Module 3- 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. • It suggests that investors need not worry about the market portfolio. They only need to decide how much systematic risk they wish to accept. • Market forces will ensure that any stock can be expected to yield the appropriate return. • Expected returns are based on beta, which is determined by the market portfolio • Supply and demand for a stock is utilitarian

The CML (capital market line) and SML (security market line) are equilibrium risk return measures. Key differences however:

1. Measure of risk on the CML is its standard deviation, while the measure of risk using the SML is beta. It is the critical assumption that the market portfolio is fully diversified, that allows us to enjoy the luxury of using beta (a lot easier to work with!). 2. CML, by definition, is strictly reserved for efficient portfolios, while SML can be used for a single security, or any portfolio (efficient or otherwise).

An arbitrage portfolio is defined by three conditions:

1. Self financing - Does not require additional funds from 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.

Both the capital asset pricing model and the arbitrage pricing theory are two similar but different ________portfolio theories

Equilibrium

The 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. • The slope of the CML is equal to the difference between the expected return of the market portfolio and that of the risk free security

Behavioral Asset Pricing Model (BAPM)

• Also known Behavioral Portfolio Theory • Investors build pyramids of assets- each layer carrying different attitudes towards risk • Completely different than the CAPM which is based on consistent attitudes towards risk • It is the validity of market efficiency that contrasts the difference between standard finance and behavioral finance • Behaviorists believe that individuals and institutions make decisions based on the way they act and feel

Prospect theory:

• Behavioral based model that attempts to explain investor preferences for cash dividends and for stocks of "good" companies • Why do investors hat to realize losses? • Two main concepts of the theory are "mental accounting" and "loss aversion" o Mental accounting - segment money in separate accounts o Loss aversion- less risk adverse when faced with potential losses, more risk adverse when faced with potential gains

Binomial Option Pricing Model (BOPM)

• Can be used to estimate the fair value of a call or put option based on the assumption that the underlying asset will attain one of two possibly known prices at the end of each finite number of periods given the price at the start of the period. • Easier using Euro style options where exercise only happens on expiration date • The relationship between the market prices of a call and put on a given stock with same expiration date and exercise price is known as put-call parity

Black-Scholes-Merton Model determines fair value of an option by:

• Current mkt price of underlying stock • Exercise price of the option • Risk free rate of return • Life of the option • Stocks dividend yield • Risk of volatility of the common stock • Risk free rate and common stock volatility are constant over the option's life

Black-Scholes-Merton Model

• Excluding taxes and transaction costs, the fair value of a call option is determined by computer model over an almost infinite number of possible pricing periods throughout the year. • Applies only to Euro options • Not applicable to stocks paying dividends

Behavioral asset pricing model:

• Investors are prone to asset segregation- look at an investment in isolation • Investors can be biased- overconfident that leads to mistakes in asset allocation etc • Investors tend to be caught up in "the crowd" • Behavioral finance recognizes the contributions of standard finance

assumptions behind the CAPM:

• Investors evaluate portfolios by looking at the expected returns and standard deviations of the portfolios over a one-period time horizon. • When given a choice between two portfolios with identical standard deviations, they will choose the one with the higher expected return. • Investors are risk-averse • There is a risk-free rate at which an investor may lend, invest or borrow money. • Taxes and transaction costs are irrelevant. • All investors have the same one-period horizon • The risk-free rate is the same for all investors • Information is freely and instantly available to all investors. • Investors have the same perceptions in regard to the expected returns, standard deviations and covariances of securities. • investors analyze and process information in the same way. • securities have different expected returns because they have different betas.

arbitrage pricing theory

• a security's price is explained by multiple economic factors rather than the single systematic risk factor

behavioral pricing model (BAPM) was developed to improve upon CAPM.

• acknowledges the contributions of standard finance • people are "normal" (BAPM) instead of "rational" (CAPM). • The main difference between CAPM and BAPM is the presence of "noise traders" and do commit cognitive errors • Determining Beta is difficult because the preferences of noise traders change over time • Beta is determined using both utilitarian and value expressive measures

Capital Asset Pricing Model:

• an equilibrium model of security prices based on assumptions of rational investor behavior and perfect security markets. • all investors will hold the same efficient portfolio of risky assets, differing only in the amounts of risk-free borrowing or lending. • the market portfolio is composed of all risky assets held by investors. • The separation theorem- the optimal combination of a risky portfolio can be determined without any knowledge of the investor's risk-return preferences. • The capital market line represents the efficient set in the world of CAPM and all investors will hold a portfolio lying on the CML. • The security market line is the linear relationship between market covariance and expected return and the slope of the SML indicates the level of aggregate investor risk aversion. • The market model is a single factor model and uses a market index, which is a subset of the CAPM's market portfolio.

Market portfolio

• an equilibrium portfolio containing all assets in the world. • When all the price adjusting stops, the market will have been brought into equilibrium.

For computing the expected returns of securities standard finance uses:

• capital asset pricing model (CAPM) • arbitrage pricing theory (APT)

The most commonly identified factors that affect expected returns in APT are indicators of aggregate economic activity, such as

• corporate earnings and dividends, • inflation • and interest rates

The market model -

• is not an equilibrium model of security prices as is the CAPM. However, the beta from the CAPM is similar in concept to the beta from the market model. • The market model differs from the CAPM in that it is a factor model while the CAPM is an equilibrium model. • Further, the market model uses a market index while the CAPM uses the market portfolio. • The market index is a subset of the CAPM's market portfolio. • The total risk of a security can be separated into market risk and non-market risk, under the CAPM. • Each security's non-market risk is unique to that security and hence is also termed its "unique risk."

The security market line (SML)-

• is the linear relationship between market covariance and expected return. • The slope of the SML indicates the level of aggregate investor risk aversion. • Like the CML, the SML is an equilibrium risk-return relationship. • In SML the relevant measure of risk for individual securities is the contribution that they make to the standard deviation of the market portfolio as measured by their respective covariances with the market portfolio or their betas. • The beta is a measure of the covariance between the security and the market portfolio relative to the market portfolio's variance.

Arbitrage Pricing Theory (APT)

• less complicated than the CAPM. • each investor, when given the opportunity to increase the return of his or her portfolio without increasing its risk, will proceed to do so. The mechanism for doing so involves the use of arbitrage portfolios. • The law of one price tells us that assets with equal betas have the same amount of undiversifiable risk and, therefore, should have identical expected rates of return. • Every asset that plots above the arbitrage pricing line is underpriced, and every asset that plots below the APT line is overpriced. • Investors will take advantage of arbitrage opportunities, thus eliminating them

Delta

• measures the impact of a change in the underlying stock price on the value of a stock option. Delta is positive for a call option and negative for a put option. A $1 change to the stock price is approximately equivalent to change in option price by delta dollars

APT vs SML

• underlying assumptions and includes a wider array of variables into the analysis than the SML. • The APT is a more general theory than the SML • The APT can be shown to be mathematically equivalent to the SML when the market portfolio is the only risk factor in both models. • the two theories do not contradict each other. • the two theories are similar because both delineate undiversifiable commonalties that form the basis for risk premiums in market prices and returns.