my presentation

“THE CAPITAL ASSET PRICING MODEL”(CAPM)

DEFINITION

• A model that describes the relationship between risk and expected return and that is used in the pricing of risky assets (stocks, securities, derivatives) or Portfolio

History

• CAPM was build on the earlier work of Harry Markowitz on• Modern Portfolio Theory (MPT) and• Diversification

• The CAPM was introduced independently by – Jack Trevnor (1961, 1962),– William F. Sharpe (1964),– Jhon Lintner(1965) and– Jan Mossin (1966)

Nobel Memorial Prize in Economics in 1990– Jointly received by Sharpe, Markowitz and Merton

Miller (for CAPM contribution to field of Financial Economics)

Black CAPM or Zero-beta CAPM by Fischer Black (1972) another version of CAPM that does not assume the existence of a riskless asset. more robust version against empirical testing and was

influential in the widespread adoption of the CAPM.

History

Background of CAPM

Modern Portfolio Theory

Capital Market Theory

CAPM

Arbitrage Pricing Theory

• CAPM is evolved by Markowitz after the Modern Portfolio Theory (MPT) of Markowitz,

• MPT describes,– “HOW investors should ACT in selecting an

Optimal Portfolio of Risky securities based on using the full information set about securities”

Background of CAPM

– Main Objective of MPT is • to maximize Profits and • Reducing the diversifiable risk by selecting an efficient portfolio that is also an

Optimal Portfolio– Optimal portfoliothe one that provides the most satisfaction — the

greatest return — for an investor based on his tolerance for risk.

–

Background of CAPM(Modern Portfolio Theory)

–Efficient Portfolio has • the highest expected return for a given

level of Risk, OR stated in another terms• The lowest level of risk for a given level

of expected return



• for determining Efficient Portfolio, Inputs for the securities being considered includes– Expected returns of individual securities,– Standard Deviations of individual securities,–Correlation Coefficient between securitiesAnd therefore Securities’ Weights of Portfolio

are the variably manipulated based on above statistical techniques to determine efficient portfolios

• Efficient Frontier:– the investment Opportunity Set– Construct a risk/return plot of all the feasible

portfolios-those that are actually attainable.– consists of the set of all efficient portfolios that

yield the highest return for each level of risk


11


Efficient Frontier:

Standard Deviation

Expected Return100% investment in security with highest E(R)

100% investment in minimum variance portfolio

Points below the efficient frontier are dominated

No points plot above the line

All portfolios on the line are efficient

• Indifference Curves:– describe an individual investor’s preferences

for Risk and Return– Investors have infinite number of indifference

curves.– Each curve is equally desirable to a particular

investor (i.e. They provide same level of Utility)– Indifference curves cannot intersect since they

represent different levels of desirability


• Risk-Averse Investors has upward sloping indifference curves

• Higher Indifference curves are more desirable than lower indifference curves

• The greater the slope of Indifference curve, greater is the Risk Aversion of investors

• Farther an indifference curve is from the horizontal axis, the greater the utility


Indifference Curves:

Indifference Curves

Indifference Curves

• The utility of these risk-indifference curves is that they allow the selection of the optimum portfolio out of all of those that are attainable by combining these curves with the efficient frontier.

Selecting an Optimal Portfolio

• One of the attainable indifference curves intersects the efficient frontier at a single point, that single point is the Optimal portfolio

• (In other words),• The efficient frontier can be combined with an

investor’s utility function to find the investor’s optimal portfolio, the portfolio with the greatest return for the risk that the investor is willing to accept.

Selecting an Optimal Portfolio

Important Conclusions about MPT

• Two parameter model i.e., – Risk-Return model OR– Mean-Variance model (because investors are assumed to make decisions

on the basis of two parameters; Risk and Return) Does not addresses the issue of investors using

borrowed money along with their own portfolio funds to purchase a portfolio of risky assets i.e., investors are not allowed to use Leverage (Risk Free Asset utilization)

Gaps in MPT theory• Few Queries arises after MPT theory• What happens if all investors seek portfolios of

risky securities using Markowitz Framework under Idealized conditions?

• How will this affect equilibrium Security Prices and Returns?

• (In other words) How does Optimal Diversification affect the market prices of securities?

• Under Ideal conditions , what is the Risk-Return trade-off that investors face?

• In general we wish to examine the models that explain security prices under conditions of market equilibrium, these are

Asset Pricing Models or Models for valuation of Risky Securities

Gaps in MPT theory

Capital Market Theory (Theory of CAPM)

Hypothesizes that “how investors should behave in selecting an Optimal Portfolio of Securities?”

Modern Portfolio Theory

Hypothesizes that “how investors do behave?”

Capital Market Theory

Capital Market Theory(Theory of CAPM)

• -----An Extension of Portfolio Theory• Answers about– “What happens if all investors seek portfolios of

risky securities using Markowitz Framework under Idealized conditions?”

• Assumption of Markowitz Portfolio Theory:-

• “Each investor is assumed to diversify his or her portfolio according to Markowitz Model, choosing a location on the efficient frontier that matches his or her return-risk preferences”

Assumptions of Capital Market Theory (Theory of CAPM)

• Additional Assumptions to make individuals more alike:– All investors can borrow or lend money at the Risk-Free

rate of return (RF)– All investors have Homogeneous expectations i.e., have

identical probability distributions for• Expected returns• Variance of returns and• Correlation Matrix(Therefore using the same set of security prices and a risk-free

rate, all investors use the same information to generate an efficient frontier)


• All investors have same one-period time horizon• No transaction costs• No personal income taxes---investors are

indifferent between capital gains and dividends• No inflation• Large number of Investors---and Investors are

price takers ( Prices are unaffected by their own trades)


Evolution of Capital Market Theory

• The Introduction of Risk-Free Asset allows us to develop Capital Market Theory from Portfolio Theory as

• The first assumption of CMT is

“All investors can borrow or lend money at the Risk-Free rate of return (RF)”

• Risk-Free Asset (Rf)– Which has no Risk of Default– One with a certainty of expected return • (Amount of money to be received at the end of

holding period is known with certainty at the beginning of period)

– And Expected Return = Nominal Return– Variance of a return = Zero– Covariance between Risk-free asset and Risky asset i = Zero– Example : Treasury Securities


• With the introduction of Rf Assets, – Investors can now invest:• Part of their wealth in the risk free assets

by lending • And remainder in any of the risky

portfolios in the Markowitz efficient set


• When a risk-free investment is available, the shape of the efficient frontier changes completely, and

• Leads to general theory for Pricing Assets under uncertainty

• And introduced Capital Market Line


30

THE CAPITAL MARKET LINE


M

rP

sP

CML

rfr

• The straight line (CML) from Rf to efficient frontier at point M, Rf—M, contains the superior Lending Portfolios, i.e

• Risk Free Lending OR Risk Free Investing• Purchase of Risk less Assets such as Treasury

Bills• Or lending money to the issuer of securities

such as U.S government


• Point M represents 100 % of an investor’s wealth in the Risky Asset Portfolio M or Market Portfolio, and is completely diversified

• Portfolio M contains only the Market Risk(systematic Risk)

• Now we assume that Investor can also borrow at Rf rate


• Borrowing the additional investable funds and investing them together with the Investor’s own wealth allows investor to seek higher expected returns while assuming greater Risk

• The straight line Rf—M is now extended upward into Rf-M-L Capital Market Line


• Definitions:• “CML specifies the equilibrium relationship

between expected return and Risk for efficient portfolios”

• The straight line ,CML, depicts – the equilibrium conditions that prevail in the

market for Efficient Portfolios – consisting of Optimal Portfolio of Risky and Risk

Free Assets


slope of the CML

slope of the CML

• Note that the Market Risk Premium (MRP) is defined as:

• MRP = E(R mkt) – R rf • so the slope of the CML – the Sharpe ratio for the

Market Portfolio – is:• Slope of CML = E(R mkt) – R rf = MRP

σ mkt σ mkt • Slope of CML is the market price of risk for

efficient portfolios

Equation for CML

As R rf is the intercept and Risk is measured by the standard deviation, So

• E(R p ) = R rf + E(R mkt) – R rf . σ p σ mkt

• WhereE(Rp) = the expected return on any efficient

portfolio on the CMLE(Rmkt)= the expected return on Market Portfolio M

σp= the S.D of the Efficient Portfolio being considered

σ mkt = the S.D of the returns on the Market Portfolio

Equation for CML

Criticism of CML(and Evolution of CAPM)

• CML applies only to Efficient Portfolios– (since only efficient portfolios are on Efficient frontier)

• CML cannot be used to assess the equilibrium expected return on a Single Security

• CML cannot be used to assess expected return on a Inefficient Portfolios

• “Above Criticism on CML leads to formulation of CAPM”

CAPM

• Capital Assets Pricing Model

• The theory regarding asset prices and markets

• Model for valuation or pricing of Risky assets

• Model that explain security prices under conditions of market equilibrium

• It allows us :• To measure relevant risk of an individual

security• To assess the relationship between Risk and

Return expected from Investing

CAPM

Assumptions of CAPM

• All investors will hold Market Portfolio – The benchmark portfolio against which other

portfolios are measured– Well diversified portfolio– Has only market risk or systematic risk– Investors are interested in Portfolio risk rather

than individual security risk

CAPM Theory

• Although all investors hold diversified portfolios BUT – What happens when an Investor adds a security

to a large portfolio?The contribution of individual’s stock risk to the

riskiness of well diversified portfolio leads to the formulation of CAPM

• When an investor adds security to a large portfolio, what matters is – the security’s average covariance with the other

securities in a portfolio

Major Conclusion of CAPM“Relevant risk of any security is the amount of risk

that security contributes to a well-diversified portfolio”

CAPM Theory

Derivation of CAPM Model

the Capital Market Theory Model is

• E(R p ) = R rf + E(R mkt) – R rf . σ p σ mkt

If expected return of stock i is related to its covariance with the Market Portfolio, then

• E(R i ) = R rf + E(R mkt) – R rf . Covi,mkt

σ2 mkt

• The new derived equation states that ,• The expected return on any Security is the

sum of Risk free rate and Risk Premium

• Risk premium reflects,– Assets covariance with the market portfolio


• E(R i ) = R rf + E(R mkt) – R rf . Covi,mkt

σ2 mkt

Where,

E(Rp) = the expected return on any efficient portfolio on the CML

E(Rmkt)= the expected return on Market Portfolio M

σ2 mkt = the variance of the returns on Market Portfolio

Covi,mkt = the Covariance of the stock with the market


• BETA• From the following model,• E(R i ) = R rf + E(R mkt) – R rf . Covi,mkt

σ2 mkt

• Beta = Covi,mkt

σ2 mkt



( ) ( )

where ( ) expected return on security

risk-free rate of interest

beta of Security

( ) expected return on the market

i f i m f

i

f

i

m

E R R E R R

E R i

R

i

E R

• BETA– The relative measure of Systematic Risk of any stock– Measures the Risk of an Individual stock relative to market

portfolio of all stocks– Sensitivity of the security’s return relative to the Market

Return– Beta relates the covariance of an asset with the market

portfolio to the variance of the market portfolio

• Beta = Covi,mkt

σ2 mkt


• BETA– Aggregate market has a beta of 1– More Volatile (Risky assets) have betas larger

than 1– Less Risky stocks have betas less than one


Security Market Line (SML)

• The graphical depiction of CAPM• CAPM theory shows a linear relationship

between an Assets risk and required rate of return for any asset, security, or portfolio.– This linear relationship is called SML

53

Security Market Line (cont’d)

Beta

Expected Return

Rf

Market Portfolio

1.0

E(R)

Implications of CAPM

• SML has important implications for security prices in equiblirium

• In equiblirium expected return of security should be that needed to compensate investors for the Systematic Risk

• Knowing the beta for any stock , we determine the required return for any stock

• What happens if investors determine that “security does not lie upon SML”– Undervaluation • Security lies above SML

– Overvaluation • Security lies below SML

Implications of CAPM

my presentation

Documents

given level of risk

highest return

highest expected return

diversifiable risk

termsthe lowest level

capm contribution

beta capm

level of riskbackground