Bartleby: Don - Betting Strategy

[Bartleby]

I have developed a stock trading system that has consistently beaten the market. I think I can improve the system if I had the answer to a math question. I posted it here because the math is very similar to Blackjack betting strategy.

I apply several formulas to about 100 stocks. The formulas work better for some stocks than for others. The trades in some companies have a good average return but high variance while trades in other companies have lower return and lower variance. Some days my system indicates that I should invest in several stocks but somehow I have to choose just the best bets. Should I choose the high-return, high-variance bets or the low return, low variance bets? I have calculated the standard deviation of all the trade for each of the different stocks. Here are the results for some of the stocks:

Stock_Trades_Gain__Deviation
__A___28___6.23%___7.46%
__B___17___5.29%___3.64%
__C___11___8.00%___5.01%
__D___17___4.79%___4.25%
__E___28___3.57%___5.26%
__F____3___5.52%___1.03%
__G___18___3.87%___4.07%
__H____5___6.32%___2.40%
__I___32___4.31%___9.97%
__J___17___4.51%___5.83%

The data show the number of trades made for each stock, the average gain, and the standard deviation. The gains are only a few percent, but the stocks are traded quite frequently so this can add up to a very good annual return.

One more factor that compounds the problem is that I have made a limited number of trades for each stock, and that number varies from stock to stock. I need to find a way to combine the numbers for average return, deviation, and number of trades to come up with a way to rank the different stock so that I know which is the better bet when my system indicates that I should invest in several stocks.

One more problem that may be related to this is how to apply the Kelly criterion to these bets. Any ideas?

[Don Schlesinger]

> I apply several formulas to about 100
> stocks. The formulas work better for some
> stocks than for others. The trades in some
> companies have a good average return but
> high variance while trades in other
> companies have lower return and lower
> variance. Some days my system indicates that
> I should invest in several stocks but
> somehow I have to choose just the best bets.
> Should I choose the high-return,
> high-variance bets or the low return, low
> variance bets? I have calculated the
> standard deviation of all the trade for each
> of the different stocks. Here are the
> results for some of the stocks:

> Stock_Trades_Gain__Deviation
> __A___28___6.23%___7.46%
> __B___17___5.29%___3.64%
> __C___11___8.00%___5.01%
> __D___17___4.79%___4.25%
> __E___28___3.57%___5.26%
> __F____3___5.52%___1.03%
> __G___18___3.87%___4.07%
> __H____5___6.32%___2.40%
> __I___32___4.31%___9.97%
> __J___17___4.51%___5.83%

> The data show the number of trades made for
> each stock, the average gain, and the
> standard deviation. The gains are only a few
> percent, but the stocks are traded quite
> frequently so this can add up to a very good
> annual return.

Annualize everything. Don't forget return is linear but SD is a square root function of time. Ranking might be done according to Sharpe ratio, which is the excess return over the riskless rate, divided by the standard deviation (again, all annualized). This is a standard way to compare desirability of investment alternatives.

> One more factor that compounds the problem
> is that I have made a limited number of
> trades for each stock, and that number
> varies from stock to stock. I need to find a
> way to combine the numbers for average
> return, deviation, and number of trades to
> come up with a way to rank the different
> stock so that I know which is the better bet
> when my system indicates that I should
> invest in several stocks.
Obviously, a form of weighting is required. It's a complicated procedure. All you can do is build a model portfolio, containing different proportions of the various trades, and see which weighting performs best.

> One more problem that may be related to
> this is how to apply the Kelly criterion to
> these bets. Any ideas?

Yes. See several books written by Ralph Vince, in which this very topic is discussed in great detail.

Don

[Bartleby]

> Annualize everything. Don't forget return
> is linear but SD is a square root function
> of time. Ranking might be done according to
> Sharpe ratio, which is the excess return
> over the riskless rate, divided by the
> standard deviation (again, all annualized).

Don, Thanks for responding. I don't think that annualizing will work because the average hold time is only about a week. The current riskless rate is close to zero so I think we can simplify the problem by ignoring it for now. Here is the result of ranking by dividing the average return by the standard deviation:

Stock_Trades__Gain__Deviation__Ratio
__F_____3___5.52%___1.03%___5.331
__H_____5___6.32%___2.40%___2.628
__C____11___8.00%___5.01%___1.598
__B____17___5.29%___3.64%___1.453
__D____17___4.79%___4.25%___1.127
__G____18___3.87%___4.07%___0.951
__A____28___6.23%___7.46%___0.835
__J____17___4.51%___5.83%___0.773
__E____28___3.57%___5.26%___0.679
__I_____32___4.31%___9.97%___0.432

The most obvious problem is that this puts the stocks with the fewest trades at the top of the list. Three to five favorable trades gives some sort of positive indication for those stocks, but it is not enough to know for sure. (Even 32 trades do not tell us for sure how well the formulas work for that particular stock, but it tells us more than 3 trades). Is there a way to combine the knowledge of the number of trades with the figures for gain and SD?

Also, I have a feeling that this puts too much emphasis on the deviation, (but I'm not sure).

> This is a standard way to compare
> desirability of investment alternatives.
> Obviously, a form of weighting is required.
> It's a complicated procedure. All you can do
> is build a model portfolio, containing
> different proportions of the various trades,
> and see which weighting performs best.

I think the only thing the model portfolios will tell us is the same thing we already determined by dividing the gain by the SD. I don't see how they will be able to factor in our level of certainty about a particular stock's gain and SD. This certainty can only increase by making more trades.

> Yes. See several books written by Ralph
> Vince, in which this very topic is discussed
> in great detail.

> Don

I will look into the Vince books. By the way, I would be glad to share this system with you once we get the math worked out. It is very easy to use (typically requiring just a few minutes per night).

[Don Schlesinger]

> Don, Thanks for responding. I don't think
> that annualizing will work because the
> average hold time is only about a week. The
> current riskless rate is close to zero so I
> think we can simplify the problem by
> ignoring it for now. Here is the result of
> ranking by dividing the average return by
> the standard deviation:

> Stock_Trades__Gain__Deviation__Ratio
> __F_____3___5.52%___1.03%___5.331
> __H_____5___6.32%___2.40%___2.628
> __C____11___8.00%___5.01%___1.598
> __B____17___5.29%___3.64%___1.453
> __D____17___4.79%___4.25%___1.127
> __G____18___3.87%___4.07%___0.951
> __A____28___6.23%___7.46%___0.835
> __J____17___4.51%___5.83%___0.773
> __E____28___3.57%___5.26%___0.679
> __I_____32___4.31%___9.97%___0.432

> The most obvious problem is that this puts
> the stocks with the fewest trades at the top
> of the list. Three to five favorable trades
> gives some sort of positive indication for
> those stocks, but it is not enough to know
> for sure. (Even 32 trades do not tell us for
> sure how well the formulas work for that
> particular stock, but it tells us more than
> 3 trades). Is there a way to combine the
> knowledge of the number of trades with the
> figures for gain and SD?

The absence of sufficient sample size is something you can't do anything about. As you work the system longer and do more trades for certain names, you can gather more data and have more confidence ion your results.

But, it does no good to blame the ranking system for the insufficiency of the data collected to date. No ranking will be valid, or reliable, when you have only a handful of trades in some instances.

I noticed you don't show any losses. Why would that be? Surely, you don't think every trade you make is going to be a winner, do you??

> Also, I have a feeling that this puts too
> much emphasis on the deviation, (but I'm not
> sure).

In the short term, SD dwarfs EV and is much more important. As you get into the longer run, EV begins to catch up.

> I will look into the Vince books. By the
> way, I would be glad to share this system
> with you once we get the math worked out. It
> is very easy to use (typically requiring
> just a few minutes per night).

Sooner or later, you're going to begin to be disappointed by the results!

Don

[Bartleby]

> The absence of sufficient sample size is
> something you can't do anything about. As
> you work the system longer and do more
> trades for certain names, you can gather
> more data and have more confidence in your
> results.

> But, it does no good to blame the ranking
> system for the insufficiency of the data
> collected to date. No ranking will be valid,
> or reliable, when you have only a handful of
> trades in some instances.

I agree with this but I keep thinking that there must be some mathematically valid way to factor in the number of trades. Insufficient trade data increases uncertainty in a way that is similar to having a high SD. It seems like there should be some way to add the two numbers together. Also, the knowledge gained from trades 25 to 30 is less than the knowledge gained from trades 5 to 10, so a valid solution should take that into account.

> I noticed you don't show any losses. Why
> would that be? Surely, you don't think every
> trade you make is going to be a winner, do
> you??

There are losses in the data above and there are losses that I have not posted. If the SD is 10% and the EV is 4% then some of the trades in that stock must be in negative territory. The set of stocks I posted are some of the best performers, (If I knew the correct ranking formula I would know if they were THE best), other stocks did not perform so well. I am currently only trading about 100 stocks that have shown the best performance. My average annual return on my bankroll since 1998 is about 40%. (It would have been much higher if not for a loss of 7% in 2001. The system is performing well again since then).

It is difficult to keep the bankroll fully invested because the system may go for many days without a recommended bet while on other days it may recommend 40 stocks. That is why a ranking system would be so useful. I also think that using the Kelly criterion would improve my return but I don?t know how to apply it to anything but Blackjack.

> In the short term, SD dwarfs EV and is much
> more important. As you get into the longer
> run, EV begins to catch up.

So do I stick with EV/SD or is there a better formula?

> Sooner or later, you're going to begin to
> be disappointed by the results!

> Don

This system is valid. I may not know the answer to my original question, but I can sure tell the difference between an Omega II and a Martingale! As a mentioned, I will be glad to share the system with you if you can help me perfect it.

[Don Schlesinger]

I think it would be best to not continue this discussion further here, for a couple of reasons:

1.This is a BJ site, and most people aren't here to discuss the stock market.

2. The SD you refer to isn't meant to be used as the denominator; the SD of the stock itself is. You're calculating the variability of the results of your trades, but without kjnowing the volatility of the stocks themselves, you have no idea whther the variability is due to the manner of trading or to the volatility of the stock itself.

3. In my 13 years at MS, I must have seen hundreds of "systems" such as yours, with people coming to the firm wanting us to bankroll them. We turned away 99% of them, simply because the systems made little sense and didn't seem worth our time or money.

4. If this approach really worked as wonderfully as you're suggesting, ranking the trades would be the very least of my worries!

Good luck!

Don

[Don Schlesinger]

>If the SD is 10% and the EV is 4% then some of the trades in that stock must be in negative territory.

No, not true at all. suppose you had many small gains of, say, 2%, 1%, etc., and then a few 4% ones, and then several very large double-digit gains. The EV could easily be +4%, with fluctuations around that mean of greater than 10%. And there would be no losses.

Don

[Bartleby]

> I think it would be best to not continue
> this discussion further here, for a couple
> of reasons:

> 1.This is a BJ site, and most people aren't
> here to discuss the stock market.

Agree.

> 2. The SD you refer to isn't meant to be
> used as the denominator; the SD of the stock
> itself is. You're calculating the
> variability of the results of your trades,
> but without kjnowing the volatility of the
> stocks themselves, you have no idea whther
> the variability is due to the manner of
> trading or to the volatility of the stock
> itself.

I don't think I need to distinguish between the two causes of variability. They both add to the total variability and if the total variability is high, the stock would rank lower.

> 3. In my 13 years at MS, I must have seen
> hundreds of "systems" such as
> yours, with people coming to the firm
> wanting us to bankroll them. We turned away
> 99% of them, simply because the systems made
> little sense and didn't seem worth our time
> or money.

I don't need a partner. I have my own bankroll.

> 4. If this approach really worked as
> wonderfully as you're suggesting, ranking
> the trades would be the very least of my
> worries!

You are right. This is pretty low on my list of concerns. But I do want to find the right answer. How can I get in touch with you?

> Good luck!

> Don

[Bartleby]

> >If the SD is 10% and the EV is 4% then
> some of the trades in that stock must be in
> negative territory.

> No, not true at all. suppose you had many
> small gains of, say, 2%, 1%, etc., and then
> a few 4% ones, and then several very large
> double-digit gains. The EV could easily be
> +4%, with fluctuations around that mean of
> greater than 10%. And there would be no
> losses.

You are correct. The actual results tend to be several small gains offset by a larger loss.

> Don