A word about when to take profits and when to take losses??

This has to be the most confusing topic in options trading, yet math gives a very clear answer that is often overlooked.? I will attempt to clarify it here.

One cannot give a precise answer to the question ?At what percent of my max profit should I close my winning trades?, without also answering ?at what percent of my max profit do I take my losers off??? The two are intertwined.? It is the ratio of the two answers that will give you a clue as to the potential profitability of the mechanical strategy you design.??

First, a little history.? In 1950, as a result of statisticians? work on how to manage signal noise issues in long distance phone calls, a formula called the ?Kelly Criterion? was born.? Quickly, they realized there were applications of the formula for gambling and it gained in popularity.? Its application for trading is one of ?position sizing.?? It helps answer the question ?How much of my account should I risk on a given trade.?

Rather than go through the more complex math, traders have ?simplified the formula? to a good approximation of the more complicated original method.? It boils down to ?Edge divided by odds? and is mathematically represented by:

Kelly % = W ? ((1 ? W) / R);


?W = percentage of winning trades

R = avg. gain of winners / avg. loss of losers

Using this formula, let?s solve for the average win/loss ratio that provides us a breakeven scenario.? From there, we can get a feel for what makes sense.? Our first order of business is to define a probability of profit for our portfolio.??

Let?s say our portfolio normally consists of 85% defined risk trades at around 65% probability of profit.? That is we sell credit spreads or Iron Condors for around 35 cents per dollar spread.? And, let?s say 15% are undefined risk trades at around 83%.? This would mean our portfolio probability of profit is around:

(.65 * .85) + (.83 * .15) = .5525 + .1245 = .677

This is our ?W?, .677.? So, setting Kelly % to zero, we now have:

0 = .677 ? (.323 / R),

And solving for ?R?, we get:

.677*R = .323 or

R = .477

So, what does this mean?? It means that if you take off your winners for 47.7% of your max potential profit, you need to take off your losers at an average of 1 times your max profit potential!? Since we often do not manage our defined risk trades and the losers will often get to close to 2 times our max profit (sell for 1/3 width of the strikes means we can lose 2 times the width), it appears taking winners off for half the potential profit is an untenable strategy!??

A couple of further points to be made:

1. ?You cannot let your undefined losers run forever and expect to make money unless you have a very small percentage of your portfolio in undefined risk tradesAND?you take your profits at a fairly large percentage of max profit.? Play with the numbers (Kelly Criterion formula) to see how you might fair.? Pick a winner to loser ratio, use 0 for the Kelly % and you can back into the probability of winning you would need to break even.

2. ?If you take winners quickly, it is true you will most likely improve your probabilities, but not by enough to make some strategies profitable.??

3. ?It is also true that we generally do 2-4% better on our percentage winners than probabilities at trade time predicts.? This is because IV is generally higher than HV.

By way of a quick example, let?s look at the following scenario.? Let?s say you like to take your winners off at 30% of max profit, that you let your defined losers go to max loss and that you take off your undefined losers only if they get to 3x your max profit.? Further, let?s say you use undefined risk for 25% of your trades (naked puts, covered calls and strangles or straddles).? What probability of profit would we need to achieve to break even?

First, let?s calculate our ?R? from the formula.? We will assume that we sell our average spread for .35 the width of the strikes and that not all our losers are max losers.? Taking some rough estimates, that would make our contribution from the defined risk as:?

.30 / 1.75 * .75 = .1286

For our undefined risk trades, let?s assume we get a rare big loser and a bunch of 2 times losers.? We will take a rough cut guess by saying our loser?s average 2.5 times our max profit.? Our undefined risk trades then yield:

.30 / 2.5 * .25 = .03

This makes our total ratio .1586 which we will round to .16.

Putting that into the equation and solving for our percent of trades that have to be profitable to break even, we get:

0 = W ? ((1 ? W) / .16); solving for W we get:

W = 86.2%

So, using the design we chose with the assumptions we outlined, you need to make money on 86.2% of our trades just to break even!? That is a tall order!

You can improve your odds of success by either taking your losers earlier, by letting your winners run longer, or by some combination of the two.? Personally, I do both with undefined risk trades and I let my winners run longer for defined risk trades. Play with the formula and find an answer that fits you!