Trend Following.4 - Reverse a Losing Strategy

A simple trading strategy will give a serial crossover signals, such as +-+-+-+-. (+) is for price crossing up the trend line, (-) is for down.

For a long only strategy, it will be like (buy-sell) pairs, we buy at (+) and sell at (-).

For a short only strategy, it will be like (sell-buy) pairs, we sell short at (-) and buy cover at (+).

For each trade, we can get the max drawdown and the return.  Then we can get the cumulative return, and compare it with a simple buy-and-hold strategy.

If a strategy is a losing strategy in the long run, we can reverse the trade to see if it's profitable.

Say the cumulative return of strategy A is the product of ReturnA.i.  The return of the reverse strategy B is the product of ReturnB.i.

ReturnA.i = (1+a.i)
ReturnB.i = (1+b.i) = (1-a.i)

so ReturnA.i * ReturnB.i = (1+a.i)(1-a.i) = 1- a.i² < 1

The product of (ReturnA.i * ReturnB.i) will approach zero in the long run.

Say X = product of (ReturnA.i * ReturnB.i) = product of ReturnA.i * product of ReturnB.i

If X < product of ReturnA.i, then product of ReturnB.i < 1.

If strategy A is a losing strategy and the product of ReturnA.i > X, then the reverse strategy is also a losing strategy.