I would like to use the cauchy distribution instead of the normal distribution to predict investment returns in the Riskamp sample spreadsheet, "Financial portfolio model." However, I don't know how to translate the parameters. I can calculate the mean and standard deviation for an investment I have backtested. How should I translate these into the location and scale parameters required for the cauchy distribution?

Technically speaking, the cauchy distribution doesn't have a mean. There's a good overview on wikipedia, have a look at

[en.wikipedia.org]

Mapping this to logical parameters, you can treat the location parameter as the median and the mode; the standard cauchy distribution has a location or median of zero.

There's no 1-to-1 map from normal to cauchy, as the tail structure is different. If you wanted to get something similar, the first thing to do would be identify the peak you want. In this example

[www.riskamp.com]

I mapped a cauchy distribution with a scale of 0.725 to a standard normal distribtion (0,1). You could use this as the basis for a distribution (meaning use the cauchy distribution as shown here, and then multiply the sample value by your desired mean).

One other thing to note is that the cauchy distribution does not support Latin Hypercube Sampling (LHS), although that's only because it has never been requested; let me know if you're interested in that and we can get it in an upcoming version.

Cheers,

Alex Edwards