Saturday, October 7, 2017

Arbitrage Pricing Theory and Factor Investing

Factor investing is becoming popular these days. It has its roots in Arbitrage Pricing Theory. According to Wikipedia
Arbitrage pricing theory (APT) is a general theory of asset pricing that holds that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors or theoretical market indices, 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 the model. If the price diverges, arbitrage should bring it back into line.

S. Ross is the Father of Arbitrage Pricing Theory. D. Musto of Wharton recently summarized the key points of Arbitrage Pricing Theory in this podcast
  • … the risk that faces the investor, the risk that ultimately is going to deliver the payoff to his bank account, is going to be the risk of this portfolio. And once you think of it that way, you realize that the correct measure of risk is not a stock’s risk by itself, but instead, the risk that it’s going to add to a diversified portfolio.
  • … stock returns follow what you could call a factor structure … All of the systematic portion of their stock returns is captured by those five factors. Everything that’s not captured by them is idiosyncratic.
  • …the risk of a stock that’s going to matter to investors is its exposure to those factors. And every factor is going to have associated with it what you would call a risk premium
  • …the idiosyncratic component of the stock’s return is not going to give you any additional expected return. It shouldn’t, because to an intelligent investor putting together an optimal portfolio, that’s just going to wash out. It’s the factor-driven part of the return that’s going to matter. And so that’s going to be driving expected returns
  • [factors] could be things like changes in expected inflation. They could be developments to GNP. They could be things having to do with interest rates — and what kind of risk premium you would need to be compensated for exposure to that factor.
Another significant contribution of S. Ross is the binomial option pricing model.

This is a very elegant way to price the whole range of derivative securities out there. So Steve, building on the work of [Fisher] Black and [Myron] Scholes, showed how you could take what they did and think about it as a binomial framework that would help you price a wide range of securities, and show you how you go about replicating the payoff of any derivative security you might be interested in, with this binomial trading technique.