Portfolio Risk and Return Part II

Systematic Risk and Equilibrium Returns of a Security

*unsystematic risk is NOT COMPENSATED in equilibrium because it can be eliminated for free through diversification. *systematic risk is measured by the contribution of a security to the risk of a well-diversified portfolio. *the expected equilibrium return (required return) on an individual security will depend only on its systematic risk.

Capital Asset Pricing Model (equation, logic, assumptions thereof)

CAPM is one of the most fundamental concepts in investment theory. It is an equilibrium model that predicts the expected return on stock, given the expected return on the market, the stock's beta coefficient, and the risk-free rate. E(Ri) = Rf + (Beta(i) * [E(Rmkt) - Rf]) In equilibrium, the expected return on risky asset E(Ri) is the risk-free rate (Rf) + a beta-adjusted market risk premium, Bi [E(Rmkt) - Rf)]. Assumptions of CAPM: *Investors are RISK AVERSE. *Investors want to MAXIMIZE UTILITY. *Markets are FRICTIONLESS - no taxes, transaction costs, or other impediments to trading. *All investors have the same ONE-PERIOD TIME HORIZON. *Investors have HOMOGENEOUS EXPECTATIONS for assets' expected returns, standard deviation returns, and returns correlations between assets. *All investments are infinitely DIVISIBLE. *Markets are COMPETITIVE. Investors take the market price as a given and no investor can influence prices with their trades.

Comparing the CML and SML

CML and SML are VERY DIFFERENT CML uses total risk on the x-axis, so ONLY EFFICIENT PORTFOLIOS will plot on the CML. SML uses beta (systematic risk) on the x-axis. In a CAPM world, ALL PROPERLY PRICED SECURITIES and portfolios will plot on the SML.

Should risk adjustment be based on total risk or systematic risk?

Depends on whether a fund bears the nonsystematic risk of a manager's portfolio. If a SINGLE MANAGER is used, the total risk (incl. nonsystematic risk) is the relevant measure. Risk adjustment using total risk (Sharpe, M2) are appropriate. If a fund uses MULTIPLE MANAGERS so that the overall fund portfolio is well diversified (has no nonsystematic risk), then performance measures based on systematic (beta) risk (Treynor, Jensen's) are appropriate.

Sharpe Ratio

Excess returns per unit of total portfolio risk. Higher Sharpe ratios indicate better risk-adjusted portfolio performance. *slope measure *since it uses total risk, rather than systematic risk, it accounts for any unsystematic risk that the portfolio manager has taken. *only useful for comparison with the Sharpe ratio of another portfolio. Sharpe = ((Rp - Rf)/risk of port) Sharpe Ratio is the slope of the CAL for the portfolio and can be compared to the slope of the CML, which is the Sharpe ratio for any portfolio along the CML.

Capital Allocation Line and Expectations of risk/correlations

If each investor has different expectations about the expected returns of, standard deviations of, or correlations between risky asset returns, each investor will have a DIFFERENT OPTIMAL RISKY ASSET PORTFOLIO AND A DIFFERENT CAL. Simplifying assumption: investors have HOMOGENEOUS EXPECTATIONS - and therefore, all face the same efficient frontier of risky portfolios and will all have the same OPTIMAL RISKY PORTFOLIO and CAL. Optimal CAL for any investor is one just tangent to the efficient frontier.

Least Squares Regression Line

Line that minimizes the sum of the squared distances of the points plotted from the line (this is what is meant by "line of best fit". Regression line is referred to as the asset's SECURITY CHARACTERISTIC LINE.

Market Model

MARKET MODEL - simplified form of single-index model. *used to estimate a security's (or portfolio's) beta and to estimate a security's abnormal return (return above its expected return) based on the actual market return.

MultiFactor Models

MULTIFACTOR MODELS - most commonly use macro factors (GDP growth, infaltion, consumer confidence) and fundamental factors (EPS, EPS growth, firm size, and research expenditures). *statistical factors often have no basis in finance theory. *The expected return for asset i is the sum of each FACTOR SENSITIVITY or FACTOR LOADING (the Bs) for Asset i multiplied by the expected value of that factor for the period. General form: E(Ri) - Rf = Bi1 x E(Factor 1) + Bi2 x E(Factor 2) + ... + Bik x E(factor K) Example: Fama and French model

Active Portfolio Management

Many PM's believe their estimates of security values are correct and that market prices are incorrect. They will invest more than the market weights in securities that they believe are undervalued and less than the market weights in securities which they believe are overvalued.

Identifying Mispriced Securities Using the SML

Since the SML shows the equilibrium (required) return for any security/portfolio based on its systematic risk, analysts often compare their forecast of a security's return to its required return based on its beta risk. A stock is OVERVALUED if it plots below the SML; expected to earn a lower percentage than what it should earn based on its systematic risk. A stock is UNDERVALUED if it plots above the SML; expected to earn a higher percentage than what it should earn based on its systematic risk.

Market Risk Premium

The difference between the expected return on the market and the risk-free rate.

Plotting standard deviation of portfolio with varying weights in risky and risk-free asset.

The risk (standard deviation of returns) and expected return of portfolios with varying weights in the risk-free asset and a risky portfolio can be plotted as a line that beings at the risk-free rate of return and extends through the risky portfolio. By combining a risk-free asset with a portfolio of risky assets, the overall risk and return can be adjusted to appeal to investors with various degrees of risk aversion.

Calculate and Interpret Beta

The sensitivity of an asset's return to the return on the market index in the context of the market model. Beta is a standardized measure of the covariance of the asset's return with the market reutrn. Bi = (cov of Asset i's return w/ market return) / (variance of market return) = (Cov im /riskm^2) or as = correlation of im x (risk of asset i)/(risk of asset m)

Treynor Measure Jensen's alpha

Two measures of risk based on systematic risk (beta) rather than total risk. Treynor measure: similar to the Sharpe Ratio and M^2, as the Treynor measure is based on slope. It is the excess returns per unit of systematic risk. Treynor measure = (Rp - Rf)/Bp Jensen's Alpha - measure of percentage returns in excess of those from a portfolio that has the same beta but lies on the SML. Jensen's Alpha = alpha(p) = Rp - [Rf + Beta p(Rm-Rf)]

Systematic v. Nonsystematic Risk

Unsystematic Risk - aka unique, diversifiable, firm-specific risk - risk that is eliminated by diversification. Since the market portfolio contains ALL RISKY ASSETS, it must be a well-diversified portfolio. All the risk that can be diversified away has been. SYSTEMATIC RISK - risk that cannot be diversified away; aka nondiversifiable risk or market risk. *applies to individual securities and portfolios, depending on correlation between securities and market returns (beta). Total Risk = Systematic Risk + Unsystematic Risk

Return Generating Models

Used to estimate the expected returns on risky securities based on specific factors. *must estimate the sensitivity of a security's returns to some specific factor. *factors that explain security returns can be classified as macroeconomic, fundamental, and statistical factors, though statistical factors often have no basis in finance theory.

Security Market Line (SML)

plots the relationship between risk and return for individual asset using Cov(i,mkt) as our measure of systematic risk.

M-Squared

produces the same portfolio rankings as the Sharpe Ratio, but is stated in percentage terms = (Rp - Rf)*(stand dev M / stand dev ) - (Rm - Rf)

Passive Investment Strategy

used by investors who believe market prices are informationally efficient.

Cost of Diversification

very low cost, if not actually free