Capital Market Theory

Capital Market Theory: An Overview Capital market theory extends portfolio theory and develops a model for pricing all risky assets Capital asset pricing model (CAPM) will allow you to determine the required rate of return for any risky asset

Capital Asset Pricing Model (CAPM) The asset pricing models aim to use the concepts of portfolio valuation and market equilibrium in order to determine the market price for risk and appropriate measure of risk for a single asset. Capital Asset Pricing Model (CAPM) has an observation that the returns on a financial asset increase with the risk. CAPM concerns two types of risk namely unsystematic and systematic risks. The central principle of the CAPM is that, systematic risk, as measured by beta, is the only factor affecting the level of return.

Capital Asset Pricing Model (CAPM) The Capital Asset Pricing Model (CAPM) was developed independently by Sharpe (1964), Lintner (1965) and Mossin (1966) as a financial model of the relation of risk to expected return for the practical world of finance. CAPM originally depends on the mean variance theory which was demonstrated by Markowitz’s portfolio selection model (1952) aiming higher average returns with lower risk.

CAPM assumptions Assumptions: All investors have homogenous expectations about asset returns and what the uncertain future holds for them. All investors are risk averse and they operate in the market rationally and perceive utility in terms of expected return. Investors are price takers They cannot influence the market individually

CAPM assumptions (cont’d) Investors look only one period ahead All securities are highly divisible for instance they can be traded in small parcels (Elton and Gruber, 1995, p.294). All investors can lend and borrow unlimited amount of funds at the risk-free rate of return. All investors have equal and costless access to information There are no taxes or commission costs

The Efficient Set for Many Securities return Individual Assets P Consider a world with many risky assets; we can still identify the opportunity set of risk-return combinations of various portfolios.

The Efficient Set for Many Securities return minimum variance portfolio Individual Assets P Given the opportunity set we can identify the minimum variance portfolio.

The Efficient Set for Many Securities return efficient frontier minimum variance portfolio Individual Assets P The section of the opportunity set above the minimum variance portfolio is the efficient frontier.

Risk-Free Asset An asset with zero standard deviation Zero correlation with all other risky assets Provides the risk-free rate of return (RFR) Will lie on the vertical axis of a portfolio graph

Optimal Risky Portfolio with a Risk-Free Asset return 100% stocks rf 100% bonds  In addition to stocks and bonds, consider a world that also has risk-free securities like T-bills

Combining a Risk-Free Asset with a Risky Portfolio Expected return the weighted average of the two returns This is a linear relationship

Combining a Risk-Free Asset with a Risky Portfolio Standard deviation The expected variance for a two-asset portfolio is Substituting the risk-free asset for Security 1, and the risky asset for Security 2, this formula would become Since we know that the variance of the risk-free asset is zero and the correlation between the risk-free asset and any risky asset i is zero we can adjust the formula

Combining a Risk-Free Asset with a Risky Portfolio Given the variance formula the standard deviation is Therefore, the standard deviation of a portfolio that combines the risk-free asset with risky assets is the linear proportion of the standard deviation of the risky asset portfolio.

Combining a Risk-Free Asset with a Risky Portfolio Since both the expected return and the standard deviation of return for such a portfolio are linear combinations, a graph of possible portfolio returns and risks looks like a straight line between the two assets.

Capital Market Line (CML) return efficient frontier rf P With a risk-free asset available and the efficient frontier identified, we choose the capital allocation line with the steepest slope

Market Equilibrium return CML efficient frontier M rf P With the capital allocation line identified, all investors choose a point along the line—some combination of the risk-free asset and the market portfolio M. In a world with homogeneous expectations, M is the same for all investors.

The CML and the Separation Theorem The CML leads all investors to invest in the M portfolio Individual investors should differ in position on the CML depending on risk preferences How an investor gets to a point on the CML is based on financing decisions Risk averse investors will lend part of the portfolio at the risk-free rate and invest the remainder in the market portfolio

Portfolio Possibilities Combining the Risk-Free Asset and Risky Portfolios on the Efficient Frontier CML Borrowing Lending M RFR

The Market Portfolio Because portfolio M lies at the point of tangency, it has the highest portfolio possibility line Everybody will want to invest in Portfolio M and borrow or lend to be somewhere on the CML Therefore this portfolio must include ALL RISKY ASSETS

The Market Portfolio Because it contains all risky assets, it is a completely diversified portfolio, which means that all the unique risk of individual assets (unsystematic risk) is diversified away

Systematic Risk Only systematic risk remains in the market portfolio Systematic risk is the variability in all risky assets caused by macroeconomic variables Systematic risk can be measured by the standard deviation of returns of the market portfolio and can change over time

Examples of Macroeconomic Factors Affecting Systematic Risk Variability in growth of money supply Interest rate volatility Variability in industrial production corporate earnings cash flow

Capital Asset Pricing Model

The Capital Asset Pricing Model: Expected Return and Risk The existence of a risk-free asset resulted in deriving a capital market line (CML) that became the relevant frontier An asset’s covariance with the market portfolio is the relevant risk measure This can be used to determine an appropriate expected rate of return on a risky asset - the capital asset pricing model (CAPM)

The Capital Asset Pricing Model: Expected Return and Risk CAPM indicates what should be the expected or required rates of return on risky assets This helps to value an asset by providing an appropriate discount rate to use in dividend valuation models You can compare an estimated rate of return to the required rate of return implied by CAPM - over/under valued ?

Fundamental Risk/Return Relationship Revisited CAPM Market model versus CAPM Note on the CAPM assumptions Stationarity of beta

CAPM The more risk you carry, the greater the expected return: Assume bi = 0, then the expected return is Rf. Assume bi = 1, then

Relationship Between Risk & Expected Return 1.0

CAPM (cont’d) The CAPM deals with expectations about the future Excess returns on a particular stock are directly related to: The beta of the stock (only consider systematic risk) The expected excess return on the market

Market Model Versus CAPM The market model is an ex post model It describes past price behavior The CAPM is an ex ante model It predicts what a value should be

Market Model Versus CAPM (cont’d) The market model is:

Jensen's alpha Jensen's alpha was first used as a measure in the evaluation of mutual fund managers by Michael Jensen in 1968. The CAPM return is supposed to be 'risk adjusted', which means it takes account of the relative riskiness of the asset.

Jensen's alpha This is based on the concept that riskier assets should have higher expected returns than less risky assets. If an asset's return is even higher than the risk adjusted return, that asset is said to have "positive alpha" or "abnormal returns". Investors are constantly seeking investments that have higher alpha.

Jensen's alpha Jensen's alpha = Portfolio Return − [Risk Free Rate + Portfolio Beta * (Market Return − Risk Free Rate)] Rit : the realized return (on the portfolio) Rmt : the market return Rf : the risk-free rate of return : the beta of the portfolio.

Note on the CAPM Assumptions Several assumptions are unrealistic: People pay taxes and commissions Many people look ahead more than one period Not all investors forecast the same distribution Theory is useful to the extent that it helps us learn more about the way the world acts Empirical testing shows that the CAPM works reasonably well

Stationarity of Beta Beta is not stationary Evidence that weekly betas are less than monthly betas, especially for high-beta stocks Evidence that the stationarity of beta increases as the estimation period increases The informed investment manager knows that betas change

Equity Risk Premium Equity risk premium refers to the difference in the average return between stocks and some measure of the risk-free rate The equity risk premium in the CAPM is the excess expected return on the market Some researchers are proposing that the size of the equity risk premium is shrinking