A Better Sharpe Ratio

Research
1

The Sharpe Ratio is widely used. Whether you like the Sharpe Ratio or not there is a better ratio to use for our purposes–one based on the Sharpe Ratio.

Getting to the point the better ratio = Excess returns compared to Spy/Standard Deviation of the excess returns.

Note that I am only suggesting this for out-of-sample or since inception returns if used on SA.

This addresses 2 problems with the Sharpe ratio.

  1. The Sharpe Ratio makes its comparison to the “risk free rate.” Great but what we are interested in is the comparison to other equity investments.

  2. Sharpe Ratios cannot be compared easily for different time periods. The Sharpe Ratio for a port from 2007 to 2009 will be radically different than the Sharpe Ratio for the same port from 2013 to 2015. Using the excess returns adjusts for different market conditions.

A lot could be said about this–I would not know where to start. Almost all criticisms of this ratio would be correct. But really there is only one good question: is it better than the Sharpe Ratio?

Let’s call it the Gerstein Ratio (if Marc likes it) based on the fact that he regularly (correctly in my opinion) stresses the importance of excess returns. Otherwise call it the P123 ratio. Or jrinne ratio if no one else likes it.

Better still is the annualized Gerstein Ratio: Gerstein Ratio * (Number of year since inception)^1/2

Again a lot could be said about this. But there can be no question that the annualized Gerstein ratio is a better comparison than the Sharpe Ratio for our purposes.

There is no question in my mind that SA subs making a determination based on this ratio (again, out-of-sample) would do well in the long-term. And that would be good for all of us.

Note: The “Annualized Gerstein Ratio” gets close to the t-statistic of a paired t-test (paired against the returns for SPY in this case). I fully agree the statistic has problems. We could discuss this forever. With me agreeing about i.i.d., normal distributions, non-random samples etc. I would just add at the end that the Sharpe Ratio has every single one of the same limitations.

2

Jim - I have thought this way for a long time. However, one can’t blindly use SPY as there are lots of strategies on SA that have little to do with outperforming the S&P 500. I think the correct way to approach this is to use the model’s underlying benchmark, not SPY. This brings up two problems: (1) how do you determine the underlying benchmark; and (2) how do you group SA models for comparison purposes. I have provided suggestions before and I don’t want to repeat them here. Perhaps others could chirp in.

Steve

3

Steve,

I fully agree. I did not add this important point just for brevity. I considered a Gerstein Ratio against one standard for most (optional) and against any desired benchmark for others (again optional) or both benchmarks (optional).

4

Sharpe talks about this variant of Sharpe ratio in The Sharpe Ratio, William F. Sharpe, Stanford University

“More recent applications have utilized benchmark portfolios designed to have a set of “factor loadings” or an “investment style” similar to that of the fund being evaluated. In such cases the differential return represents the difference between the return on the fund and the return that would have been obtained from a “similar” passive alternative. The difference between the two returns may be termed an “active return” or “selection return”, depending on the underlying procedure utilized to select the benchmark.
…
The Sharpe Ratio of the selection return can then serve as a measure of the fund’s performance over and above that due to its investment style.”

Walter

5

You are describing the Information Ratio, which is widely used. I requested this feature last year:

https://www.portfolio123.com/mvnforum/viewthread_thread,8591#44825

6

Gerstein ratio. I like, I like!!!

@#&*^@

Oh well, another dream dashed on the jagged rocks of financial reality.

Yeah, we should add the Information Ratio.

As to a Gerstein ratio, it’s back to the drawing board. I might even have to settle for Pr2SalesQInd. :frowning:

7

https://www.portfolio123.com/feature_request.jsp?view=open&cat=2&featureReqID=986