Monday, September 25th, 2006
Finding the optimal risk for your trading account (Risk, part V)
Last we looked at the Kelly Criterion as a way to find out how much of your portfolio you should risk to achieve optimal returns. But ‘optimal’ returns differ for each and every one of us. Some want big profits and big volatility. Others want to generate a consistent return of 10 per cent per year with reasonably low volatility.
There is another useful formula, the ‘inverted sharpe ratio’, which is outlined by Kenneth Grant in his book Trading Risk: Enhanced Profitability through Risk Control. Unlike Kelly, this formula enables us find out how much volatility we need in our account to reach our return objectives.
As an aside, I really like Grant’s book because it adds depth to the conventional trading risk management discussions, which often focus solely on how much to risk on each trade. As I’ve said before, it is largely how much of your total portfolio you risk that determines return.
(Article continues)
Grant has worked with the likes of hedge fund legend Paul Tudor Jones and knows his stuff. His concepts require some time to get your head around, particularly if you’re not good at math, but I have found that the effort has more than paid off. Please don’t be intimidated by a few simple equations below. I was always hopeless at math but found this stuff quite easy.
THE SHARPE RATIO
Grant’s technique is to invert the Sharpe ratio. I’m not going to go into the intricacies of the Sharpe ratio, which most people have heard of. But basically it is a measure of risk-adjusted performance. The higher your Sharpe Ratio, the better the returns you’re getting for how much risk you’re taking. The formula is below:
The Sharpe Ratio = (Return – Risk-free rate)/Portfolio volatility
Return is how much your account earns and the risk-free rate is usually the return on government bonds.
But what is volatility? The simplest measure is one standard deviation of profit/loss volatility. To work this out, set up a simple Excel spread sheet. Each day type in your account value and how much it changes.
Then use the standard deviation formula provided with Excel to calculate the standard deviation.
Grant suggests this should be done over a minimum period of 20 days. Remember it has to be annualized so multiply the daily number by 15.9 (the square root of the number of trading days in a year) to get the annualized volatility figure.
INVERTING THE SHARPE RATIO
As Grant says “you can invert this (Sharpe ratio) equation to determine what level of return you are likely to generate for a given level of risk assumption.” To do this, he substitutes the Sharpe ratio for what he calls ‘Sustainable Sharpe’, which is the Sharpe ratio you would be comfortable sustaining. To get that you’re going to have to start calculating the Sharpe ratio for your account to find a figure you’re comfortable with.
Inverting the first equation leads to:
Portfolio volatility = (Return – Risk-free rate)/Sustainable Sharpe.
This allows us to find out how much volatility we need in our account to achieve our target return. We simply substitute return in the equation for our ‘target return’, which is the one we determined in the second article in this series.
Let’s assume the following:
Target rate = 25 per cent
Risk-free rate = 5 per cent
Return- Risk-free rate = 20 per cent
Sustainable Sharpe = 2 per cent
Plugging the numbers in and solving the equation means that to achieve our 25 per cent target rate would require 10 per cent annual volatility.
PRACTICAL USES
How can we use that practically?
If we have a spreadsheet with volatility (or daily standard deviation) of our account we can see if it’s enough, or too much, to achieve our return objective. Say we wanted to shoot for 25 per cent returns, but our annualized standard deviation is just 5 per cent, we’re unlikely to achieve our target and will have to turn up the juice by risking more on each trade and more of our total account.
The key is to start recording volatility every single day and then playing around with the numbers.
This entry was posted on Monday, September 25th, 2006 at 8:55 pm and is filed under Risk management. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.
September 27th, 2006 at 6:19 am
Great series. Many things that most traders don’t think about. I am intrigued by this inverse-sharpe ratio and will definitely pick up Grant’s book to explore this concept.