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I've had this conversation with a few people outside of this thread, and after studying this a while I have concluded diversification is better, exactly the opposite of what you conclude.

Here is my reasoning:

Trader C is Mr. Concentrator. He has a $100 account. He takes 2 uncorrelated trades per month. He wins 90% of the time. When he wins, he makes $2.5 on his account. When he loses 10% of the time, he loses $10.

In one year, on average he'll win 24*.9 = 21.6 trades at $2.5 each = $54.
In one year, on average he'll lose 24*.10=2.4 trades at $10 each = -$24.

Overall in one year, he'll earn $30.

$$$$$$$$$$$$$

Trader D is Mr. Diversified. He has a $100 account. He takes 10 uncorrelated trades per month. He wins 90% of the time. When he wins, he makes $0.5 on his account. When he loses 10% of the time, he loses $2. Note that his wins and losses are exactly 1/5 of Trader C's wins and losses. This is because he is making 5x as many trades. This is accomplished by sizing his positions.

In one year, on average he'll win 120*.9 = 108 trades at $.5 each = $54.
In one year, on average he'll lose 120*.1=12 trades at $2 each = -$24.

Overall in one year, he'll earn $30.

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OK, so overall, Trader C and Trader D, on average, will both earn the same return over time. Their performance looks equivalent, and it is as far as profits go.

The question is: would you rather be Trader C, or Trader D? Or does it even matter?

I encourage everyone to stop here, and think about the answer to that question. The answer is revealed in the next post.

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The question is: would you rather be Trader C (the concentrated trader), or Trader D (the diversified trader)? Or does it even matter?

Even though both traders, in my example, have the same average annual gain, it turns out it matters a lot, especially if you are concerned with drawdown and downside risk.

The answer has to do with standard deviation of the trade results. All other things being equal, if you want to minimize the downside, you always want to strive for the lowest standard deviation of trade results as possible. This leads to smaller drawdowns, as one tangible benefit. The drawback is that it gives up some upside potential.

If we look at Trader C's trades in one year (24 trades), his trade standard deviation is: 3.53

If we look at Trader D's trades in one year (120 trades), his trade standard deviation is: 0.75

That is a huge difference - almost a factor of 5. That is why it is better to be Trader D - lower standard deviation leads to smaller dispersion of trades, which shows up as smaller drawdowns.

Another way to show this is by running some Monte Carlo simulations, over 1 year's worth of trades. By showing final equity in a histogram, it is easy to see that Trader C has a more widely dispersed set of results than Trader D. Again, if everything else is the same, you want to have a tight distribution of final equity values (unless you are only trying to maximize gain).

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Note that on the far right of the chart above, Trader C has many more occurrences of big profit. So, if you were purely trying to maximize your odds of large final equity, without regards to downside risk, you'd want to be Trader C. That is the only benefit I can see in being Trader C.

If you want steadier results, diversification is the way to go.

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End Note:

Of course, this is all an exercise, and makes a lot of simplifying assumptions. For instance, it assumes that both traders have the same win rate. Maybe Trader C, since he only deals with 2 markets, will be able to achieve a higher win rate, since presumably he knows the markets better. That would change this analysis. And I assumed uncorrelated trades for both traders. If Trader C's 2 markets become tightly correlated for a short time, he could be in trouble. Think about the 2008 meltdown, where many things seemed to be correlated.

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The following 10 users say Thank You to kevinkdog for this post:

Good points kevin, but it assumes a few points I have some concerns with:

- All 10 trades in Diversification being equal only happens on paper theory. I am having trouble finding even 5 liquid enough FOP markets, let alone 10. Also at the same time, all 10 markets will not have the optimum IV/range. Selecting 2 or 3 of the best markets AT THAT TIME (IV moves around..eg. sometimes oil is high, sometimes wheat is), you can be flexible with concentration, you don't have to pick 3 markets out of the 10 and stick with them all year. You move around to where the best opportunities lie. Harder (impossible IMO) to do this with 10 positons.

- You left out compounding in your example. I am going to assume you & some (or most ?) people compound throughout the year, please correct me if I am wrong. If you assume every month is the same then yes the $100 example will turn out to be $30. If you factor compound in, it can be quite different (not so much over 1 year, but 3 years the difference is clear). 10 trades @ 90% win rate assumes a loss every month. This will slowly but "snowbally" bite into compounding and kill off some of its effects as opposed to Concentrated positons, where the chance of loss is just 20%, as opposed to a 100% loss rate. Yes you lose more when you lose but the extra buildup from longer preservation of profits allows compound to work its power.

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However I must note the advantage of diversifying for people with a history of undisciplined exits. Personally in a few years of selling options I've never had a loss gap through my stop so I do not really see this advantage, but in a period of absolute armageddon this will apply. If you "forget" or "refuse" to close out losing positions that are at your stop, it is less damaging for this to happen to 10% of your account than 33% or 50% of your account, assuming uncorrelated positions.

The following user says Thank You to k20a for this post:

The same conclusion holds for any number of markets greater than 2. I could have picked 3, 5, 10, 100 or whatever number of markets - the conclusion is the same. Being diversified leads to steadier returns.

Again, compounding doesn't change the conclusion. Here are the results for 5000 simulations, for 3 years of compounded trading, of Trader C and Trader D

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Annual Percent Return is roughly the same

Max DD is a lot less for Trader D

Risk Adjusted Performance (Return/DD, aka Calmar ratio) is a lot better for Trader D

Compounding doesn't change the conclusion.

So, does being more concentrated (Trader C) have a benefit? Yes, as mentioned earlier, the upside for Trader C is higher, as shown below. But the downside is also lower. And, the drawdown you have to endure to get the higher returns is much larger

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Yes I agree with you in theory. But in the real world in which we have to trade in - do you still make the same conclusion, after taking into effect having to deal with liquidity/optimal opportunity. I can only deal in about 3 commodities markets with my account size. Other markets I cannot get any fills.

Being diversified leads to steadier returns if all markets offer the same r:r & volume while all being uncorrelated. Which I believe is not the case in commodity futures.

Anyway we have reached the same conclusion for theory but I still hold my view for real world trading, all good. If can find 4 or more trades of the same high quality(low correlation, high liquidity, optimal iv/range), then diversify. Becomes harder as account grows.

I am getting a different value to you in compounding, I will check those values again.

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While the totals are higher, most of the growth is in exotic options including options that aren't traded on Globex. OI for options on CL, NG, RB, HO, C, S, GC, ES are lower compared to last year. CL is down by over 50% compared to 3 years ago.

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The ones higher YoY are EW, LH, LC, FC, & W.

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Well as promised, here are some of my recent trades I have done for SPY. With current volatility, they are best used for selling on expiration day. IB uses my timezone for timestamping trades, so all trades are -12hrs for new york time.

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Expiration trade just last Friday. Looking on the chart price basically went sideways after 2.30pm, so at 3.30pm I sold strangle for 7c which is $7 for 25 contracts, minus commissions netting $153 for a 30 minutes trade.

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Last week's trade..Price was already flat near the open and throughout the day but I still waited until 2.30pm to sell. With price already been flat all day, I went for both strangles and straddles. Went for 10 contracts of $38, and closing it when it about halved for $20, netting total $180. Sold more other puts and calls as the day went on for another $100 or so.

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This was from last month..I had more margin free so took 100 contracts of $4, netting $332 for the day. Price was flatlining all day..

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Have a look at the chart above and look at the strike price range sold. If you take away the horizontal time axis and vertical price axis and I told you it was a daily bar, would you do the trade ? Options decay on all timeframes - you can sell intraday, few days, weeklies, few weeks, few months..all the same to me.

I use the SPY to pick up extra premium on the leftover margin available. Cross margining also reduces the margin a lot which makes this viable. The margin is going to expire at the end of day, maxing out your account has no margining risk - for equities at least..margins are adjusted EOD, at least for IB.

Risk ? I will exit the trade when premium doubles so essentially this is a 1:1 trade with a very high win rate. You are not exposed to overnight/weekend risk. Friday, especially late afternoon trading session, tend to be very quiet. Who's going to schedule for news to be released just before the market closes ? Big instituitions pin option strikes of big caps which makes up the SPY etf putting extra pressure on price flatlining. Unexpected news do pop up, but there is no way for price to gap through your stop for something so liquid like SPY options.

Picking up a $100 or $200 extra per week is potentially $5k or $10k extra a year. I do this every single week I have time to trade the Friday close. There is also Tuesday expiration trade every week too so you can double dip if you are keen on being active.

If I total up all my expiration trades vs monthly/weekly trades my win rate is higher on expiry trades.

Forgive me if this should not be posted in the futures thread, but the exact same method can be used on futures too. But obviously once a month is not as fun and liquidity will probably be a problem.

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