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Hello Bob
Thanks for your reply - I hadn't noticed it immediately as I have a specific
folder which catches all your submissions!
>From what you have suggested a % return on risk per trade (normalised by a
variable account size) will probably work - Thanks alot
Regards
Michael Stewart
> At 1:31 PM +0000 12/5/01, Michael Stewart wrote:
>
> >If your futures system trades a variable number of contracts how can you
> >fairly estimate the rate of return - would/could it be a) P&L / Total
> >account size for the period or b) the sum of P&L's for each trade /
account
> >size for each trade or c) P&L / Average account size for the period
> >
> >Whilst on the subject of 'return' - are there any seasoned traders who
maybe
> >happy to share their own performance objectives/results - return for an
> >'average' month for example as a return on initial margin (as return on
> >account size can be so misleading).
>
> A periodic return is usually the account value at the end of the
> period, less the account value at the beginning of the period,
> divided by the investment required to achieve the return. If you are
> increasing your trade size as your account increases, then your ideal
> account size would grow exponentially and you would calculate the
> returns on the logarithm of the account value. If you are NOT
> increasing your trade size as your account increases, then your ideal
> account size would grow linearly and you would calculate the returns
> on the account values directly.
>
> At 1:56 PM +0000 12/5/01, Michael Stewart wrote:
>
> >And if you traded twice - say one trade of 10 lots and another trade of 5
> >lots within the same day?
> >
> >To work out the return you need to ascribe a value to the margin required
> >for each lot - so if you look at the return based on the max account size
> >your understating the return whereas if you take the min your
overstating?
>
> This is a very complicated question. Presumably, there is some reason
> you changed the size. Perhaps the risk per contract was 2X higher in
> the second case and you wanted the total risk of both trades to be
> the same. In this case you could use the gain in the day divided by
> the risk level to normalize the calculation to "percent return on
> risk".
>
> Some people use the account size to normalize the calculation to
> "percent return on account".
>
> But you are illustrating the problem of using return alone as the
> measure. "Return" is a useless number without also considering the
> risk. You can double the return by trading twice as many contracts.
> You need to use a "risk-adjusted" return, such as the Sharpe Ratio to
> properly evaluate any system.
>
> How often do you see someone buy into this year's high-return mutual
> fund only to see it tank the following year?
>
> Periodic (logarithmic) returns have a probability distribution that
> is approximately "normal" (Gaussian), as predicted by the Central
> Limit Theorem. Looking at the return for any period gives you no
> relevant information on what the return for a future period is likely
> to be. But the standard deviation of the periodic returns can give
> you a decent idea of future returns. About two thirds of the returns
> will be within one standard deviation of the mean (average of all
> periods) and about 95% will be within two standard deviations of the
> mean. (The tails of the distribution tend to be fatter than "normal"
> so this latter value is less accurate.)
>
> For example, if you measure a return of 30% for this year, is that
> unusual? If you measure the average return for many years as 20% with
> a standard deviation of 10%, then a 30% return is equal one standard
> deviation away from the mean (20% + 10% = 30%). Since about two
> thirds of the occurrences are expected to be within one standard
> deviation, this means that about one-sixth of the occurrences will be
> in each tail of the distribution. So we can expect the returns to
> exceed 30% in only one out of every six years. Similarly, we would
> expect returns to be less than 10% in one out of every six years
> (= 20% - 10%).
>
> The Sharpe Ratio in this example is
>
> Annualized_average_return / annualized_standard_deviation_of returns
> = 20% / 10% = 2.0 (assuming you are futures)
>
> Now if you double the number of contracts traded, your return would
> be 60% in that year, your average return for many years would be 40%
> with a standard deviation of 20%. The 60% return for this year is
> still one standard deviation away from the mean so you would still
> expect to see the 60% return only one year out of every six.
>
> The Sharpe Ratio is still 40% / 20% = 2.0 and we see it is
> independent of the number of contracts you traded.
>
> Back to your original question, note that you can calculate the
> dollar returns in a period and the dollar standard deviation of
> returns without even converting to a percentage and their ratio (the
> Sharpe Ratio) remains the same. So as long as you use the same
> convention for normalizing the dollar values to percentages, the
> Sharpe Ratio is independent of what you used. (Prof. Sharpe calls
> this some "notional value").
>
> Also, since the Sharpe Ratio calculation uses typically 30 to 200
> different periodic samples of the equity curve for the calculation,
> it almost impossible to "curve-fit" a good Sharpe Ratio. We all know
> it is easy to get fooled by curve-fitting a single value of return,
> net-profit, or other single numbers.
>
> Bob Fulks
>
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