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A Quiz about Money Management

  • #1
  • First Post: Apr 16, 2010 10:27am Apr 16, 2010 10:27am
There are two traders, both of them risked 1 unit of captial for each of their trade. Both of them have taken 60 trades. After all of their trades closed:

Trader A has a Profit Factor of 3 and average Risk:Reward per trade = 1:1

Trader B has a Profit Factor of 2 and average Risk:Reward per trade = 1:2

Which trader has earned more?

The answer will be announced a few days later.
  • #2
  • Edited 11:14am Apr 16, 2010 10:55am | Edited 11:14am
Quoting kk007
There are two traders, both of them risked 1 unit of captial for each of their trade. Both of them have taken 60 trades. After all of their trades closed:

Trader A has a Profit Factor of 3 and average Risk:Reward per trade = 1:1

Trader B has a Profit Factor of 2 and average Risk:Reward per trade = 1:2

Which trader has earned more?

The answer will be announced a few days later.
Trader A has earned more.

H. Rearden
  • #3
  • Apr 16, 2010 11:00am Apr 16, 2010 11:00am
Both of them have same profit.
  • #4
  • Apr 16, 2010 11:04am Apr 16, 2010 11:04am
It's trader B, does it make it you happy? It's Friday but no more nonsense poll please...........
Trading is the game of fear and greed.
  • #5
  • Apr 16, 2010 11:10am Apr 16, 2010 11:10am
Quoting ForexQuant
Both of them have a same same profit.
Yes you are correct:

60 trades with the same risk per unit.

Trader A:

Risk/Reward 1:1 ($50/$50)

15 losing trades x $50 = ($750)
45 winning trades x $50 = $2250

2250/750 = 3 (profit factor)

$2250 - ($750) = $1500

Trader B:

Risk/Reward 1:2 ($50/$100)

30 losing trades x $50 = ($1500)
30 winning trades x $100 = $3000

3000/1500 = 2 (profit factor)

$3000 - ($1500) = $1500

H. Rearden
  • #6
  • Apr 16, 2010 2:29pm Apr 16, 2010 2:29pm
I belive if we are willing to risk $1 then we expect a minimum of $2 profit.


  • #7
  • Apr 19, 2010 10:35am Apr 19, 2010 10:35am
Yes. Both traders have the same amount of profit.

Give you another question to take away, and this one is slightly harder than the initial one.

Quote
Now, both traders have the same amount of profit. Does this mean that the two traders perform equally well? Why?

If you can answer this, you grasp a main aspect of money management.
  • #8
  • Apr 19, 2010 10:36am Apr 19, 2010 10:36am
Are you ok? Buddy. This is not a poll. And your answer is WRONG!

Quoting Fx chartist
It's trader B, does it make it you happy? It's Friday but no more nonsense poll please...........
  • #9
  • Apr 19, 2010 10:48am Apr 19, 2010 10:48am
Quoting kk007
Yes. Both traders have the same amount of profit.

Give you another question to take away, and this one is slightly harder than the initial one.



If you can answer this, you grasp a main aspect of money management.

I would say that the trader with 1:2 RR is in a better statistical position since he only has to have winning trades just over 30% of the time to make money while the trader with a RR of 1:1 has to win more than 50% of the time to be profitable.

H. Rearden
  • #10
  • Apr 19, 2010 12:45pm Apr 19, 2010 12:45pm
Quoting H. Rearden
I would say that the trader with 1:2 RR is in a better statistical position since he only has to have winning trades just over 30% of the time to make money while the trader with a RR of 1:1 has to win more than 50% of the time to be profitable.

H. Rearden
Trader A has smaller risk (Lower drawdown) than trader B although they made same amount of money.
  • #11
  • Apr 19, 2010 1:02pm Apr 19, 2010 1:02pm
Quoting ForexQuant
Trader A has smaller risk (Lower drawdown) than trader B although they made some amount of money.
The overall DD situation is correct....but

...how can he have a smaller risk? If I risk 10 bucks to make 10 bucks, my risk is bigger than if I risk 10 bucks to make 20.

Also, the question asks about whether the traders perform equally well based on the profits.

That leads to a definition problem: do you rate performance based on winning percentage (or win/loss ratio, which favours trader A) or do you rate performance based on risk/reward, which favours trader B?

So, its a trade-off. More trades with a lower reward or less trades with a higher reward leading to the same result.

Depends on the traders personality I would say. Most people who can't stand losing prefer trader A's way, while traders who can accept that losing is part of the game might opt for trader B's way - knowing that they can be wrong more often than not and still make money.

H. Rearden
  • #12
  • Apr 19, 2010 1:07pm Apr 19, 2010 1:07pm
Quoting H. Rearden
The overall DD situation is correct....but

...how can he have a smaller risk?...
Based on the limited data on this scenario, I think the risk adjusted return is a better way to evaluate their performance. I never used winning rate alone to judge a system because it only tells part of the story.
  • #13
  • Apr 19, 2010 2:52pm Apr 19, 2010 2:52pm
Quoting ForexQuant
Based on the limited data on this scenario, I think the risk adjusted return is a better way to evaluate their performance. I never used winning rate alone to judge a system because it only tells part of the story.
True.
  • #14
  • Apr 19, 2010 11:58pm Apr 19, 2010 11:58pm
Quoting kk007
Are you ok? Buddy. This is not a poll. And your answer is WRONG!
Thanks, I'm fine mate.

Regarding about my answer, If I'm wrong, so you're. You know, a quick calculation would give the answer to trader B make more ( 40 W and 20 L) or at least equal money (30W and 30 L) to trader A, so I chose trader B. However, it's not quite right as I didn't take into account all the possible scenario/case. So, this question have multiple answer that A, B or A=B all are right.

As the subject's writer, I think you should have a better answer than us..........
Trading is the game of fear and greed.
  • #15
  • Edited 1:31am Apr 20, 2010 1:20am | Edited 1:31am
Quoting Fx chartist
Thanks, I'm fine mate.

Regarding about my answer, If I'm wrong, so you're. You know, a quick calculation would give the answer to trader B make more ( 40 W and 20 L) or at least equal money (30W and 30 L) to trader A, so I chose trader B. However, it's not quite right as I didn't take into account all the possible scenario/case. So, this question have multiple answer that A, B or A=B all are right.

As the subject's writer, I think you should have a better answer than us..........
I have no idea why you said that you got multiple answer to this scenario. Do you have any calculations to support your statement?
  • #16
  • Apr 20, 2010 1:45am Apr 20, 2010 1:45am
Quoting ForexQuant
I have no idea why you said that you got multiple answer to this scenario. Do you have any calculations to support your statement?
I think he doesn't know what he is talking about.

About OP's question:
Both of them did equally well. Assuming:
1)Both continue to trade the same amount of time over a long period of time
2)They both trade the same amount of trades during that period
3)Their strategy produces the same results as in scenario 1.

It is not clear enough to say that one is performing better than the other. Though, the part about dd does make sense.
  • #17
  • Apr 20, 2010 3:18am Apr 20, 2010 3:18am
Reward:

Trader A:

Wins +1 with p=0.75, Loses -1 with p=0.25. Expectation per trade=0.75*1 + 0.25 *-1 = 0.5.

Trader B

Wins +2 with p=0.5 loses -1 with p=0.5. Expectation per trade=0.5*2 + 0.5*-1 = 0.5.

Same expectation, hence same expected profit after N trades as seen before.

Risk:

Trader A: variance 0.75*(1-0.5)^2 + 0.25*(-1-0.5)^2 = 0.75
0.75*(0.5)^2 + 0.25*(1.5)^2 = 0.75

Trader B: variance 0.5*(2-0.5)^2 + 0.5*(-1-0.5)^2 =
0.5*(1.5)^2 + 0.5*(1.5)^2 = 1.5^2 = 2.25

So unless I made some dumb mistake, it appears that Trader A has a better Sharpe ratio, as I'd expect from the higher profit factor.
In any professional setting, Trader A beats Trader B.

For equally sized acceptable portfolio fluctuations Trader A can apply more leverage resulting in higher monetary profit.

I originally wrote: "In what way is this quiz about money management instead of performance attribution?"

I think I now have an answer. In practice, if Trader B is getting returns of +2 and -1, and trader A is getting returns of +1 and -1, then Trader B is using a higher effective bet size. So if one considers the phrase "money management" to be proper position sizing (I've never really understood the words personally) then this could make sense.
  • #18
  • Apr 20, 2010 3:52am Apr 20, 2010 3:52am
Quoting mbkennel
Reward:

Trader A:

Wins +1 with p=0.75, Loses -1 with p=0.25....
Great post. However it does not answer the question of who is performing better. Your post merely explains who has better position sizing. It doesn't mean that A performed better than B or vice versa. The question itself does not provide a clear enough definition of the word "performance"
  • #19
  • Apr 20, 2010 3:58am Apr 20, 2010 3:58am
Quoting H. Rearden
Depends on the traders personality I would say. Most people who can't stand losing prefer trader A's way, while traders who can accept that losing is part of the game might opt for trader B's way - knowing that they can be wrong more often than not and still make money.
Both of these are personality flaws for a trader. Yes, some famous traders hate to lose, but it doesn't make it a virtue. The quality we really want is not to hate losses, but to hate bad trades. The need to know we can be wrong more often that we win shows a lack of understanding or acceptance of the relationship between winrate and R:R.

Quoting H.Rearden
The overall DD situation is correct....but

...how can he have a smaller risk? If I risk 10 bucks to make 10 bucks, my risk is bigger than if I risk 10 bucks to make 20.
No it's not. In your example, you have risked 10 bucks in both trades, so financially, both trades have the same risk. However, comparing the risk of two trades isn't really that simple, for reasons I'll go into below.

Quote
Now, both traders have the same amount of profit. Does this mean that the two traders perform equally well? Why?
No. Trader A trades with lower risk. They may make the same amount per trade, but Trader A is more likely to survive over any particular sample. Why is the risk of Trade A lower? Because the higher our winrate the better (all else being roughly equal). Variance will be lesser and therefore we're less likely to experience large drawdowns or bust completely*.

This brings us back to the first question. While profit was equal over that 60 trade sample, Trader A is likely to be more profitable over the longterm as he has better survivability.

*This is why I said traders "knowing they can be wrong more often than not and still make money" is a silly mentality.
  • #20
  • Apr 20, 2010 4:24am Apr 20, 2010 4:24am
Quoting Mr J
No. Trader A trades with lower risk. They may make the same amount per trade, but Trader A is more likely to survive over any particular sample. Why is the risk of Trade A lower? Because the higher our winrate the better (all else being roughly equal).
Exactly but it eludes the most people and even some of the established gurus. It is counterintuitive and against the gospel which is preached on this forum. As the most are losers they tend to feel good any time they hear that even if they lose often they still can make money.
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