Lokanandha Reddy Irala 1 Capital Asset Pricing Model

Capital Asset Pricing Model

Lokanandha Reddy Irala 2 Capital Asset Pricing Model

MPT Revisited The Markowitz portfolio theory

explains how investors-acting upon a set of estimates-select an optimum portfolio, or set of portfolios.

If investors act as prescribed by the MPT, then it is interesting to see how the aggregate of investors will behave, and how prices and returns are determined in the market.

Such models –known as general equilibrium models- will allow us to determine the relevant measure of risk for any asset and the relationship between expected return and risk for any asset when markets are in equilibrium.

Lokanandha Reddy Irala 3 Capital Asset Pricing Model

CAPM-The Assumptions No transaction costs & personal Income

taxes Assets are infinitely divisible Perfect competition

An individual cannot affect the price of a stock by his buying or selling action. While no single investor can affect prices by an individual action, investors in total determine prices by their actions.

Return and Risk are the only decision criteria

Unlimited short sales Unlimited lending and borrowing at the

risk less rate.

Lokanandha Reddy Irala 4 Capital Asset Pricing Model

CAPM-The Assumptions Homogeneity of expectations.

Investors are assumed to be concerned with the mean and variance of returns (or prices over a single period)

All investors are assumed to define the relevant period in exactly the same manner

All investors are assumed to have identical expec tations with respect to the necessary inputs (expected returns, the variance of returns and correlation structure between all pairs of stocks.) to the portfolio decision.

Marketability of assets All assets are marketable. All assets, including human

capital, can be sold and bought on the market.

Lokanandha Reddy Irala 5 Capital Asset Pricing Model

The SML For very well-diversified portfolios,

non systematic risk tends to go to zero and the only relevant risk is systematic risk measured by Beta.

Since we assume that the investor is concerned only with expected return and risk, the only di mensions of a security that need be of concern are expected return and Beta.

Lokanandha Reddy Irala 6 Capital Asset Pricing Model

Let us hypothesize two portfolios with the characteristics shown here:

Investment Expected return Beta

X 14 1.2

Y 18 1.4

Lokanandha Reddy Irala 7 Capital Asset Pricing Model

Now consider a portfolio Z made up of one half of portfolio X and one half of portfolio Y.

Then, the return on Z is given by

16)18)(5.0()14)(5.0(1

YYXXZ

n

iiip

RWRWR

RWR

Then, the Beta of Z is given by

3.1)4.1)(5.0()2.1)(5.0(1

YYXXZ

n

iiip

RW

W

Lokanandha Reddy Irala 8 Capital Asset Pricing Model

In Let us plot these three potential investments in the beta-return space

Notice that they lie on a straight line. This is no accident. All portfolios composed of different

fractions of investments X and Y will lie along a straight line in Expected Return -Beta space.

18

16

14

1.2 1.3 1.4Rp

Z

Y

X

Rp

Lokanandha Reddy Irala 9 Capital Asset Pricing Model

A

18

16

14

1.2 1.3 1.4Rp

Z

Y

X

Rp

Such an investment cannot exist for very long.

This portfolio offers a higher return and the same risk as portfolio Z.

Hence, it would pay all investors to sell Z short and buy A.

Now hypothesize a new investment A that has a return of 17% and a Beta of 1.3

Lokanandha Reddy Irala 10 Capital Asset Pricing Model

An investor could sell Rs.1000 worth of portfolio Z short and with the Rs.1000 buy portfolio A. The characteristics of this arbitrated portfolio would be as follows:

Investment (Rs.)

Expected Return (Rs.) Beta

Portfolio Z -1000 -160 -1.3

Portfolio A +1000 170 1.3

Arbitrage Portfolio 0 10 0

Lokanandha Reddy Irala 11 Capital Asset Pricing Model

Deriving the Security Market Line

(1, Rm)

(0, Rf)

1.0

Rp

M

Lokanandha Reddy Irala 12 Capital Asset Pricing Model

Thank You

Questions?