How the arbitrage pricing model determines the cost of equity

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The arbitrage pricing theory (APT) describes a method for determining the cost of equity and the
expected return of securities. It was developed by Stephen Ross, and it is also referred to as the
arbitrage pricing model (APM). The APT, in contrast to the Capital Asset Pricing Model (CAPM)
is not a balanced market model, but merely an arbitrage-free securities market model.

Arbitrage pricing theory maintains that it is possible for the expected return of a financial asset
to be simulated as a linear part of numerous macro-economic factors. Or theoretical market
indices, such that reactivity to variations in each factor is signified by a factor-specific beta
coefficient.

In turn, the rate of return will therefore be applied to determine the right price for an asset. In
principle, the price set must be identical to the expected final price which is discounted at the
model derived rate. In the event, that the price varies, necessary adjustments aimed at aligning
it can be carried on the basis of arbitrage.

The APT model describes the mechanism by which the arbitrage made by investors leads to the
convergence of the price of an asset and also balance in its expected price, according to the
model. Note that under a true arbitrage, the investor enjoys a guaranteed pay off, whereas
under the APT arbitration, the investor only has a positive expected pay off.

Thus, the APT model assumes an arbitrage in expectations mode, i.e., arbitrage by investors
adjusts the price achieved in such a way that it is positioned in line with the returns expected by
the model.

There are basic approaches to identify the factors of the arbitrage pricing theory, such as using
macroeconomic indicators. Empirical studies have shown that five factors explain sufficiently the
cost of equity, and these include the index of industrial production, the short-term real interest
rate, the short-term inflation, long-term inflation, and the general risk.

The arbitrage pricing model has been developed because of practical problems with the CAPM,
which applies very strict assumptions about a market equilibrium. It is assumed that all investors
hold shares in a market portfolio, so that the relative amount of each security in each portfolio is
the same.

For this market balances out an equilibrium price results for each security, which depends on its
correlation with the market portfolio. The CAPM would be the special case, known as the single
price factor of the market portfolio.

These assumptions have proven to be impractical. On one hand, the market portfolio is very
difficult to identify, on the other, the need rose to econometric models with more than one factor.