How to Use Risk Management to Double Your Gains

29th Jan by Jack Corsellis

15 comments 412 reads

How can risk management significantly increase your gains? This post looks at how simple maths, Monte Carlo simulations and understanding probability can help you.

Firstly, a simple example using the flipping of a coin.

Imagine for this example you have a 50% chance of heads and a 50% chance of tails. If the coin lands on heads you win £1.20 and if it lands on tails you lose £1. Due to knowing the probability of winning and expected value for wins and losses we can calculate the expected value and expected return over a given number of coin flips. The maths is as follows:

Expected Value = % of Wins x Unit of Risk - % of Losses x Unit of Risk

Expressed another way using the above coin flipping example, Expected Value = [0.5(1.2) - 0.5(1)] = 0.1

Therefore, the coin flipping strategy has an expected value of 0.1. Our coin flipping strategy having a positive expectancy is essential to the remainder of this post. If you want to consistently lose money, look no further than having a negative expectancy for your strategy.

Let's progress with our coin flipping strategy and imagine you had a portfolio balance of £100,000. What would you risk per coin flip (trade)? 2%? 4%? 8%? 10% 25%? Would you then keep this at a fixed amount, such as £2,000 (2%) for every coin flip (trade) even if your account value was growing or shrinking? Or would you use a fixed fractional percentage of your account value so your bet size in monetary terms increases or decreases subject to your account size but your risk is fixed and remains the 'relative' same.

Do you have any idea what is optimal? This is where this post gets exciting if you're this way inclined. Otherwise, you probably stopped reading at the first Expected Value calculation! Onward!

So let's say you use 'conventional wisdom' and decide to risk 2% of your account equity per flip (trade) which is £2,000. You also decided not to use 2% as a fixed fractional percentage and thus bet the £2,000 on each flip (note, you could go bankrupt doing this and the Monte Carlo simulations expand on this point). What is your expected return over the course of 250 coin flips (trades) I hear you ask.

Remember our Expected Value formula from earlier, it all leads into this example:

Expected Value…

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gpacker

29th Jan

Hi Jack,

Excellent detail and highly important - Unfortunately hugely overlooked.

I would guess that the 90% statisic often used (losing traders) is primarily down to this, and the lack of understanding in regard probabilities etc.

Hope you dont mind me adding the link here of the video I created by Peter Brandt (professional trading) which gives summary of what you raise here, also a spreadsheet to calculate your own stats..

https://youtu.be/kxjYGO-N1VA

Thanks

Jack Corsellis

Thank you. I've checked out your YouTube channel before actually and it's very impressive - I'm a big fan of the animations and having my own YouTube channel (https://www.youtube.com/c/jackcorsellis) can appreciate the level of work you put in. Keep up the great content!

Best,

Thanks Jack!

You have a new subscriber... I see you have been busy and made that 'elusive' 1000 subscribers, welldone.
I like your branding throughout the videos and will no doubt look at some later.

All the best.

Let me know if you want to do a collaboration on the Wyckoff method using your video production skills, would be great and very educational. Jack@wyckoffeducation.com is the best way to contact me.

Absolutely - Great idea.

Nick Ray

I would suggest that anyone be very careful about using the Kelly Criterion for position sizing of stocks.

Although the theoretical result is correct when the probabilities are exactly known (as they are for games of chance) things are more complicated when the probabilities are "Bayesian" - i.e. future predictions with no way to calibrate them.

Although we'd expect Heads to win 50% of the time in reality, and over small sample sizes, this cannot be assured. The larger the sample size the closer the correlation to the expected probability. Meaning, if we were to flip a coin 1,000,000 times we'd expected there to be a much closer outcome to 50/50 opposed to flipping a coin 10 or 100 times.

This exemplifies the issue. With coin tossing the more samples you take the more accurately you can estimate the probability. But with stock performance, you do not get a more accurate estimate of future return by taking more samples from the past (!).

A second problem is that the probability distribution is not Gaussian - it has "fat tails" (high kurtosis) and in fact the tails might be so "fat" that the area under the probability curve is not finite - meaning that you cannot compute meaningful values for standard deviation and mean, because the computed values do not "converge" as you use more and more samples. And if you are not sure of the values for these two numbers the predictions of the Kelly criterion no longer apply.

Having said that, if you want to explore this way of sizing portfolio positions the academic literature calls this a "growth-optimal portfolio" (which gives a useful Google search term to go further). The resulting portfolios tend to have very high volatility.

Stepping back one peg in terms of riskiness, you can use "mean-variance optimization" (MVO) which creates rather more benign portfolios which optimize the long term Sharpe Ratio rather than the long term growth (expected return).

aflash

1 thumbs-up is not enough. I was getting blinded & convinced but Nick brought us back to earth.

TANSTAAFL

(which - as fans of Heinlein will know - means "There ain't no such thing as a free lunch.")

Nick, you clearly know a thing or two about risk management. What do you use for your own portfolio(s) for sizing positions and how effective have you found this over a large sample set of trades?

What do you mean blinded and convinced Adrian? It's a post to get you thinking about your own risk management and to highlight scenarios that if you have a positive expectancy for a trading system, a string of bad outcomes can lead to poor results - even though the actual process is sound.

Howard Adams

HI Gareth (& Jack)

I second the idea to do an animation of Wyckoff method.

Over past months - Jack's excellent video's and the Wyckoff method - has really opened my eyes to how to examine the contextual settings of a share price.

Very usefully, Wyckoff provides clear guidelines on specific data points by which to assist in the interpretation of trading volumes and their associations with share prices. Thus, offering guidance of entry points, exit points and most usefully (I have found) strong signals as to when NOT to make an investment at all.

Regards
Howard

Hi Jack

Very useful posting with substantial analytics.

Regards
Howard

Hi Howard,

Thank you for both sets of feedback. We are discussing via email how best to produce a video using Gareth's skills.

Jack

Hi Jack (& Gareth)

Here's one pair of eyeballs you can count on :)

Howard

I tried growth optimal portfolios but they were too aggressive for me. My Fantasy Fund s called GOP from that period.

Mostly I use Sharpe ratio optimisation but I force the portfolios to be equal weight and top slice positions instead of selling out. This has the useful effect of always selling into strength. I generally rebalance (and reselect) about every six months.

I am however gradually using more fundamentals for initial stock selection and then using volatility mnimisationn for sizing.

(Trying to type this in town on my phone and struggling so I'll leave it there for now)

How to Use Risk Management to Double Your Gains

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Jack Corsellis

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