Roy's Safety-First Criterion (SFRatio) helps to choose a better portfolio

So, you’re thinking about investing in stocks. You learned a lot about the stock market and spent hours researching stock tips, terms, and definitions. Of course, you also managed to come up with this extra money you can afford to lose – because your skeptical friends tell you that you’d lose them for sure. The problem is that this one time you don’t want to listen to your friends. In fact, you want to prove them wrong. You promised yourself to succeed, and you’re determined to do it. There is just one question: how can you increase your chances for success?

Roy to the rescue

In case you have a Roy among your friends, we don’t mean him (although, who knows, he might have a piece of advice for you, too). The Roy we want to introduce to you is Arthur D. Roy, who in his work, published in 1952, described a risk management technique. This method helps investors to decide which portfolio is safer and which carries bigger risk. It’s called Roy’s Safety-First Criterion, or simply – SFRatio.

How it works

All right, you already know which Roy you’re reading about, so now it’s time to find out how exactly his idea can help you in investing. Ready for some math and numbers? Of course you are, otherwise you wouldn’t be drawn to investing in the first place, right? Okay then, let’s move from theory to practice.

Imagine that you are an investor, and if you are one already just imagine yourself having set a minimum threshold, below which you don’t want your returns to fall. Now imagine that there are two investment options: portfolio X and portfolio Z. Using Roy’s criterion you will be able to calculate which of the two portfolios is riskier, in other words which is more likely to fall below the return threshold you are willing to tolerate. Let’s go over this calculation (yes, here comes the math part).

Little bit of math

In order to create Roy’s safety-first criterion in symbols we’re going to need some letters. For a start, let’s take two: P & R, which we will support with another two: a & m. That’s all. Now here is what stands for what:

P – probability
Ra – the actual return
Rm – the minimum return an investor is willing to accept

All right now, we have letters and we know what they mean. Keeping in mind that Roy’s safety first criterion allows an investor to calculate the probability that his or her actual return will be smaller than the minimum acceptable return, we can write the following: P(Ra

Since investment portfolios consist of various investments, which generate different returns, we need to sum up all of them. In order to do that we’re going to need one more letter. Why not use E, which represents the capitalized Greek “S” meaning summation. This way we get the following:

SFRatio - Roy’s safety-first criterion
E(Ra) - the mean return from all investments in the portfolio
Rm – the minimum return an investor is willing to accept

We are also going to need the standard deviation of portfolio return. It is a measure showing the spread of a set of numbers by taking the square root of their variance.

This leads us to the final calculation:

SFRatio = [E(Ra) - Rm]/Standard deviation of portfolio return

Nothing better than an example

Very well. By now we learned who is behind SFRatio and what letters we need to write the formula. Before you start proving to anyone who doubts in you that you’ve got what it takes to make it in the finance sector, let’s use an example.

You’re the investor, remember? You have two portfolios: X and Z, right? The first one has the expected return of 16% and standard deviation of 12%. The second one has the expected return of 7% and standard deviation of 9%. Let’s say that you won’t be satisfied with returns from your portfolio that are lower than 3%. Let’s calculate which investing opportunity works better for you:

SFRatio(X) = [16-3]/12 = 13/12 = 1.083
SFRatio(Z)= [ 7-3]/9 = 4/9 = 0.44

Based on our calculations, using Roy’s safety-first criterion you should pick the portfolio X, which is less likely to fall below the return threshold you’re willing to accept. There is one more thing you need to remember. In investing you can never stop learning, so be sure to check out our How To section for more guidance.