Sharpe Ratio

[jasont 10]

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 10]

  jasont said:

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 10]

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 10]

  jasont said:

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 10]

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 10]

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 10]

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 10]

  jasont said:

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.

[jasont 10]

Thanks Frank you have been a big help in explaining the usefulness and applicability of the method.

[sevensa 10]

  jasont said:

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.

 

This is one of the drawbacks of Sharpe Ratio in that it penalizes both up and downside volatility equally. Sortino Ratio attempts to address this issue.

[jasont 10]

Thanks Sevensa that makes a lot of sense and it is a major downfall of assessing a particular plan. I will look into the Sortino Ratio to see how it works.

[darthtrader3.0beta 10]

I think you have to keep in mind with the sharpe ratio is that alot of the customers of alternate investment vehicles that would use a sharpe ratio, don't want to see massive spikes in the equity curve either. I mean there is no free lunch, your not going to get a massive spike without getting really one off lucky or taking more risk.

Its like the mirror of a draw down. A draw down is not a huge deal if its your own money, its a much bigger deal if someone else is going to invest in you since then they want to know what the worse case scenario is if you step on a land mine the day after their money is in.

If you finish the year up 50% with your own money but took a 30% drawdown midway through the year, your still up 50%, who cares. If someone else is investing in you, it could mean they are down 25% while your up 50% because they got in at the wrong time.

Sharpe is interesting if your courting OPM, if its just your own money to me it seems to make more sense just to stick to profit factors since the equity curve your measuring with your own money is in reality always going to start at zero for the time period you measure. Your not going to "get in" at the wrong time if its your own money and own system.

[Frank 10]

Customers of alternative investments want to see a strategy that has a definable edge and is structured toward 'lots of small bets' rather than a few big bets.

 

If you have an edge AND have lots of small bets, the risk is controlled because the 'risk of a bad run of luck' will be minimized over many bets -- just as a top poker player will have low variance over 10,000 hands played, but might have a 30% (high) chance of losing significant money on the next 50 hands played.

[bugmenot22 10]

Here's a couple of spreadsheets that may help

 

Calculate Sharpe Ratio in Excel

 

Calculate Sortino Ratio in Excel