Security Analysis &

Portfolio Management

“Capital Asset Pricing Model "By

B.Pani M.Com,LLB,FCA,FICWA,ACS,DISA,MBA

9731397829 bpani2001@yahoo.co.in

Beta (β)Beta is the relative measure of systematic risk. It measures the sensitivity of the return of the security vis-à-vis the market return.

β = Cov(X,Y)/ Var(X)

where X = Return on the market

Y= Return on individual security

It can also be calculated by the following formulae

β = (NΣX*Y -ΣX*ΣY ) /( NΣX2 - (ΣX)2)

where N = number of observation.

Interpretation of beta

β > 1 --------------------------- Aggressive Securities

β< 1----------------------------- Defensive securities

Explain why the beta of the market is 1

Illustration: Calculation of BetaTime period Return on

Security XReturn on MarketIndex

1 10 112 8 73 -4 -24 22 85 8 96 -11 -57 14 128 12 119 -9 310 12 10

Calculate beta and identify whether security X is an aggressive or a defensive security.

Risk Break - Up

Total Risk of a security = σ2

Systematic Risk of a security = β2σ2 m

where β = Beta of an individual security

σ2 m= Variance of the market portfolio

Write the formulae of Unsystematic risk

Other risk calculations

Semi-variance or downside riskSemi-variance is defined in analogy to variance, but using only returns below the mean. If the returns are symmetric – i.e., the return is equally likely to be x percent above and below the mean- the semi-variance is exactly one-half of the variance.

One approach defines downside risk as the square root of the semi-variance.

• Beta is a statistical variable and should be considered with its statistical significance (R square value of the regression Using beta as a measure of relative risk has its own limitations. Most analysis consider only the magnitude of beta. line). Higher R square value implies higher correlation and a stronger relationship between returns of the asset and benchmark index.

• If beta is a result of regression of one stock against the market where it is quoted, betas from different countries are not comparable.

• Staple stocks are thought to be less affected by cycles and usually have lower beta. Procter & Gamble, which makes soap, is a classic example. Other similar ones are Philip Morris (tobacco) and Johnson & Johnson (Health & Consumer Goods). Utility stocks are thought to be less cyclical and have lower beta as well, for similar reasons.

• 'Tech' stocks typically have higher beta. An example is the dot-com bubble; although tech did very well in the late 1990s, it also cratered in the early 2000s, worse than the overall market.

Target Semi-variance

A generalized semi-variance that focuses on returns below a target instead of just below the mean.

Beta, • variation in asset/portfolio return

relative to return of market portfolio– mkt. portfolio = mkt. index

-- S&P 500 or NYSE index

= % change in asset return

% change in market return

interpreting • if

– asset is risk free• if

– asset return = market return• if

– asset is riskier than market index

– asset is less risky than market index

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PORTFOLIO RISK

• CALCULATING PORTFOLIO RISK– Portfolio Risk:

• DEFINITION: a measure that estimates the extent to which the actual outcome is likely to diverge from the expected outcome

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PORTFOLIO RISK

• CALCULATING PORTFOLIO RISK 2 Security case

where = the covariance of returns

between security1 and security2.It measures the degree to which the two securities vary together.It is product of the correlation coefficient and the two standard deviation.

Security security1 security2

Security 1 w12 w1w2

Security 2 w2w1 w22

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PORTFOLIO RISK

• CALCULATING PORTFOLIO RISK IN CASE OF n SECURITIES

– Portfolio Risk:

where ij = the covariance of returns

between security i and security j

2/1

1 1

N

i

N

jijjiP XX

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PORTFOLIO RISK

• CALCULATING PORTFOLIO RISK– Portfolio Risk:

• COVARIANCE– DEFINITION: a measure of the relationship between two

random variables– possible values:

» positive: variables move together» zero: no relationship» negative: variables move in opposite directions

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PORTFOLIO RISK

CORRELATION COEFFICIENT

wherejiijij

jiijij /

Asset Pricing Models

• CAPM– Capital Asset Pricing Model– 1964, Sharpe, Linter– quantifies the risk/return tradeoff

assume

• investors choose risky and risk-free asset

• no transactions costs, taxes

• same expectations, time horizon

• risk averse investors

implication

• expected return is a function of– beta– risk free return– market return

]R)R(E[R)R(E fmf or

]R)R(E[R)R(E fmf

fR)R(E is the portfolio risk premium

where

fm R)R(E is the market risk premium

so if

• portfolio exp. return is larger than exp. market return

• riskier portfolio has larger exp. Return

• Portfolio with larger beta will have larger expected return

fR)R(E fm R)R(E

)R(E )R(E m

>

>

so if

• portfolio exp. return is smaller than exp. market return

• less risky portfolio has smaller exp. return

fR)R(E fm R)R(E

)R(E )R(E m

<

<

so if

• portfolio exp. return is same than exp. market return

• equal risk portfolio means equal exp. return

fR)R(E fm R)R(E

)R(E )R(E m

=

=

so if

• portfolio exp. return is equal to risk free return

fR)R(E

)R(E fR

= 0

=

example

• Rm = 10%, Rf = 3%, = 2.5

]R)R(E[R)R(E fmf %]3%10[5.2%3)R(E

%5.17%3)R(E %5.20)R(E

• CAPM tells us size of risk/return tradeoff

• CAPM tells use the price of risk

Testing the CAPM

• CAPM overpredicts returns– return under CAPM > actual return

• relationship between β and return?– some studies it is positive– some recent studies argue no relationship

(1992 Fama & French)

• other factors important in determining returns– January effect– firm size effect– day-of-the-week effect– ratio of book value to market value

January Effect

• A general increase in stock prices during the month of January. This rally is generally attributed to an increase in buying, which follows the drop in price that typically happens in December when investors, seeking to create tax losses to offset capital gains, prompt a sell-off.

day-of-the-week effect

• The weekend effect (also known as the Monday effect, the day-of-the-week effect or the Monday seasonal) refers to the tendency of stocks to exhibit relatively large returns on Fridays compared to those on Mondays. This is a particularly puzzling anomaly because, as Monday returns span three days, if anything, one would expect returns on a Monday to be higher than returns for other days of the week due to the longer period and the greater risk.

CAPM’s Answers

• Specifically:Total risk = systematic risk + unsystematic risk

CAPM says: (1)Unsystematic risk can be diversified away. Since there is

no free lunch, if there is something you bear but can be avoided by diversifying at NO cost, the market will not reward the holder of unsystematic risk at all.

(2)Systematic risk cannot be diversified away without cost. In other words, investors need to be compensated by a certain risk premium for bearing systematic risk.

Pictorial Result of CAPM

E(Ri)

E(RM)

Rf

SecurityMarketLine

[COV(Ri, RM)/Var(RM)]= 1.0

slope = [E(RM) - Rf] = Eqm. Price of risk

Use of CAPM

• For valuation of risky assets

• For estimating required rate of return of risky projects