# Trading Performance Criteria, from Leo Jia

April 22, 2014 |

I have been thinking about what could be a good set of criteria to measure trading (strategy) performance for individual traders.

The criterion of average return divided by the variance of the returns seems to have its shortcomings. One reason is that some large positive returns can cause the variance to go up resulting in an indication by the criterion that the performance deteriorates. But some large positive returns are good to have.

Other criteria like Sharpe ratio seem more suitable for institutions.

I think using properties of the linear regression line of the cumulative return curve might be a better choice.

Two useful properties are the slope and the "width" of the linear regression line. By "width" I mean the deviation of the cumulative return curve around the linear regression line.

A good performance should have high slope on the one hand. And if we do not consider reinvesting profits, it should have narrow "width" around the linear line.

So then the value of slope/width seems meaningful.

If we take the linear regression line as a risk free benchmark, then this value may be very similar to the definition of Sharpe ratio, but practical for individuals.

Would anyone please comment on the pros and cons of this, or any other better ways to measure performance.

## Alexander Good writes:

Great post!

I think it makes sense to measure linearity of PNL and convexity separately so I agree with you that R sq is a good one to employ. I am curious how width differs from the strategy's std though…

One thing that you can do as a cheap proxy is median return * sqrt(252)/std return and then for skew then have a (rolling max peak to trough draw down)/(rolling max peak to trough draw up).

You can benchmark your strategy vs. bonds, the S&P and a traditional 60-40 mix or your other strategies. It's very hard to beat a vol weighted portfolio of stocks and bonds so it's a good benchmark in my humble opinion assuming you're trading your PA and you don't have large retirement holdings. I assign different weights to skew and median return depending on my portfolio construction.

In portfolio construction you'll often find things with strongly positive skew have good inverse correlation to market PNL series and are typically 'long vol' (idea ripped off AQR's value and momentum everywhere).

Trending strategies frequently have very positive skew (momentum) whereas mean reversion tend to have skew that looks like the S&P (value). So if I'm net long beta my marginal utility of doing trending models is higher whereas if I'm net short I tend to size up mean reversion strategies.

Would be curious to know what other people are using/ how other people think about this/ if they have good papers on the subject.

## Leo Jia writes:

Aren't they different?

std of returns has this term: (Ri - mu)^2, where mu is the same for all i's.

The width has this term instead: (CRi - Vi)^2 where Vi is the value on the linear regression line at time i and is all different across all i's.

## Alex Castaldo writes:

Personally I just like to look at the equity curve visually, and it is not difficult to store large numbers of graphic files in a folder and quickly "flip" through them by hitting a key on the computer.

But for automated evaluation Leo's two criteria (slope of regression, and "width around the regression" (which is also called the SEE or standard error of estimate.in regression textbooks) make sense to me.

However I know there are many other criteria that have been proposed. There is one with a foreign name that I think starts with "v" but that I can't remember. I am sure some people here know what I am talking about, it was much blogged about 2 or 3 years ago.

In looking for it I accidentally googled another measure of equity quality, the k-ratio , that believe it or not has 3 different versions.

Any other ways to measure equity curve "quality"?

## anonymous writes:

As with many things involving non linear information, my experience suggests that one must mix, blend or combine different 'quantities' to form a unique and proprietary time series.

For example, some form of 3D 'curve' that combined the three quantities return, AUM & volatility that gets thicker as AUM in the strategy grows and changes colour as volatility of returns increases perhaps…

## Ralph Vince writes:

percent of 6 month periods underwater
percent of 1 year periods underwater
percent of 2 year periods underwater

percent of time at equity highs
percent of time within 1% of equity highs
percent of time within 5% of equity highs
percent of time within 10% of equity highs
percent of time within 20% of equity highs

I have all of these programmed up in javascript which you can peruse at lspindexes.com and click the "compare" tab.

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