Re: Optimal f code for Tradestation Part I

[Bob Fulks <bfulks@xxxxxxxxxxxx>]

At 1:34 PM -0400 6/9/00, CRLeBeau@xxxxxxx wrote:

>I agree.  Prudence dictates that we must always assume that our biggest loss
>(and biggest winner) are yet to be seen.  However, if we decide to trade at
>less than optimal f, then it is no longer the "optimal" bet size and maybe we
>should be using some other formula.


Economists have long used the concept of "utility curves" to show
investment preferences.

There is a simple chart I use to illustrate many of these concepts.
Two versions are attached. The first one, Chart1, is an expanded
version of the second, Chart2, for clarity. (This post is split into
two parts to avoid exceeding the size limit on one post.)

Using the S&P 500 index for the past five years, I postulated a
simple trading system:

At the end of each week you determine the value of your account, then
multiply it by a "leverage factor", then invest that amount in the
S&P 500 for the following week, borrowing the amount needed to do so.
Using a leverage factor of 1.0 is the same as Buy/Hold. Using a
leverage factor of less than 1.0 means investing only part of your
account in the market. Uninvested funds draw 5% interest and you pay
7% interest on the "margin loan". The question is "what would your
account have done over the past five years as a function of the
leverage factor". (This is clearly a "fixed fractional" system since
the "leverage factor" is assumed to be constant over time.)

The attached charts shows a plot of annualized return vs. annualized
standard deviation of returns with the various values of the leverage
factor shown as points on the curve.

Referring to the first chart, if you are a "little old lady" who
needs 8% per year to live on, then your utility curve might be as
curve A. All points on curve A are equally useful to her (constant
utility). (There is a family of such curves of different utility to
her.) The point where her utility curves intersects the investment
curve is the optimum operating point for her, realizing about 8% per
year by investing only a small portion in the market and keeping most
of her money in T-Bills (or CDs, etc.). In effect, it would take a
very big incremental return for her to assume more risk that she has
to to get her 8% return.

But if you were a 35 year old engineer saving for retirement, you
might have a utility curve such as in curve B. You would prefer
higher returns and could absorb deeper corrections associated with
using leverage because you are in the market for the "long term".

(Continued in part II)

Bob Fulks
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