Correlation cont'd.
Ok, so far most of this is probably old news to most of you. I needed to post it as background for those just getting started.
The whole idea of combing models is to improve the consistency of the results. We've seen in a macro way how they can provide some benefit. Now, how do we know which models to combine? Also how much of model 1 should we trade with how much model 2 and how much of model 3? Also if I had a model 4 how could I tell if I should add it in as well?
Those are questions I wanted to answer when I started down this path. Hopefully it won't be too difficult to follow.
If you've taken a elementary stats class you'll know that std. deviation measures dispersion from the norm. Norm being defined as the median or average. You'll also note that the level of std. deviation measures the distance away from the median. We also know that if we can estimate the number of std. deviations away something is, we can look it up as a Z score in a normal distribution table to see how far away from the norm we are.
One of the nice tools in trading are the sharpe ratios which are designed to measure consistency. One of them is the modified sharpe ratio. It's defined as average return / std. deviation. For example, if the average return is $100 and the std. deviation is $50 then the sharpe ratio is 2.0. So in other words for me to breakeven or start to lose money I'd have to have a return that was 2 std. deviations worse than the average return. If you look up 2 std. deviations in a stats book under z score you'll note that it equates to 95.44%. So if my returns are normally distributed then I have a 95.44% chance of breaking even or making a profit.
The modified sharpe ratio can be thought of as a z score. The higher the number, the closer we are to achieving consistent profitability. In my case I want to be 99% sure of making a profit each month. So if I were to look it up in a normal distribution table I'd know the Z score I need is approx. 2.58 or a modified sharpe ratio of 2.58.
We also know that the returns are not going to be normally distributed. There will be fat tails so whatever sharpe ratio we come up with, it will be higher than we should expect in normal trading. This is where using the modified sharpe ratio and non-correlated methods pays off. I don't have a way to measure directly the benefit of using non-correlated methods but I know it improves the smoothness of the equity curve. If I combine that with a high modified sharpe ratio I can have a high degree of confidence that my models will be consistently profitable.
Ok, so far most of this is probably old news to most of you. I needed to post it as background for those just getting started.
The whole idea of combing models is to improve the consistency of the results. We've seen in a macro way how they can provide some benefit. Now, how do we know which models to combine? Also how much of model 1 should we trade with how much model 2 and how much of model 3? Also if I had a model 4 how could I tell if I should add it in as well?
Those are questions I wanted to answer when I started down this path. Hopefully it won't be too difficult to follow.
If you've taken a elementary stats class you'll know that std. deviation measures dispersion from the norm. Norm being defined as the median or average. You'll also note that the level of std. deviation measures the distance away from the median. We also know that if we can estimate the number of std. deviations away something is, we can look it up as a Z score in a normal distribution table to see how far away from the norm we are.
One of the nice tools in trading are the sharpe ratios which are designed to measure consistency. One of them is the modified sharpe ratio. It's defined as average return / std. deviation. For example, if the average return is $100 and the std. deviation is $50 then the sharpe ratio is 2.0. So in other words for me to breakeven or start to lose money I'd have to have a return that was 2 std. deviations worse than the average return. If you look up 2 std. deviations in a stats book under z score you'll note that it equates to 95.44%. So if my returns are normally distributed then I have a 95.44% chance of breaking even or making a profit.
The modified sharpe ratio can be thought of as a z score. The higher the number, the closer we are to achieving consistent profitability. In my case I want to be 99% sure of making a profit each month. So if I were to look it up in a normal distribution table I'd know the Z score I need is approx. 2.58 or a modified sharpe ratio of 2.58.
We also know that the returns are not going to be normally distributed. There will be fat tails so whatever sharpe ratio we come up with, it will be higher than we should expect in normal trading. This is where using the modified sharpe ratio and non-correlated methods pays off. I don't have a way to measure directly the benefit of using non-correlated methods but I know it improves the smoothness of the equity curve. If I combine that with a high modified sharpe ratio I can have a high degree of confidence that my models will be consistently profitable.
