic risk is very small same industry, then we are exposing • Consequently, the total risk for a ourselves to risk that we could diversify diversified portfolio is essentially away equivalent to the systematic risk

3 Systematic Risk Principle Measuring Systematic Risk

• There is a reward for bearing risk • How do we measure systematic risk? • There is not a reward for bearing risk • We use the beta coefficient to measure unnecessarily systematic risk • What does beta tell us? • The expected return on a risky asset – A beta of 1 implies the asset has the same systematic depends only on that asset’s systematic risk as the overall market risk since unsystematic risk can be – A beta < 1 implies the asset has less systematic risk diversified away than the overall market – A beta > 1 implies the asset has more systematic risk than the overall market

Security Market Line Capital Asset Pricing Model

• The security market line (SML) is the • The capital asset pricing model (CAPM) representation of market equilibrium defines the relationship between risk and return • The slope of the SML is the reward-to-risk ratio: (E(R ) – R ) / β •E(RA) = Rf + βA(E(RM) – Rf) M f M • If we know an asset’s systematic risk, we • But since the beta for the market is can use the CAPM to determine its ALWAYS equal to one, the slope can be expected return rewritten • This is true whether we are talking about • Slope = E(RM) – Rf = market risk premium financial assets or physical assets

SML and Equilibrium

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