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Arbitrage Pricing Theory and Multifactor Models of Risk and Return

4 important questions on Arbitrage Pricing Theory and Multifactor Models of Risk and Return

What are factor loadings/betas?

The coefficient/beta for each factor shows the sensitivity of share return to that factor, it is therefore called a factor loading. E.g. a utility company is primarily sensitive to interest rates as its cash flows are relatively stable.

Factor loading provide a framework for a hedging strategy. But note that this is not a theory, but just a description of the factors that affect security returns. Most obvious question to ask is of course, how to get the expected excess return

What about the APT, arbitrage pricing theory?

Developed by Ross (1976). Different path to get to the SML with three propositions:
- Security returns can be described by a factor model
- There are sufficient securities to diversify away firm-specific risks
- Well-functioning security markets do not allow for persistence of arbitrage opportunities.

It thereby follows the law of one price; if equivalent, then they should be equally priced (regardless of risk aversion). This rule is perhaps the most fundamental concept of capital market theory.

What is the difference between arbitrage and risk-return dominance?

The dominance argument is weaker as it describes limited portfolio changes by investors, which needs aggregation to restore prices. For arbitrage a single investor is enough as it would want an unlimited large position. The CAPM is an example of the dominance argument as it leans on the mean-variance assumption.

Strict arbitrage is a possibility for derivatives as they are based on underlyings. Primitive securities need to rely on the diversification argument. Risk arbitrage is not pure arbitrage and reflect investments in M&A deals.

Why diversified portfolios?

If the numbers of stocks is large enough, or the stakes in each stoke relatively small, the non-systematic (idiosyncratic) risk approaches zero. Making this component negligible helps us to arrive at the SML as it reflects that there is no risk premium for diversifiable risks. No scattered plot!

In practice we can reduce the exposure to firm-specific risks, but making is negligible is hard and requires 10.000 different stocks.