Index: > A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Home > Arbitrage pricing theory

First Prev [ 1 2 ] Next Last

Arbitrage pricing theory (APT) holds that the expected return of a financial asset can be modelled as a linear function of various macro-economic factors, where sensitivity to changes in each factor is represented by a factor specific beta coefficient. The model derived rate of return will then be used to price the asset correctly - the asset price should equal the expected end of period price discounted at the rate implied by model. If the price diverges, arbitrage should bring it back into line.

1 The APT model

If APT holds, then a risky asset can be described as satisfying the following relation:

where

is the risky asset's expected return,
is the risk free rate,
is the macroeconomic factor,
is the sensitivity of the asset to factor ,
and is the risky asset's idiosyncratic random shock with mean zero.

That is, the uncertain return of an asset is a linear relationship among factors. Additionally, every factor is also considered to be a random variable with mean zero.

Note that there are some assumptions and requirements that have to be fulfilled for the latter to be correct: There must be perfect competition in the market, and the total number of assets may never surpass the total number of factors (in order to avoid the problem of matrix singularity), respectively.

2 Arbitrage and the APT

Arbitrage is the practice of taking advantage of a state of imbalance between two (or possibly more) markets and thereby making a risk free profit. In the APT context, arbitrage consists of trading in two assets – one which is mispriced and one which is correctly priced. The arbitrageur sells the asset which is too expensive and uses the proceeds to buy one which is correctly priced, or sells a correctly priced asset and uses the proceeds to buy the asset which is too cheap. (See Rational pricing.)

Under the APT, an asset is mispriced if its current price diverges from the price predicted by the model. The asset price today, should equal the sum of all future cash flows discounted at the APT rate, where the expected return of the asset is a linear function of various macro-economic factors, and sensitivity to changes in each factor is represented by a factor specific beta coefficient.

The correctly priced asset here, is, in fact, a portfolio consisting of other correctly priced assets. This portfolio has the same exposure to each of the macroeconomic factors as the mispriced asset. The arbitrageur creates the portfolio by identifying x correctly priced assets (one per factor plus one) and then weighting the assets such that portfolio beta per factor is the same as for the mispriced asset.

When the investor is long the asset and short the portfolio (or vice versa) he has created a position which has a positive expected return (the difference between asset return and portfolio return) and which has a net-zero exposure to any macroeconomic factor and is therefore risk free. The arbitrageur is thus in a position to make a risk free profit:

Where today's price is too low:

The implication is that at the end of the period the portfolio would have appreciated at the rate implied by the APT, whereas the mispriced asset would have appreciated at more than this rate.

The arbitrageur could therefore: 1) short sell the portfolio today 2) buy the mispriced-asset with the proceeds. At the end of the period she would 3) sell the mispriced asset 4) use the proceeds to buy back the portfolio and 5) pocket the difference.

Where today's price is too high:

The implication is that at the end of the period the portfolio would have appreciated at the rate implied by the APT, whereas the mispriced asset would have appreciated at less than this rate.

The arbitrageur could therefore 1) short sell the mispriced-asset today 2) buy the portfolio with the proceeds. At the end of the period he would 3) sell the portfolio 4) use the proceeds to buy back the mispriced-asset and 5) pocket the difference.

3 Relationship with the Capital asset pricing model

The APT along with the Capital asset pricing model (CAPM) is one of two influential theories on asset pricing. The APT differs from the CAPM in that it is less restrictive in its assumptions. It allows for an explanatory (as opposed to statistical) model of asset returns. It assumes that each investor will hold a unique portfolio with its own particular array of betas, as opposed to the identical "market portfolio". In some ways, the CAPM can be considered a "special case" of the APT in that the Securities market line represents a single-factor model of the asset price, where Beta is exposure to changes in value of the Market.

Politics	Business	Finance

Topics: Arbitrage Pricing Theory Asset Portfolio Apt Factor Price Model...

ArbitrageIn economics, arbitrage is the practice of taking advantage of a state of imbalance between two (or possibly more) markets: a combination of matching deals are struck that exploit the imbalance, the profit being the difference between the market prices.

Arbitrage pricing theoryArbitrage pricing theory APT holds that the expected return of a financial asset can be modelled as a linear function of various macro-economic factors, where sensitivity to changes in each factor is represented by a factor specific beta coefficient.

Non User