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Pricing Models
... First of all, let’s examine both Arbitrage Pricing Theory and Capital Asset Pricing Model.
The Arbitrage Pricing Theory is a sound alternative to the Capital Asset Pricing Model. The APT offers us an alternative explanation to CAPM concerning risk-expected return relationships. The Arbitrage Pricing Theory specifies returns as a linear function of more than one single factor, whereas the Capital Asset Pricing Model usually specified returns as a linear function of only one factor – systematic risk.
The Arbitrage Pricing Theory.
Let’s explain the main basics of the Arbitrage Pricing Theory.
The APT divides “systematic risk into smaller component risks. Recent research has suggested that the 4-factor version of the APT is better at predicting the return on a stock than the simplest version of the CAPM. In some of its basic ideas, but not in its details, the APT builds on rather than replaces the CAPM” (Risk and Return, n.p.)
E (ri − rf) = E (rj − rf)
âi âj
According to “Financial Markets: Theories and Evidence”, the Arbitrage Pricing Theory rests on the following assumptions:
1. The returns are generated according to a linear factor model;
What is linear factor model?
ri = E (ri) + âi •F + ĺi
- âi asset i’s sensitivity to the common factors;
- f common factor, with ĺ (F) = 0;
- Ei firm-specific return, with zero mean, and independent of the common factor or other firm’s idiosyncratic component (Investment Classes 6: The CAPM and APT Part 1 – theory);
2. The number of assets are close to infinite;
3. Investors have homogenous expectations (however, this assumption is the same as the Capital Asset Pricing Model proposes);
4. Capital markets are perfect (the Capital Asset Pricing Model has the same assumption as well).
As for two first assumptions, they are the subjects to debates.
The Capital Asset Pricing Model
According to the “Investment Classes 6: The CAPM and APT Part 1 – theory”, the CAPM is based on the following assumptions:
1. Perfect markets (the same as the APT).
What does it mean? It means perfect competition, no transaction costs, no short-sale constraints, no taxes, the assets are traded publicly and are perfectly divisible. The risk-free rate is the same both for landing and borrowing.
2. Identical investors
It means that the holding period is the same, the homogenous expectations, normality or mean-Variance utility, etc.
So, does it mean that APT is stronger than CAPM? It is very difficult to claim that one theory is stronger than another. At the same time, the APT claims that “relatively new factors generate correlation” (Burton 20-28) and states that “the expected returns on a security or an asset class ought to be a function of its exposure to those relatively new factors”. These facts fully agree with the main idea of the Capital Asset Pricing Model. ...
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