A three-factor model is any model that tries to explain expected returns in terms of three factors. It is usually specified in terms of a linear equation of the sortLadyGeek wrote:I'm confused on your terminology.ghariton wrote:I've been speculating for a while that three-factor models -- volatility, skewness and kurtosis -- give more insight into security valuation than the more traditional approaches.
The "three-factor models" I'm thinking of, aka Fama and French three-factor model use regression analysis to curve-fit past performance. Goodness of fit (R^2) is the corresponding metric. (See: Fama-French three-factor model analysis)
volatility, skewness and kurtosis are the 2nd (some associate volatility with variance), 3rd, and 4th moments of a probability distribution. See: Moment (mathematics)
Y = A + B(1)*X(1) + B(2)*X(2) + B(3) *X(3)
although there is no strong theoretical reason that it be linear. The B's are usually estimated by running a multiple regression, using historic data.
Fama and French have suggested that one of the variables be volatility (either relative to the market, i.e. beta, or on its own, i.e. variance), value (e.g. price/book ratio) and size of company. Some others suggest a four-factor model, where there would be an X(4) measuring momentum. But other measures can be reasonable candidates for the three (or four) factors.
I would continue to use volatility as X(1), but I would use the expected skewness of returns as X(2) and expected kurtosis as X(3). As usual, since we don't have measures of expected skewness and kurtosis, we would probably use historic data to calculate the first four moments of the distribution of expected returns.
In this formulation, B(2) would be the price of positive skew, reflecting the empirical observation that many people like the possibility of large wins even if of low probability (e.g. lottery tickets, IPOs) and are willing to pay for it, by accepting a lower expected return (or equivalently by bidding up the price). Similarly B(3) would be the price of kurtosis or fat tails, i.e. the possibility that very rare events are in fact not that infrequent. Most people would accept a slightly lower expected return, or equivalently pay a higher price, to avoid "fat tails", (e.g. hedging with options -- now the price includes the premium of the option).
The regression analysis would attempt to estimate just how much people in aggregate are willing to pay for positive skewness, or to avoid fat tails. If a successful model could be developed, it could be used to "value" securities and to detect which ones are mispriced -- the philosopher's stone of investment analysis .
George