Salience Theory

Does anyone have enough advanced mathematics under their belt to explain to me how to calculate the salience of a stock’s one-month daily returns? The papers that explain salience theory are here:

I don’t have a problem with calculating sigma in these papers, but I can’t figure out how to calculate omega, even if I take into account that, according to one of these papers, “θ = 0.1 and δ = 0.7.” One problem for me is that I don’t know what s-prime is.
Thanks!

Yuval,

Edit: Here is another paper that I found easier to interpret.
Salience theory and the cross-section of stock returns: International and further evidence

Jim

I skimmed the papers. Seemed like a fairly basic concept but implementation is going to be difficult. If you make money when everyone else is losing, that stands out more than someone who made excess returns when others were also making money. The relative out-performance might be the same but more eyeballs on the guy who made money when others were losing…and this drives up prices…and has worse returns.

Seems like you could get a similar result by taking a group of stocks which outperformed by x amount over the past 20 days. I would assume that stocks with low or negative 20 day beta would be your most salient stocks as their excess returns were in contrast to what the market was doing and should stand out more.

But maybe I am wrong. Probably am. Just a thought. Although turnover would be crazy high. And if this works best in microcaps, I am not sure how practical it would be to actually trade this.

Just some thoughts to get the discussion going.

Thank you, Jim, for the paper. It is indeed slightly easier to interpret. What had me stumped was

I finally figured that out, though I’m not 100% sure I did it correctly.

Here’s the procedure in a nutshell. You take the absolute value of the stock’s daily returns and subtract the absolute value of the benchmark’s returns. You then divide that by the sum of the two returns and 10%. That gives you the salience of each day’s return. You do this over a month. You then rank all those salience values from 1 to 20. After that you perform a bunch of hocus-pocus which in essence equals about 0.42 * exp(-0.37*rank). (This is the part that really confused me before.) Lastly, you take the covariance between the daily returns and that transformed rank value.

The results are going to be relatively close to the covariance between the returns and the salience, at least if you look at how one stock compares to another. That’s a good thing, since P123 doesn’t have an easy way to rank transformed daily returns over a month.

Now since slope is covariance divided by variance, the covariance of the stock’s daily returns and their salience is the linreg slope of those two, multiplied by the square of the standard deviation of the daily returns. So one could approximate salience theory by using P123’s linear regression tools. A good project for a rainy day . . .

Yuval, Nice! Thank you for the summary of the papers.—Jim