RE: A question about system design.

[Bob Fulks <bfulks@xxxxxxxxxxxx>]

At 7:09 PM -0500 7/15/00, M. Simms wrote:

>MY Back-testing indicates it is a "streaky" methodology with HIGH,
>HIGH variances of returns.


At 9:49 AM +0200 7/16/00, Bengtsson, Mats wrote:

>Do you have a recommendation for how to measure variance of return
>and what to expect of a good system?


Mathematically:

   Variance = Standard_Deviation * Standard_Deviation

(But he may be using the term generically to mean "variability".)

I use the Sharpe Ratio as a measure of a "good system" and it is
also related to the standard deviation.

   Sharpe_Ratio = Excess_Return / Standard_Deviation_of_Returns

where all terms are annualized. A good system has a Sharpe Ratio
of over about 3.

For example, if:

   Monthly return = 4%
   Standard Deviation of monthly returns = 4.1%
   Risk_free annual return rate = 5% (usually the T-Bill rate)

then:

   Annualized return = 12 * 4% = 48% (assuming no compounding)
   Annualized standard deviation = SQRT(12) * 4.1%  = 14.2%

   Sharpe_Ratio = (48% - 5%) / 14.2% = 3.0

Notice that the Sharpe Ratio increases when either the return
rate increases or the standard deviation of returns decreases.

Bob Fulks