It is believed that fund managers with timing ability should be able to predict the market trend, gain higher returns by improving the risk level of the portfolio when they are long, and reduce the risk of the portfolio when they are short. Therefore, CAPM characteristic line is no longer a straight line with fixed slope, but a curve whose slope will change with the market situation, and the regression model corresponding to this curve is called T-M model for short.

The formula is as follows:

Rp - Rf =a + b(Rm -Rf) + c(Rm - Rf)^2 + ep

Among them, Rp is the combination rate of return, A is the index of securities selection ability and C is the index of market opportunity ability. If c is positive, it can be explained that the market timing ability does exist, because it can make the characteristic line correspondingly steep when (Rm-Rf) is large. If a is positive, it indicates the existence of securities selection ability.

When there is a t in the subscript, that is, at different points, consider a more complete formula.

R p，t -R f，t =a + b*(R m，t -R f，t) +c*(R m，t -R f,t)^2 + ep

In the formula, b(β) is the systematic risk of fund portfolio investment, R f and t are the risk-free rate of return at time t, R p and t are the rate of return of fund at time t, and ep is the error term.

Source of this formula:

TreynorandMazuy。 Canmutualfundoutgoesthemarket？ [J], Harvard Business Review,1966,44:131-136