Financial Management

Session - 12

CAPM

Measuring Risk

• Variance:– Average value of the squared deviations from mean

• Standard deviation– Positive square root of variance, a very common measure

for risk

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Expected Return, Risk and Diversification

• As managers, we are concerned about the overall risk of the business’s portfolio of assets.

• The return on a portfolio (rp) is the weighted average of the returns on the assets in the portfolio, where the weights are the proportion invested in each asset.

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Portfolio Risk: Variance

• Let cov1,2 represent the covariance of two assets’ returns. We can write the portfolio variance as:

• It can be shown that for a large portfolio of multiple of assets, the portfolio variance depends more on the covariances than on the respective variances of individual assets.

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Diversifiable and Non-diversifiable Risks…Cont’d

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Modern Portfolio Theory• We see that the best portfolios are no longer those along the

entire length of the efficient frontier; rather, the best portfolios are now the combinations of the risk-free asset and one— and only one—portfolio of risky assets on the frontier.

Estimating Beta

• Beta measures the responsiveness of the security’s return to movement in the market

• For the average stock beta =1• If Beta>1 , it means that stock is contributing much to

the risk of the portfolio than the average stock• Beta<0 , means securities do well when market does

poorly and vice versa.

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Estimating with Regression

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Secu

rity

Ret

urns

Return on market %

Ri = i + iRm + ei

Slope = i

Beta and the portfolio risk

• The contribution of an individual security to the risk of a well diversified portfolio depends on two factors:– The importance (weight) of the security in the portfolio and– The sensitivity of the security to market movements (beta).

• So, in a portfolio, the risk of individual security is measured by its beta (β).

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)()(

2,

M

Mii R

RRCov

Standard deviation Vs beta

• Which provides better measure of risk?• If investor holds only one security then the SD of the

security is a true measure of risk• If investor holds a well diversified portfolio the SD of

the portfolio is a measure of risk of the whole portfolio but for the individual security beta is an appropriate measure

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Beta varies with time and within sector

• Beta values have three firm specific drivers– Degree of Operating leverage– Degree of Financial leverage– Business risk

• With time all these factors changes and hence beta

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Capital Asset Pricing Model

• The model was introduced by Jack Treynor, William Sharpe, John Lintner and Jan Mossin independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory.

• This model establish a relationship between risk and expected return– Expected return and market– Expected return and individual securities

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Capital Asset Pricing Model…Assumptions• All investors have rational expectations. • There are no arbitrage opportunities. • Returns are distributed normally. • Perfectly efficient capital markets.

• Investors are solely concerned with level and uncertainty of future wealth

• Risk-free rates exist with limitless borrowing capacity and universal access.

• The Risk-free borrowing and lending rates are equal.

• No inflation and no change in the level of interest rate exists. • Perfect information, hence all investors have the same

expectations about security returns for any given time period.

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Capital Asset Pricing Model• William Sharpe took the idea that portfolio return and risk

are the only elements to consider and developed a model that deals with how assets are priced.

• This model is referred to as the capital asset pricing model (CAPM).

• All the assets in each portfolio, even on the frontier, have some risk.

• However, regardless of the level of risk one chooses, one can get the highest expected return by a mixture of a portfolio in the efficient frontier and a risk free asset (lending or borrowing).

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CAPM…Cont’d

• The CAPM uses this relationship between expected return and risk to describe how assets are priced.

• The CAPM specifies that the expected return on any asset is a function of the return on a risk-free asset plus a risk premium.

• The return on the risk free asset is compensation for the time value of money.

• The risk premium is the compensation for bearing risk.• If we represent the expected return on each asset and its

beta as a point on a graph and connect all the points, the result is the security market line (SML).

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CAPM…Cont’d

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Beta is dead!• Fama and French

– The cross sections of expected stock returns (JoF)– Common risk factors in the return of stock and bonds (JFE)

• Concluded that relationship between average reurns and beta is weak over the period 1941 to 1960 and virtually non-existent from 1963-1990

• Average return on a security is negatively related to both the firm’s price earning ratio (P/E) and the firm’s market to book ratio (M/B)

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CAPM….Limitations• The CAPM includes some unrealistic assumptions. E.g.,

it assumes that all investors can borrow and lend at the same rate.

• The CAPM is really not testable. The market portfolio is theoretical and not really observable.– (Risk Return and Equilibrium: Some Empirical Tests, JPE)

• CAPM captures all market risk in one variable.

• CAPM does not explain the differences in returns for securities that differ over time, differ on the basis of dividend yield, and differ on the basis of the market value of equity (the so called “size effect”).

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Thank You!

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