[jasont]

I have been going through some extensive testing and noticed some talk around in regards to the Sharpe Ratio. I was hoping a few people could please enlighten me in regards to some info on it.

From what I found around the net was that it is calculated by dividing the average gains by the standard deviation. Some places offered different specifications to this as to whether or not to include the starting capital in this calculation or not. I also couldn't find a solid explanation on what is deemed a positive outcome Sharpe Ratio. Getting a touch confused at this point.

[firewalker]

Originally Posted by jasont »

I have been going through some extensive testing and noticed some talk around in regards to the Sharpe Ratio. I was hoping a few people could please enlighten me in regards to some info on it.

From what I found around the net was that it is calculated by dividing the average gains by the standard deviation. Some places offered different specifications to this as to whether or not to include the starting capital in this calculation or not. I also couldn't find a solid explanation on what is deemed a positive outcome Sharpe Ratio. Getting a touch confused at this point.

Afaik the starting capital is not included in the formula. You can find the correct formula on Wikipedia or Investopedia. In the formula you'll see there is a so called "risk-free" component which is used to compare your system to the most conservative investment (although "risk-free" these days is relative in itself!), but you know what I mean like a savings account or 10-year bonds.

The Sharpe ratio is used to offer a measurement to check whether taking more risk is worth the higher return. The higher the Sharpe ratio, the better you are being rewarded for taking risk on your assets/investments/trades. This does not mean the net result in the end is more profitable, it only says something about the "reward-to-variability".

Here are two examples. Suppose the risk-free result is 2%.

Trader A has a system which gives him a potential of 200% profit/year and the standard deviation of his trades is about 15% (he has pretty wild swings in his account). Sharpe => (200-2)/15 = 13,2.

Trader B has a system which gives him only 50% profit/year, but his stdev is only 1%. Sharpe => (50-2/) / 1 = 48.

So although Trader A is more profitable, the risk premium per unit of risk is higher for B.

[jasont]

Thanks FW. I was previously working on it according to average $'s made per week divided by the standard deviation of those $'s. I got some weird results so I suspect using the %'s rather than actual $'s would be the right way to go in the calculation.

[firewalker]

Originally Posted by jasont »

Thanks FW. I was previously working on it according to average $'s made per week divided by the standard deviation of those $'s. I got some weird results so I suspect using the %'s rather than actual $'s would be the right way to go in the calculation.

If you used absolute profits in terms of relative, the results should be the same, but since the "risk-free" return is a % you'll then need to transform that number into the net profit based on the starting capital.

Take again example of Trader A:

Trader A has a system which gives him a potential of 200% profit/year and the standard deviation of his trades is about 15% (he has pretty wild swings in his account). Sharpe => (200-2)/15 = 13,2.

Now using absolute values, (let's say starting capital = $10K).
Sharpe => ($20000 - $200)/$1500 = 13,2...

[jasont]

Hmm. Something doesn't quite sit right with me with this particular method. On a daily basis, using the average daily gain and standard deviation of those results you get a certain result. Then using a weekly average gain and standard deviation of those results you get a different result. Obviously that represents the difference in volatility between daily results to weekly results but to me it seems rather useless.

If one had a system that produced an average gain of 10% per month but the standard deviation was 15% then the ratio would look something like 0.66. Simply if one had small losses and large gains the standard deviation would be bigger thus the ratio would appear worse than a system which produced small losses and small gains yet produced poorer results.

Maybe I am way off on this one but I fail to see where the value of using it lies for judging a system.

[Frank]

in order to create a more 'research-intuitive' measure -- re-work the formula. This is done through focusing on the statistical significance of the measure as a key component.

In statistics, you can easily be 'fooled by randomness' unless you are careful. the Sharpe Ratio is a prime example of this.

Enter the 'Fundamental Law Of Active Management' (Grinold, Kahn) where the true 'Reward-Risk' measure should be thought of as the Information Ratio (IR) Where:

IR is apporximately equal to =
'Expected Return' x SqRt(# of independent bets a strategy has)

note the first part of equation factors in big wins and small losses into the 'expected return' for a single trade 'opportunity'.

the second part of the equation is the part that directly links the 'statistical significance' of the strategy. ie, just a few independent trades a year will not yield a big IR, unless the 'expected' return is huge.

The point here is that Sharpe Ratio can be 'garbage in, garbage out' -- you need to focus on the statistical significance of each strategy you design and measure that strategy properly -- by directly building that into the equation. A strategy that generates 4 trading opportunities a year is no good -- why? because that is not enough opportunities to drive the expectancy in a statistically significant way. you are very prone to being 'fooled' by the historical results unless you drive the number of 'observations' up to a big number. lots of little bets like what a casino does with its 'edge' is the only way that these numbers truly 'work' -- otherwise you are just fooling yourself with numbers.

[jasont]

Thanks for bringing my attention to that Frank. So I take it that the formula is 'Expected Return' (Average Gain Per Trade) X SqRt of the total number of trades. Do you mind me asking what the overall number should tell me exactly? My thoughts is that it is the average gain made over the set period of trades. Should the number be a certain size for any particular reason or is it used as a comparison to other strategies to find which one performs better over time?

[Frank]

Originally Posted by jasont »

or is it used as a comparison to other strategies to find which one performs better over time?

yes.

it is used to compare 2 different strategies --- and should be used as a framework on how to think about trading.