PRESENTED BY:NAVEEN KUMAR

SHIKHA SHARMASHIVANI BHATIA

Arbitrage pricing theory

Concept of Arbitrage Pricing Theory

This was developed by S. Ross, using a notion that security returns are not based on one single factor of the market; instead each security is linked with multiple factors and returns get influenced by these factors.

APT also emphasis the fundamental of ‘one single price’.

APT has two basic outcomesa) It helps in assigning price to securities by identifying the securities as underpriced Overpriced Efficiently pricedb) It also focuses on the fact that returns for a particular share is derived from its

association with multiple factors.

Assumptions of APT

Investors are risk averse and utility maximizers Investors have homogeneous beliefs. Markets are perfect. Multi-factor effect Dominance principle Equilibrium of the market Efficient frontier

Expected return under APTExpected return: the most likely level of return, which

should be maintained as per the performance of the company and association of individual shares with different factors.

Alpha: can be termed as return, which can be expected if all other factors have zero value or the security has zero beta with all the factors.

Systematic return component: this is the part of total expected return, which is on account of security with different systematic factors, which affect returns from share.

Random error term: represents the extraordinary return from a security only when some extraordinary event takes place.

Expected return = αi+βij1xj1+βij2xj2+βij3xj3.....+βijnxjn +ei

Risk: fluctuation in the expected return is represented with the help of variance in the return.

Var(i) = β2ij1x var(j1) + β2

ij2x var(j2)+ β2ij3x var(j3).......+

β2ijnx var(jn)+ var(e)

Beta: sensitivity measurement, representing volatility of the return for a given change in the factor to which this beta value associate.

Βij1 = covariancei,j1

σ 2ji

Arbitrage process

Two identical securities with the same level of risk must have the same price i.e. mean return for each of the security. However due to market imperfections and short term disequilibrium in the market, two identical securities might be priced differently; but this will last only in the short run.

Arbitrage process

By arbitrage in portfolio context, we mean selling the securities or portfolios, which generate low or less returns for a particular level of risk and buying the other security or portfolio, having the same level of risk but generating high or more returns. The arbitrage process will continue till the time both the securities do not find a place on the efficient frontier.

Portfolio Mean Return(%) Risk(σ%) A 10 1 B 15 1.50 C 20 2 D 17 1.25 E 9 1.25 F 13 1.50

From the table and graph, a portfolio manager can identify the portfolio A D & C are on efficient frontiers. Whereas portfolio B E & F do not find a place on efficient frontier.

Generating profit with zero initial outflow

An investor can generate extra return with zero initial outflow.

Let us assume that an investor short sells the portfolio ‘E’ of the value Rs. 10,000 and buys the portfolio ‘D’ by using these Rs 10,000. after doing this and waiting for period of one year, he has to pay 9% for the short sale of portfolio ‘E’ but he will receive 17% from the portfolio ‘D’.

Present Cash Return After Cash Flow Flow One Year After 1 YearShort Sell ‘E’ +10,000 -900 - 10,000Buy ‘D’ -10,000 +1700 +10,000Net cash flow 0 +800 0

Thus by making such arbitrage, one can have Rs 800 with zero initial investment.

Limitations of APT It does not specify the type and number of factors affecting

risk and return. It is difficult to identify the factors affecting return and risks. Different investors might identify different factors for the

same securities Difficult in calculating beta values Effect of one factor on the return and risk cannot be assessed

precisely If the list of factors affecting the return and risks is infinite,

then this theory does not find the practical implication. With passage of time, type and number of factors for one

security might change leading to inconsistency in comparison.