Is the Futures Mag Article Wrong or Me?

I have a question that may seem quite the boring topic on the surface, but focuses on one of the most important aspects to trading that we all tinker with all the time – the exit.

I want to know if the results in an article by Michael Gutmann called “Calibrating Profit and Loss Strategies”, as included in the February issue of Futures Magazine, is correct or not? I don’t think so. Find the article here (without graphics):

http://www.allbusiness.com/banking-finance/financial-markets-investing-securities/11768158-1.html

For the purposes of this thread, only the first few sections up through ‘Two-Tiered Scale Strategy’ are relevant.

If you care to know more background on the topic, please read my next post. If you don’t, this is a good time to move on before getting sucked into a query on basic mathematics and probability calculations.

 

The Trade
As one thinks mathematically about how a trade can pan out, one approach is to think in terms of probabilities of success for each leg of a trade. For example, one common trading approach is to enter a trade with two contracts then manage it like the following (same theory can be applied to equities as well):
•Take a pre-determined stop loss if the trade moves against you
•Sell one contract if a pre-determined first target is hit, then move stop loss to breakeven
•Sell the other contract if a pre-determined second target is hit

Outcomes
So this trade can have only one of three outcomes:
1. Stop Loss with two contracts
2. First target is hit, second contract exited at breakeven
3. First and second targets hit

The Probabilities
Based on backtesting or actual results, probabilities of success can be applied to each outcome. For example, perhaps you know that 33% of your trades have outcome #1. That means that 67% of the time outcome #2 is achieved. So, what about outcome #3? Well, maybe outcome #3 only is achieved 30% of the time. But not 30% of all trades, the probability of 30% is only an outcome once the first target (outcome #2) is hit.

Question
So, what is the correct way to calculate an expected value of a potential trade? In my view, what we ideally want is a way to measure expectancy (a la Van Tharp).

Next post compares the two approaches . . .

 

In his article, Gutmann calculates “expected values” for a number of trade scenarios and exit strategies. Again, to keep it simple, we’re only talking about the trade scenario previously mentioned (two-tiered scale strategy).

Based on an initial stop loss risk of 8 ticks, a first profit target of 4 ticks and a second profit target of 8 ticks, Gutmann calculates an expected value to a traders P/L equal to 1.69. However, he never explains what this 1.69 number specifically represents. The reader is left to believe that for every trade put on there is an expected value equal to 1.69 ticks – ie, a trader would expect to make 169 ticks after 100 trades.

However, based on my calculations, a trader would actually lose money under the presented trades scenarios. I believe the real expected value is a negative .99. So basically 1 tick, on average, would be lost on each trade.

The Values
1st profit target win percentage = 67% = X1
2nd profit win percentage = 30% = X2
1st profit target = 4 ticks = PT1
2nd profit target = 8 ticks = PT2
Initial stop loss = 8 ticks = SL1

The Comparison (see the attached spreadsheet if you want the Excel viewpoint)

Gutmann’s expected value calculation:
Outcome #1 = (1-X1)(-2SL1)
Outcome #2 = (X1)(PT1)
Outcome #3 = (X1)(PT1) + (X1)(X2)(PT2)

Result = 1.69

My expected value calculation:
Outcome #1= same
Outcome #2 = (X1)(1-X2)(PT1)
Outcome #3 = (X1)(X2)(PT1 + PT2)

Result = -.99

So, which one is right?

I believe the flaw in Gutmann’s calc can be seen easiest in the calc for outcome #2 which is included in the calc for outcome #3 as well. That appears to be double-dipping. Actually, this same approach is used in the three-tiered scale strategy, so there’s triple-dipping going on which makes the three-tiered strategy seem so much better - but that's a separate discussion.

My method calculated the specific expected value for each specific outcome. So, in the example provided, a stop loss of 8 ticks would be taken 33% of the time. The first profit target for four ticks on one contract would occur 46.9% of the time. And 20.1% of the time, both the first and second profit targets would be achieved.

So, that's the question. I wonder if anybody read all the way to this point . . .

 

Spreadsheet mentioned above . . .

 

I think there is not such thing as "probability outcome". Probability is defines as the ratio of the favorable to the total number of outcomes.

 

based on the numbers you gave the simple answer is approx +1.67. My understanding from your given numbers is that your most optimal outcome is a gain of 12 points not 8.

so e(x)=0.33*-8+0.67*(0.3*12+0.7*4)

whats wrong with 1.67 (or 1.69) then?

 

JScott, thanks for the thread, Very interesting topic. According to your calculations both strategies are unprofitable. So what type of exit strategy do you recommend?

 

But once that first target is hit, a favorable outcome (reaching the second profit target) can be calculated as a ratio of all possible outcomes. In this case, there's only one other outcome that makes up the total number.

So, intradaybill, not sure if I'm reading your comment correctly . . .

 

Check me here, but I think your loss needs to include 2 contracts, so it should be a 33% of losing 2 x 8 ticks.

If you change that, I think you get -.99 as well.

 

true, my wrong ;-) getting late here, but you are absolutely right, -0.99, omitted the second contract in scenario 1.