Module 11 - Asset Pricing Models

Capital Asset Pricing Model (CAPM)

- provides an intuitive way of thinking about the return that an investor should require from an investment, given the asset's systematic risk. - suggests that an investor need not worry about the market portfolio, only need to decide how much systematic risk they wish to accept and market forces will ensure that any stock can be expected to yield the appropriate return - positive economics, presents a descriptive model of how assets are priced - major implication is that the expected return of an asset is related to the measure of market risk for that asset, known as BETA - involves (10) assumptions

Capital Market Line (CML)

- represents the linear efficient set in the world of CAPM. all investors will hold a portfolio lying on the CML. it is the efficient frontier when borrowing and lending at the risk-free rate is permitted - most desirable asset allocation line, denotes the set of most desirable risky portfolios that can be generated by borrowing and lending at the risk free rate of interest - assumes homogenous expectations and perfect markets. STRICTLY USED FOR EFFICIENT PORTFOLIOS - slope = risk premium = E(Rm) - Rf, often called the reward per unit of risk borne

Standard Finance

- security prices are rational - investors are rational and utilitarian

Factors in APT

1. changes in the rate of inflation 2. changes in the index of industrial production 3. changes in the yield spread between high-grade and low-grade corporate bonds, a measure of investor confidence 4. changes in the slope of the term structure of interest rates, as measured by the difference between the yields on long-term government bonds and T-bills

Equation for Security Market Line (SML)

Ri = Rf + [Bi x (Rm - Rf)] Ri = required return of the security Rf = risk-free rate Bi = beta of the security Rm - Rf = risk premium of the market - 3 names: CAPM formula, SML formula, or required return - formula is part of the Jensen index (alpha) which subtracts the required return (SML) from the realized return to generate alpha. - performance that plots above SML = (+) alpha = undervalued assets - performance that plots below SML = (-) alpha = overvalued assets - performance that plots on SML = 0 alpha = equilibrium

Equation for Arbitrage Pricing Theory (APT)

Ri = a + b1F1 + b2F2 + ... + bkFk + ei Ri = rate of return on security a = zero factor: the expected return when all factors = 0 Fk = the value factor, such as the rate of grown in industrial production ei = random error term bk = sensitivity of security to the factor

Prospect Theory

behavioral-based model that attempts to explain phenomena such as investor preference for cash dividends and preference for stocks of "good" companies. main component is cognitive errors. involves mental accounting and loss aversion MENTAL ACCOUNTING = investors tend to segment their money in separate accounts LOSS AVERSION = many investors have been shown to be less risk adverse when faced with potential losses and more risk adverse when faced with potential gains

Risk Premium

difference between the expected market return and the risk free rate E(Rm) - Rf market risk premium is the amount of return that the market must pay to compensate investors for taking on the additional risk of the market over that of the US Treasury Bill

Market Model

the return on a common stock is assumed to be related to the return on a market index using the following equation: Ri = Ail + (Bil x Rl) + Eil Ri = return on security i Rl = return on market index Ail = intercept term Bil = slope term Eil = random error term * this is a single-factor model in which the factor is a market index (it is not an equilibrium model) * utilizes a market index (like the S&P 500) whereas CAPM uses the market portfolio

Black-Scholes-Merton Pricing Model

- provide formulas for determining the price of options, that is, their premiums - first closed-form option-pricing model

Binomial Pricing Model

- provide formulas for determining the price of options, that is, their premiums - mathematically simple models that have been developed to deal with a broad class of valuation problems that include options, stocks, bonds and other risky financial claims

Separation Theorem

"optimal investment decision to buy the market portfolio is separate and independent from the financing decision about whether to borrow or lend to finance the investment in the market portfolio. the optimal combo of risky assets for an investor can be determined without the knowledge of the investor's preferences toward risk and return" highly risk-adverse investors = lending portfolio that lies between the risk-free rate and the market portfolio more aggressive investors = leveraged portfolio that lies above the market portfolio on the CML

Behavioral Finance

- believes that standard finance is incomplete because it ignores all of the psychological factors that influence market pricing - believe that individuals and institutions make decisions based on the way they act and feel - investors are value-expressive (personal tastes and other factors not consistent with "rational thought") - includes behavioral flaws such as asset segregation, biased expectations and self-control ASSET SEGREGATION - individuals who look at an investment in isolation and do not consider the overall portfolio, leads to mistakes BIASED EXPECTATIONS - "overconfidence" investors are overconfident in their prediction abilities, and therefore make mistakes concerning asset allocation, market selection and market timing SELF-CONTROL - a flaw that behavioral investors also exhibit, simply being caught up in the actions of the crowd

Security Market Line (SML)

- derived from CAPM - in equilibrium, the risk premium on any asset is equal to its beta times the risk premium of the market portfolio - slope = risk premium of the market portfolio - measure of risk is beta, critical assumption of SML is that the market portfolio is fully diversified - can be used for a single security or any portfolio (efficient or otherwise)

Arbitrage Pricing Theory (APT)

- developed by Stephen Ross - alternative to CAPM that has gained acceptance in the financial community - a security's price is explained by multiple economic factors rather than the single systematic risk factor - based on the law of one price: if a security's price is different in different markets, then a riskless profit exists for investors to buy the security from the market with the lower price and sell it in the market with the higher price - assumes that each investor, when given the opportunity to increase the return of his or her portfolio without increasing risk, will proceed to do so - the mechanism for doing so involves the use of arbitrage portfolios - an arbitrage portfolio is defined by three conditions: (1) self financing - does not require additional funds from the investor (2) riskless - there is no sensitivity to any factor; there is zero variance and covariance with other portfolios and there is negligible nonfactor risk (3) positive return - the riskless arbitrage will result in a positive return

Behavioral Pricing Model (BAPM)

- developed to improve upon CAPM - at its heart is the study of behavioral finance, which acknowledges the contributions of standard finance but argues that people are "normal" instead of "rational" - investors build "pyramids of assets" with each layer in the pyramid carrying a different attitude toward risk Model premise: market interaction between information traders and noise traders, who do not have mean-variance preferences and do commit cognitive errors Expected returns: determined by behavioral betas, measures of risk with respect to the mean-variance-efficient portfolio which depends on the preferences of noise traders Beta: behavioral betas are difficult to determine because the preferences of noise traders can change over time Supply & demand for stock: determined by the behavioral beta, which is both utilitarian and value-expressive

Assumptions of CAPM

1. investors evaluate portfolios looking at the expected returns and SD's of the portfolio over a one-period time horizon 2. investors are never satiated - when given a choice between two portfolios with identical SD, they will choose the one with the higher expected return 3. investors are risk-averse - when given a choice between two portfolios with identical expected returns, they will choose the one with the lower SD 4. individual assets are infinitely divisible - an investor can buy a fraction of a share 5. there is a risk-free rate at which an investor may lend, invest or borrow money 6. taxes and transaction costs are irrelevant 7. all investors have the same one-period horizon 8. the risk-free rate is the same for all investors 9. information is freely and instantly available to all investors 10. investors have homogenous expectations - they all have the same perceptions in regard to the expected returns, SDs and covariances of securities

Equation for Capital Market Line (CML)

Rp = Rf + [(Rm - Rf)/SDm]SDp Rp = expected return of efficient portfolio Rf = risk-free rate (this is the vertical intercept and often called the reward for waiting) Rm-Rf = risk premium SDm = standard deviation of market SDp = standard deviation of efficient portfolio y axis = expected return x axis = SD

Market Portfolio

portfolio consisting of all securities in the world, the proportion invested in each security corresponds to its relative market value. the relative market value is simply equal to the aggregate market value of the security divided by the sum of the aggregate market value of all securities