# Interest

The simple formula was used for a long time and many people complained about it. And they were right: Most systems are compounding and then, contrary to what you claim, the simple formula doesn’t make sense. Anyway, if you want to use it you can still find it in the advanced statistics.

The simple formula was used for a long time and many people complained about it. And they were right: Most systems are compounding and then, contrary to what you claim, the simple formula doesn’t make sense. Anyway, if you want to use it you can still find it in the advanced statistics.

Do you mean interest as in the risk free rate (T-bills), or returns on your trading equity?

Suppose you start with \$100K and after a while your system has \$150K. Most systems will use the full \$150K for their trading. So if they traded with 4 units when they had \$100K, they will trade 6 units when they have \$150K. So they are compounding, i.e. reinvesting their profits.

Now suppose that you have a system that has 10% profit every month. If the system does not compound, then its profit after one year will be 120%. But if it compounds then the account value will be multiplied by 1.10 every month. After twelve months the account value \$314K, which is 214% profit. This is what is computed with the compounding formula.

Suppose that your profit is not exactly 10% every month, but that it is varies from month to month. So your account value is multiplied by some factor r(i) every month i, but r(i) is not always 1.10. If the geometric mean of the r(i) is 1.10, then you will still end with 214% profit after one year. So it does not matter that the profits are variable. As long as you re-invest, the only things that counts is the geometric mean of the return rates r(i). The compounded annual return is a function of it.

The monthly statistics assume that the profits are re-invested every month, and the daily statistics assume that they are re-invested every day.

You suggest that this is a way to leverage interest, but it isn’t that simple. For a profitable system that is older than 1 year, the compounded annual return will be smaller than the other version. Indeed, the simple annualized returns that were previously reported were quite misleading for old systems, and some people complained about that. For a young profitable system the compounded version is larger, but that doesn’t mean that it is wrong. I would rather say that the uncompounded version yields an under-estimate in that case (assumed that the system is compounding).

A completely different point is that for very young systems the estimate can be excessively large. However, this is true for both versions. The problem is that all statistics are very unreliable for young systems. That’s why I suggest to consider the confidence intervals (see the guide for the advanced statistics). You can see a CAR of 1300% for a 3 week old system, but then the lowerbound of the confidence interval of the Sharpe ratio (based on the log return rates) will usually still be negative, which implies that the lowerbound of the CAR must be negative too. Well, common sense will hopefully also tell you that you shouldn’t believe that 1300%.

1. T-bonds have nothing to do with it. The CAR for your system should be 116% if I use the values of today and the number of calendar days of your system (1.48^(365/186) - 1). I’m not sure where the 160% from the basic statistics table comes from, but I can explain the corresponding outcomes in the advanced statistics table (139.2% for the daily values and 162.3% for the monthly values). These are not based on the number of calendar days but on the number of days for which an account value is passed, which excludes holidays. The 139.2% is based on the account value of yesterday (147,771) together with the number of days for which an account value was passed (154) and the expectation of that number during a year (344). This is a temporary fix to the problem discussed in the thread "annualized rate of return calculation?, particularly my post of 4/11/07 (18:43) and the responses thereafter. It is scheduled for a revision this summer. The monthly value is larger because it is based on a previous, larger account value. The last partial month of daily account values is not used in the computation of the monthly statistics.

2) See my explanation in the previous post.

3) Your suggestion %profit made until today / # days is equal to the simple (uncompounded, arithmetically extrapolated) annualized return divided by the number of days in a year. So if you don’t trust the last one then you can’t trust the first one either. I explained why the compounded measure is used instead.