How to Pick Your Parameters

Anyone who thinks about any kind of quantitative strategy will face the problem of picking parameters --- smoothing parameters, number of lags, holding periods, etc. If you work in on a quantitative team you will be expected (1) to make wise choices and (2) explain why your choices were wise. I'm starting a page on this theme, and we will surely revisit it at least a few times. Please help me add to it. This is one of the biggest services that we can provide to our friends.

Naturally, we have no pat answers, only some examples and suggestions.

Grid Search Return Plots

The example to consider here is Figure Two from the Credit Suisse piece on using the VIX. They had two parameters --- one that controlled their VIX relative position and one that was their holding period post investment. They do a three dimensional plot of their returns versus these parameters. There is a lot of computation that is packed into one picture.

This is asking a lot from your data, so you hope that the picture is relatively smooth.
If it is not smooth, you should worry about picking an "optimum" grid point that might have been an artifact of the testing period.

Colby Meyers Type Plots

Remember, they had an "indicator" and they wanted to see how well it predicted returns at various time horizons. Their choice was 1 month, 3 month, 6 month, and year --- but obviously this is not a critical part of the technology. They also "binned" relative returns into bullish and bearish of various degrees. This was smart, though there are lots of ways to do this and you should think hard about your particular case. The nicest feature of their tables was the relatively fine bins into which the indicator was sliced.

The results from the Colby Meyers analyses were largely negative. This is too bad, but we can't ignore it just because we don't like it.
The way in which most indicators flunked was instructive. There was no smoothness or pattern to the bull/bear value that was associated with an interval.

Foster's Trick

Suppose you have say five predictors F(1,t), F(2,t),..., F(5,t) of the period t returns R(t). Fit the regression: R(t)=a_1 F((1,t)+...+a_5F(5,t) + epsilon(t). and then use the combined predictor that is given by the regression. That is --- replace the a's by their estimates to get your forecast.

This trick can be varied in many ways.

Singh and Shah Trick

The idea here is that if you have a strategy that leads to "wild" swings in the portfolio (and there for large trading costs), you can smooth your portfolio weights. This cut trading costs, but it also "robustifies" the original strategy to some extent.

Rebalancing Between Strategies

Consider two completing strategies that may only differ by the parameter choice --- to be specific suppose one uses a 20 day EMA and the other uses a 30 day EMA as one of the strategy drivers. You don't have to "pick" one or the other, you can run a port folio that does periodic rebalancing between the two.

Again, there are lots of variations here. Funds of Funds may have a bad name now, but one of these days Strategy of Strategies could be a winner.