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CAPITAL ASSET PRICINGTHEORY AND ARBITRAGE

PRICING THEORY

M N SHAFI

10CB 14

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CAPM THEORY

The CAPM theory helps the investor to understand the riskand return relationship of the securities .

A model that describes relationship b/w risk and expected

return on an invmt

The general idea behind the CAPM is investor can mix risk

free assets with the risky assets in a portfolio to obtain desired

rate of risk-return combination

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In CAPM cash is investing in 2 ways

1. Time value of money / risk freeinvmt for over a period of time

2. Risk

amount of compensation the investor needs for taking on additional

risk. Is calculating by risk measure beta

Expected return should equal the rate on a risk free + risk premium

If the expected return does not meet or exceed the required

return , the investment should not be undertaken

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Under the theory of the CAPM total risk is partitioned

into two parts:

Systematic risk / Non Diversifiable Risk Unsystematic risk / diversifiable risk

The beta coefficient measures systematic risk

Systematic Risk Unsystematic Risk

Total Risk of the Investment

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Exercise Investor is investing in risk free & risky assets

Let assume , Borrowing and lending rate to be 12.5%

Return on risky asset to be 20 %

Case.1 if he invest 50% in risk free and 50% risky asset

His expected return of the portfolio would be,,,,,,,

Rp = Rf Xf + Rm (1- Xf)

= 12.5 .5 + 20 ( 1- .5)

= 6.25 + 10

= 16.25%

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Case.2

If there is a zero invnmt in riskfree asset and 100% in risky, the

return is,,,,Rp = RfXf + Rm (1- Xf)

= 0 + 20%

= 20%

Case.3

If - .5 in risk free asset and 1.5 in risky asset , the return is

Rp = RfXf + Rm (1- Xf)

= (12.5 - .5) + 20 1.5

= - 6.25 + 30

= 23. 75

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Calculating portfolio risk

Variance of the risk free asset is zero . i e, portfolio risk solely

depends on the portion on investments on risky assets The variance of the risky asset is assumed to be 15.

Proportion in risky asset (1-Xf) PORTFOLIO RISK

0.5 7.5

1.0 15

1.5 22.5

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Capital Market Line. (CML)

A is an undervalued

portfolio. Expected

return is greater than

the required return.

Demand for Portfolio

A will increasedriving up the price,

and therefore the

expected return will

fall until expected

equals required

(market equilibrium

condition is

achieved.)

Required

return on A

Expected

return on A

B is a portfolio that

offers and expected

return equal to the

required return.

ER

RF

B

C

A

CML

C is an overvalued

portfolio. Expected

return is less than

the required return.

Selling pressure will

cause the price to falland the yield to rise

until expected equals

the required return.

Required

Return on C

Expected

Return on C

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BETA

Most popular risk indicator for stock Measure the volatility of price in the mkt

it gives a fair idea on how the stock will react for the mkt

movements

in other words how does the stock price move relative tooverall mkt

If is 1 , it will fluctuate in price at the same rate of mkt

Greater than 1 have greater price volatility than the overall

mkt & more risky

Less than 1 of stocks have less price volatility than the mkt& are less risky

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Beta & Risk

If you are accepting more risk, you should expect more

reward

For eg. If a stock with of 1 is expected to return

8%, while a stock with of 1.5 should return 12%

For short term investors is a good measure of risk , but for

long term carefully consider company's fundamentals.

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Security market line (SML)

Relationship b/w Risk expected rate of return and

For individual securities.

If the unsystematic risk is eliminated, then the matter of

concern is systematic risk alone.

This systematic risk could be measured by beta

The beta analysis is useful for individual securities and

portfolios whether efficient or inefficient.

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Security market line (SML)

M = 1

ER

RF

MERM

SML

Expected

return

Risk (beta)

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ARBITRAGE PRICING THEORY

(APT)

What is Arbitrage ???

The purchase of currencies, securities, or commodities in one

mkt for immediate resale in others to profit from unequal

prices

Simultaneous purchase and sale

Is a practice of taking advantage of a price

difference b/w two or more markets

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ARBITRAGE PRICING THEORY (APT) According to APT theory investor tries to find out the

possibilities to increase returns from his portfolio without

increasing the funds in the portfolio.

Basic requirement of an Arbitrage portfolio.

Wants to change the proportion of the securities without anyadditional financial commitments.

For eg. The investor holds A, B, and C securities and he

want to change the proportion of securities without anyadditional financial commitments. (X a, X b& X c ).

Increase in the invt in the security A could be carried

out only if he reduces the propotion of invt either in B or C.

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Exercise The investor holds the A, B, and C stocks with the following

returns and sensitivityto changes in the industrial production.

The total amount ib Rs. 150,000 /-

the investor would increase his investment in stock A and B by

selling C. The new composition of weights are,

R b Original weights

Stock A 20% .45 .33

Stock B 15% 1.35 .33

Stock C 12% .55 .34

0.53

0.355

0.115

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From the APT analysis it can be

concluded that

The return in the arbitrage portfolio is higher than the old

portfolio

The arbitrage and the old portfolio sensitivity remains the

same

EFFECT ON PRICE.

To buy stock A and B the investor has to sell stock C

The buying pressure on stock A and B would lead toincrease in their price

Selling of stock C may result in fall in the price of the stock

C

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