Finance- Week 9

Capital asset pricing model

Theoretical model used to price individual securities Pricing security= estimating required rate or return (using CAPM), then obtaining price estimate based on security's future expected cash flows (dividends and future price) CAPM relates securities required return to its non-diversifiable/ systematic risk - Higher systematic risk= higher required (expected) return - Total risk is not relevant to pricing securities, or inefficient portfolios of securities

CML vs SML

Using CML we can only price efficient portfolios - Efficient portfolios perfectly positively correlated with market portfolio (Ppm= 1.0) Using SML we price any portfolio or security regardless of its correlation with market portfolio and level of unsystematic risk

CAPM intuition

All investors hold efficient portfolios comprising market portfolio M and the risk free security - Investors who don't diversify gain- no increase in expected return for bearing this additional (diversifiable) risk Any security A is held in an efficient portfolio as part of market portfolio, M Expected return on A reflects its contribution to non-diversifiable erisk of market portfolio - Contribution of A to non-diversifiable risk of market portfolio depends on covariance within market portfolio not own risk (SD)

Asset pricing

Asset is something expected to generate returns in the future- therefore it has price/value today If we know expected return, we can work out price - Nearly all asset pricing models are models of what determines expected return Major determinant of assets expected return is its risk - Greater risk, higher expected return

Betas and correlations

Beta is not same as return correlation between security/ portfolio and market portfolio!

Two important special cases 1. Beta of the risk free asset

By definition, the variance of rf is zero Hence its covariance (with anything) is also zero

What CML v CAPM can price

CML price portfolio B (efficient) but not security A (inefficient) CAPM can price both According to CAPM, both security A and portfolio B will have same expected return because they have same systematic risk levels A has higher total risk level than B but this is not relevant

Capital market line

Can only be used to price efficient portfolios- pricing portfolio is used in context of obtaining portfolios expected return CML assumes portfolios fully diversified and efficient with zero unsystematic risk - Efficient portfolio has lowest level risk for given expected return CML cannot be used to price individual securities because these ≠ efficient and will always have some unsystematic (diversifiable/ firm-specific) risk

Separation theorem

Capital market line Investors L and R maximise utility by choosing a combination of risk free security and X, regardless of their individual risk preferences Composition of risky portfolio separate from risk free/risky security choice Line through rf and X is the capital market line (CML) which dominates FF'

Introducing a risk free security

Consider risk free F and risky portfolio A Options - Invest 5000 in risk free security and rest in risky portfolio, you are lending funds at risk free rate and the remainder in portfolio A - Invest 15000 in A by borrowing 5000 of risk free investment Higher return with option 2 but higher risk

Investor choice without a risk free security

Different investors will choose different portfolios of risky securities Blue curve is efficient frontier Utility increases as we move in north westerly direction (higher return, lower risk)

Efficient frontier

Efficient frontier FF' is an envelope of risk-return frontiers made up of individual portfolios of risky assets FF' plots risky portfolios which have lowest risk σ for a given expected return E(r)

CAPM can be written as

Expected return on A = risk free return + risk premium Risk premium= amount of risk * market price of risk - Amount of risk= measured by covariance of security with market portfolio (beta/ ß of security) - Market price of risk= return above risk free rate investors earn for holding (risky) market portfolio - Higher market price of risk/ higher amount of risk= greater risk premium Security market like equation...

Estimating market risk premium

Generally estimated as historical average premium- ranged between 6-8% p.a. in Australia Can be based on forecasts as well

Estimating risk free rate

Generally estimated as the yield to maturity on long term government bonds 10 year bond rate in Australia, 10 or 30 year rates in US

Estimating, interpreting and using betas and the market model

Historical betas can be estimated using following market model regression Market model is empirical model while CAPM is theoretical model Market model related to CAPM Betas measure how sensitive returns on particular stock are relative to unexpected changes in market portfolio's return

What is the effect of lending and borrowing funds on investors end of period wealth

If we assume returns normally distributed Option A- lend funds and invest (5000/5000) - 95% probability realised return lies within [E(r)-2σ), E(r)+2σ] or (-6%, 24%) Option B- borrowing and then investing (-30%, 60%) - More variation An investors best investment= combination of risk free security and risky portfolio X (tangent to line through rf)- line rfX now dominates FF'

Security market line

In equilibrium, all risky securities are priced so that their expected returns plot on SML Securities with ß less/more than 1 earn expected return lower/higher than market portfolio x axis of CML used to price efficient portfolios differs from x axis of SML used to price individual/ portfolio securities

The market portfolio

In equilibrium, portfolio X must be the (value weighted) market portfolio of all risky securities Why is X the market portfolio - Suppose stock A is 5% of total risky securities by market value - Suppose that 2% of portfolio X is composed of stock A (stock A in excess supply, price of stock A falls and expected return rises, reduces weight in portfolio M and increasing weight in portfolio X) In equilibrium X must be market portfolio (now denotes as M)

How CML equation can be rewritten

Intercept of CML= rf (risk free rate) Slope of CML= [E(rm)-rf]/σm - The expected return on market portfolio (in excess of risk free rate) per unit of the market portfolio's total risk

Main assumptions in capital asset pricing model

Investors are risk averse individuals who maximise the expected utility of their end of period wealth - Investors make portfolio decisions decisions on basis of only expected return and return variance Investors have identical expectations about security returns Returns on these securities= normally distributed Capital markets are perfect Unlimited borrowing and lending at risk free rate is possible Set of risky securities is fixed and securities are traded

Which risk matters (in relation to assets)

Portfolio theory- risk is sd of return distributions, returns measured over one time period Nothing in what follows is inconsistent with assumption (not sd of assets return distribution though) Want to price (determined expected return on) efficient portfolio, use CML - But want expected return on individual asset (like a share) - Cant use CML, have to use CAPM CAPM says sort of risk relevant to pricing individual asset is not its 'total risk' σ, it is systematic risk Say assumptions underlying portfolio theory are true, every investor follows - Every investor holds market portfolio (+/- position in risk free asset), dealing with single time period - Mathematic exercise to show that expected return on asset given by CAPM equation, CAPM is called security market line

Estimating other CAPM parameters- what

Riskfree rate, rt Market retirn E(rm) or the market risk premium (R(rm)-rf)

Two important special cases 2. The beta of market portfolio M

The covariance of any variable with itself is its variance

Capital market line equation

The efficient portfolio's expected return equals riskfree rate plus market risk premium (=E(rm) - tf) weighted by portfolio risk proportionate to market portfolio risk [σp/σm)

CAPM and beta

ß= 1: security/portfolio has same risk as market portfolio ß= 0: security/ portfolio has zero risk ß<1: security/portfolio has lower risk than market portfolio ß>1: security/ portfolio has higher risk than market portfolio Negative betas arent possible yeah?