Sortino vs. Sharpe

Research
1

Some observations on Sharpe and Sortino ratios.

When the Sharpe ratios was originally suggested as a feature the idea of having Sortino also came up.

I at the time had an opinion that at least for the purposes of sorting/ranking different strategies (here sims and ports) the two indicators should not differ a lot.

My assumption was based on the thinking was - ok, Sortino is trying to “not penalize” a strategy where the volatility comes from upward moves, that’s good. But if the volatility comes from upward moves this should ultimately bring up the average return. That is already reflected in the numerator of the Sharpe ratio. So to me Sharpe should already give better rating to a system where an eventually higher volatility comes “more” from upwards moves.

Now after we have Sharpe and Sortino calculated over a good bunch of sims and ports I decided to prove my theory with some statistics.

If my assumption is right the Sortino vs. Sharpe dependency should be, if not purely linear, at least monotonic. Monotonic in math terms should mean if we have a set of pair values the ordering of the set by either value (in the pair) should be one and the same. If we graph the value pairs set we should see an only increasing (monotonically increasing) or only decreasing (monotonically decreasing) steps/slopes between the plotted pairs.

I decided to visually analyze the dependency by putting about 40 Sortino-Sharpe value pairs from randomly selected P123 sims, with a testing period greater than 1600 days on a scatter diagram. (See attached). To me Sharpe, Sortino or any other performance indicators (alpha, etc.) should be compared between strategies only of they are run over the same or close calendar period. General market behavior definitely has an impact on these.

Well the dependency is not perfectly monotonic as one can see. Slight difference in the ordering is seen in a number of cases.

What is interesting to me though the dependency is very close to a linear one. If we draw a linear approximation/regression line and get its parameters we can see that with a very small error (R2 = 0.98) we can calculate Sortino off Sharpe using the linear expression 1.68 x Sharpe + 0.19.

At least to me, it still makes sense to continue using the Shape ratio predominantly. In the general case a strategy with higher Sharpe will have a higher Sortino.

I guess it would be nice if one finds the time to study whether the cases where a strategy ranks higher with the Sortino ratio is really a better strategy by looking at the distribution of the drawdowns in the performance graph etc.

Vlad

SortinoVsSharpe.jpg
SortinoVsSharpe.jpg647×530 39.4 KB

2

Vlad,

That is a very good study. It shows that in general either indicator will give you the same info.
However, in the chart, there are 2 areas that show the advantage of the Sortino Ratio.

In the area of the chart where Sharpe is 1.3 to 1.5 and Sortino is 2.0 to 2.8 there a significant reversal in the data line. If you compare the Sharpe values for these 2 points the second one at 1.5 looks like a better Sim that the one at 1.4. But the Sortino value of the first point is 2.8, or 40% higher than the second point at 2.0. Obviously the Sim for the first point has a much better Reward/Risk ratio than the Sim for the second point.

Additionally, there is another significant reversal on the chart at a Sortino Ratio of 5.5 to 5.0 where the Sharpe Ratio would imply that the second point is better, and the Sortino Ratio implies otherwise. Most of the other points on the chart have a small enough deviation from the linear line to not make much difference between the two indicators.

What I want to know is what was the Sim that had the 7.0 Sortino Ratio at the top of the chart? This is an excellent Reward/ Risk ratio!

Denny :sunglasses:

3

Denny,

That is correct. There are cases where the Sortino orders the sims differently and if I have the time I will look at the particular sims and see whether I like the performance graph of the higher Sortino better.

The Sortino 7 one. Hmm, let me look. I can search by Sharpe > 3.5 … Hold on …
…it is “Simulation GWF Copy of Denny’s Small Cap 99/14 Author gfagerlin”

Sharpe 3.86 Sortino 6.98.

Did not look at the actual sim.

Thanks for you comments.

Vlad

4

When I run that sim with prices from “next open” the Sharpe goes down to 2.5 Sortino to 4.2 and the max drawdown to -33%.

I would like to be able to filter sims by what kind of trade prices were used. Maybe by saying "exclude sims with ‘previous close prices’ "

Vlad

5

Vlad,

That’s very interesting! That his Sim was developed from an original Sim I made public in July 2004, which can be viewed here: Denny’s Small Cap 99/14, http://www.portfolio123.com/port_summary.jsp?portid=56479

I re-ran my original Sim through today with the rebalance changed to next open, and it can be viewed here: Denny’s Small Cap 99/14 a1, http://www.portfolio123.com/port_summary.jsp?portid=95309

The differences between the 2 Sims is due to the many improvements that Marco and Co. have made to the P123 Tools since the original Sim was developed. Although the performance of the new Sim is significantly reduced from the original one, the new Sim should be a much more accurate predictor of future potential performance.

The 33% drawdown occurred in July 2002 at the same time that the S&P500 had a 40% drawdown. Since then its max drawdown has been 18% in May of this year. But the most interesting thing to me is that it is up right at a 100% gain for the last year since the Sim rules were originally developed! This Sim had a 7.5% loss over the last 2 weeks which is much better tham most of the market. A search of community Ports will find many successful Ports also following the same rules.

This should help some of the new members be more confident in the future performance of well developed Sims using the P123 Tools.

Denny :sunglasses:

6

I completely agree.

7

Vlad,

You said, "I would like to be able to filter sims by what kind of trade prices were used. Maybe by saying "exclude sims with ‘previous close prices’ ".

I second that. It would be very nice to able to filter the search results for only sims that use Next Open pricing. If you add this as a feature request, I’ll vote for it.

Brian

8

Vlad,

Both ratios are useful. One might suspect that the Sortino is a better measure because it does not penalize upward deviation. However, there are circumstances under which the Sharpe is a better measure of desirable performance.

Consider a trading system producing an equity curve that goes up steadily (monotonically) for a year (let�s say 4% each month), then flattens out for two years to give essentially very little gain or loss during that period, and then goes up steadily for a year (say 4% each month). In this example, the average gain is good during the four years, but no gain occurs during the middle two years.

The Sortino would be extremely high since it would see essentially no downward deviations. However, this would be hard system to live through for the two years of no gain. The Sharpe on the other hand would penalize the long flat period.

Ben

9

Very good illustration, Ben (eaves).

Ultimately before I decide to trust a system I will look at the performance page. (A picture is worth a hundred words and a thousand numbers). I like how P123 presents that page. I can see the equity curve and look for the long inconsistent periods you are talking about. Also the drawdown graph they have is amasing. If I find isolated large drawdowns I find such system very dnagerous. If I see a system where the drawdowns are sread around as small relatively even (by magnutude) spikes - I like it.

Where summarised single number indicators are very useful is exactly sorting out a bunch of results that are even worth looking at in detail. That is why it is so nice to have Sharpe and Sortino available as a filtering and sorting value.

Very good example of yours, again.

Vlad

10

Now that we have Sortino in the filtering options and also in the statistical view as a sortable column, I can clearly see a difference in sorting by Sharpe and Sortino.

Great stuff P123! Again.

Vlad