Capital Asset Pricing Model and Arbitrage Pricing Theory

Question

Explain Capital Asset Pricing Model returns on individual assets and Arbitrage Pricing Theory returns on investments.

Answer 1

In the Capital Asset Pricing Model returns on individual assets are related to returns on the market as a whole together with an uncorrelated stock-specific random component. In Arbitrage Pricing Theory returns on investments are represented by a linear combination of numerous random factors, with related factor weighting. Portfolios of assets can also be decomposed in this manner. Provided the portfolio has a sufficiently huge number of assets, then the stock-specific component can be avoided. Being able to avoid the stock-specific risk is the key to the 'A' in 'APT.'

We write the random return on the ith asset by

Here the R‾_j are the factors, α's and β's are constants and ε_i is the stock-specific risk. A portfolio of all these assets has return

Here the '···' can be avoided if the portfolio is well diversified. Assume we think that five factors are enough to represent the economy. Therefore we can decompose any portfolio in a linear combination of all these five factors, plus some evidently negligible stock-specific risks. When we are shown six diversified portfolios, so, we can decompose each in the five random factors. Because there are more portfolios than factors we can determine a relationship among (some of) these portfolios, efficiently relating their values, or else there would be an arbitrage.