Risk (pain) vs Reward (gain)

But for most people it is: pain but no gain.

 

lol. That's how the market works, it's not Robin Hood.

 

Yes...Wisdom comes from experience and insights

With wisdom comes priorities:
1. First priority to control losses
2. Second priority to improve profits

 

After a ton of testing of various return distributions, I believe I came up with something sensible. The balance between the risks and the gains is found in what I call optimal leverage, which can be calculated as follows:

Let R be the distribution of trade returns:
R: {r(1), r(2), r(3), ..., r(N)}
where
N is the number of trades,
r(i) is the ith trade return

Trade return as defined as
r = (S / B) - 1
where
S is the sell price,
B is the buy price.

Then optimal leverage OL is found from the following maximization:

OL = argmax{sum[-exp(-L*L*r(i))]}
where
exp() is the exponential function,
L is the parameter found by maximization,
sum[] is over all trade returns r(1), r(2), ..., r(N).

The argmax notation is used to indicate that we want to find which L maximizes this sum:
sum[-exp(-L*L*r(i))]

I know, this requires more explanation. I think I'll write it up in detail and will publish it somewhere.

In the meanwhile, here is a simple example. Suppose the returns of a trading system S can be described as "For every trade, there is a 50% chance of a 2% gain, and a 50% chance of a 1% loss". So, we have
R = {0.02, -0.01, 0.02, -0.01, ...},
or equivalently, simply
R = {0.02, -0.01}

Then optimal leverage OL is:
OL = argmax{sum[-exp(-L*L*r(i))]} = argmax{-exp(-L*L*0.02) - exp(-L*L*(-0.01))}

Numerically solving this maximization problem for L (you can use Excel solver for this) gives us:
OL = L = 4.8

That is, the optimal leverage OL for system S is 4.8 to 1. For example, if used with the ES contract, we want to use about $21,875 for every traded ES contract:
Capital per contract = (contract value) * (contract multiplier) / OL = (2100 * 50) / 4.8 = $21,875.

That is, if your account size is $218,750, and you are trading system S, then the optimal trade size for the next trade is 10 ES contracts.

Hope this is clear. If not, I can explain further. In the meanwhile, I'd be interested to see if you folks can use this for your own trade distribution to see if the calculated optimal leverage makes sense.