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A Quiz about Money Management

From a purely mathematical standpoint it is true that trader A will always perform better.... provided that they always take the same amount of trades over the same amount of time.

In practice, trader A will most likely take much more trades than trader B. Your argument based on these parameters are biased to begin with. However within the confines of this discussion, I agree that trader A is superior.

In real life, it is not always true. In theory, a scalper will make the most money with the lowest risk. However it is not possible to scalp 24hours. Even 12 hours may be streching it a little. Imagine having to keep this up for the rest of your life just to perform better than trader B. That is why such a large majority of succesful traders are like trader B.

Again my argument here is that the word "better performance" is not well defined.
  • Post #22
  • Quote
  • Edited 6:31am Apr 20, 2010 6:17am | Edited 6:31am
Quoting Mr J
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.



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...
Mr. J -

Risk should be relative to anticipated return. Or would you tell me that if trader A would risk 10 bucks (as trader B does) for a 5 buck reward (RR of 1:0.5) still have financially the same risk? I hope you are not going to take that bet.

Ok, final note from me on the topic:

"...all else being equal..."

This is where the problem lies. You can know your risk, while you can only guess your reward. These results (as mentioned before) are based on hindsight and are at best hypothetical. To take them and extrapolate into the future is not realistic.

The information given is too basic. While some of the points made here are valid, they have not much to do with the reality of trading. Your risk profile may allow you to trade like trader A or B. Position sizing should be variable, depending on market volatility and trade model.

Then there are the market phenomena that are to be exploited by any trading model. Modern algorithms are mainly based on high win rates with low risk/reward ratios, executing 10 thousand round trips and more in a session.

Long term break-out models are based on the opposite - higher risk/reward ratios while often displaying low win rates. Both models can deliver great results over time while the profitability depends on the overall construction in context of all parameters.

Also, rolling standard deviations will show that when leverage is changed throughout a portfolio time series, the Sharpe ratio has its limitations since it measures the returns - not the risk itself.

Good trading to all.

H. Rearden
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Or would you tell me that if trader A would risk 10 bucks (as trader B does) for a 5 buck reward (RR of 1:0.5) still have financially the same risk? I hope you are not going to take that bet.
I didn't say that at all. All I said was that the financial risk of both bets were the same, while you were suggesting that they were different. Both in your example risk $10, that is fact.

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Risk should be relative to anticipated return.
You made no mention of return. You stated only the risk and reward, with no other information. Like I said previously, that information is not adequate.

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This is where the problem lies. You can know your risk, while you can only guess your reward. These results (as mentioned before) are based on hindsight and are at best hypothetical. To take them and extrapolate into the future is not realistic.
This isn't true. If we set a profit target, we know the reward. You are correct in that this is a theoretical exercise, but that is why we leave margin for error in the real world. This isn't a practical discussion anyway.

As for my comment "all else being equal", criticising it is overlooking the point. If we could choose between two trades with the same expectancy, we should choose the one with the higher winrate, unless there is some unusual factor to be considered.

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The information given is too basic. While some of the points made here are valid, they have not much to do with the reality of trading.
This is ironic, as I was criticising your example for being too basic. Understanding the underlying maths of trading has everything to do with the reality of trading. Read your example again please - you stated that two trades risked $10, and then suggested that one risked less than the other, with no additional information. Now you suggest considering relative risk, in which case the answer still doesn't change (they're still the same). And again the information is still inadequate.

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Your risk profile may allow you to trade like trader A or B. Position sizing should be variable, depending on market volatility and trade model.
If someone prefers Trader B, then they are mathematically illiterate. Trader A makes as much as Trader B, but with less variance and overall risk. Who would pick B?

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Both models can deliver great results over time while the profitability depends on the overall construction in context of all parameters.
We're comparing equivalent trades and strategies, so your examples of HFT and longer term models are not relevant. Of course they could have completely different characteristics, dependent on the situations and timeframes they are used.

In this thread we are comparing trades and strategies which are similar; they have the same expectancy, similar number of opportunities etc, but differ in terms of R:R and winrate. And when comparing two such strategies, unless there's an important issue that is being ignored (such as on strategy no being viable over the longterm), the one with the higher winrate is preferable.

I think you're overlooking or misunderstanding my argument.
Quoting Mr J
I didn't say that at all. All I said was that the financial risk of both bets were the same, while you were suggesting that they were different. Both in your example risk $10, that is fact.

You made no mention of return. You stated only the risk and reward, with no other information. Like I said previously, that information is not adequate.

This isn't true. If we set a profit target, we know the reward. You are correct in that this is a theoretical exercise, but that is why we leave margin for error in the real world. This isn't a practical...

Mr J,

First of all, I am not arguing with you. I am merely stating my thoughts on the topic.

Secondly, what is the point in talking about risk on its own without consideration of what you are going to take a risk for?

Thirdly, you cannot choose between trades with the same expectancy - expectancy by definition is something you don't know. So you only choosing between two scenarios for which you really don't know the outcome, while you know only what you are risking.

You also don't know whether you are going to win on your next trade or the next or the next and so on. Expectancy is a measure based on past data which is liable to change.

If I do decide to take a risk - whether $10 or $10000, I would always look for a deal that might pay out more than my initial risk - bearing in mind that I can be disappointed with the result.

Lastly, your assumption that I am mathematically 'illiterate' is plain rude - so I ask you politely to f*ck off.
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First of all, I am not arguing with you. I am merely stating my thoughts on the topic.
And I'm doing the same. This is an argument, as we're disagreeing and discussing points. It doesn't have to get fiery or uncivil to be an argument .

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what is the point in talking about risk on its own without consideration of what you are going to take a risk for?
I didn't do this.

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Thirdly, you cannot choose between trades with the same expectancy - expectancy by definition is something you don't know. So you only choosing between two scenarios for which you really don't know the outcome, while you know only what you are risking.
Margin for error. We don't know the true expectancy for either strategy, and it's likely constantly changing anyway, so we use an estimated range. We don't have to know precise values to make an informed decision. It's no different to what we do when we trade.

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You also don't know whether you are going to win on your next trade or the next or the next and so on. Expectancy is a measure based on past data which is liable to change.
Of course, and I wouldn't suggest otherwise. Not sure where you're going with this though.

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Lastly, your assumption that I am mathematically 'illiterate' is plain rude - so I ask you politely to f*ck off.
That wasn't addressed to anyone in particular. You seem to be taking this personally and looking to defend yourself, rather than argue the point, and much of what you have written does not seem relevant to my point.
  • Post #26
  • Quote
  • Edited 12:10pm Apr 20, 2010 11:59am | Edited 12:10pm
Why so many people like to separate the risk reward ratio and winning probability in performance evaluation? Experienced trader should know that both of them must be taken into consideration in performance analysis. RRR alone or Win% alone only hinted the characteristic of trading system.

I really have no idea if you prefer trader B. If you prefer trader B, please show a proper math why trader B is preferable by assuming all other variables are equal for both traders.
I thought this is the best thread I have read on FF this year. This knowledge is priority for any speculators.

Trader A has better risk-adjusted return and better sharpe ratio as mentioned.

Another alternative is to observe the optimal bet size for fixed fraction bets using calculus or Kelly's formula. Trader A has an optimal bet size of 50% and Trader B has an optimal bet size of 25%.

In other words, Trader A can generate superior excess returns above Trader B if he increases bet size to 50%. Trader B's maximum return is limited to 25% bet sizes due to higher variability of returns.
Quoting soyabean
I thought this is the best thread I have read on FF this year. This knowledge is priority for any speculators.

Trader A has better risk-adjusted return and better sharpe ratio as mentioned.

Another alternative is to observe the optimal bet size for fixed fraction bets using calculus or Kelly's formula. Trader A has an optimal bet size of 50% and Trader B has an optimal bet size of 25%.

In other words, Trader A can generate superior excess returns above Trader B if he increases bet size to 50%. Trader B's maximum return is limited to 25% bet...
But, then again, who would win when the black swan arrived?
Quoting thelws
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"
A performed better. Better Sharpe ratio is better.
Quoting jamjamjam
But, then again, who would win when the black swan arrived?
Any decent gambler knows not to bet Full Kelly .
Quoting jamjamjam
But, then again, who would win when the black swan arrived?
I do agree that trader with lower reward/risk is more vulnerable to black swan risk. However since both trader has different profit factor therefore it is not possible to evaluate the impact of black swan based on the limited info.

Btw we just wanted to know who has perform relatively well based on the historical trades, OP didnt ask who may perform better in the future so black swan risk should not put into considerations.
Quoting jamjamjam
But, then again, who would win when the black swan arrived?
Haha, then again, black swan only takes out 1 bet

And yes, if the bets are not independent, never full kelly
Quoting Mr J
Any decent gambler knows not to bet Full Kelly .
Optimal kelly's betting size is just for a guidance. Trading system with lower risk always has higher optimal kelly's betting size.
Quoting ForexQuant
Optimal kelly's betting size is just for a guidance. Trading system with lower risk always has higher optimal kelly's betting size.
I could not have made the joke I made if I was not already aware of this.
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?
A=B : A (45W , 15L) , B (30W , 30L)
B>A : A (45W , 15L) , B (40W , 20L)

*** A>B : A (3W , 1L, 56BE) , B (1W, 1L, 58BE) -----> depend on how you treat the break-even trade.

So, does it make sense if someone said A=B is right and B>A is wrong?
Trading is the game of fear and greed.
Quoting Fx chartist
A=B : A (45W , 15L) , B (30W , 30L)
B>A : A (45W , 15L) , B (40W , 20L)

*** A>B : A (3W , 1L, 56BE) , B (1W, 1L, 58BE) -----> depend on how you treat the break-even trade.

So, does it make sense if someone said A=B is right and B>A is wrong?
Perhaps, you are right that the question did not mention that breakeven is not used.

The question has also made no mention that partial profit taking did not used, no mention that trailing stop did not used, no mention that traders would not change to ride a long-term trend, no mention that executional errors are absent, etc.

However, in a normal quiz setting, the "face value" should be taken without bringing in complication, like what other respondents did, because exceptional cases could sometimes be unlimited.

Anyway, your initial simple answering of Trader B is definitely WRONG. Also, your response shows that you don't understand the maths behind the question:

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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.
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B>A : A (45W , 15L) , B (40W , 20L)
If it’s OK with kk007 I'd like to leverage up the debate (pan intended) with an additional – albeit a more qualitative question.
Let's assume that until now Trader A has only traded a single asset (F1) and that he is ready to leverage up. Let's further assume that his next best performance is achieved on asset F2 with Profit Factor of 2 and a Risk Reward of 1:1. Finally, F2 and F1 correlation is 80%.
How would you recommend he should leverage up:
1) Risk two units of capital in each F1 position (enjoying the benefits and risks associated with his F1 performance).
2) Trade another unit of capital with F2 (with the disadvantage of a lesser expected performance but with greater diversification).

Again, the figures here are stubs – feel free to replace them with any other roughly similar figures.

Any thoughts?
Quoting Pdat100
If it’s OK with kk007 I'd like to leverage up the debate (pan intended) with an additional – albeit a more qualitative question.
...
come'on guys.. surely someone has an opinion..
Quoting Pdat100
If it’s OK with kk007 I'd like to leverage up the debate (pan intended) with an additional – albeit a more qualitative question.
Let's assume that until now Trader A has only traded a single asset (F1) and that he is ready to leverage up. Let's further assume that his next best performance is achieved on asset F2 with Profit Factor of 2 and a Risk Reward of 1:1. Finally, F2 and F1 correlation is 80%.
[font=Calibri][size=3]How would you recommend he should leverage...
When one says F1 and F2 are correlated, do you mean the underlyings are correlated (cointegrated) or their trade results are heavily cross-correlated?
If it's the first, then that doesn't necessarily mean the trades are going to be really so correlated.

If trade results are anti-correlated then you can even add a zero or negative expectation trading system to a positive expectation trading system and get a better overall Sharpe. The problem of course is that in real life you are never sure about forward-time correlation!

Here's what I would do if I had the time, data, software systems & motivation: I would try to estimate the true correlation between trading results of systems F1 and F2 using large amounts of decent simulated data (bootstrapped or simulated with a GARCH model). These aren't used to establish expected return, but some level of "kinematic" correlation which is due simply to the trading rules in the system.

Then use that to compute a decent level of cross-asset allocation, and from that optimize some desired performance criterion,robust to a certain degree of mis-estimation on the correlation parameters.

And then in practice I would start out trading even less of system F2 than optimally indicated because simulations can't take into account real market costs & execution, and real-money results are more reliable than fake-money results.
Quoting Pdat100
come'on guys.. surely someone has an opinion..
Not sure whether i understand your question or not but personally I would trade the one with higher profit factor since both of them have high correlations. The diversification has little effect in this case.
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