So you've got a portfolio of individual stocks, and you're looking at it next to a benchmark like the S&P 500. "Pretty good!" You might be thinking to yourself.
But is it really that good?
The risk level of your portfolio might be totally different than that of the S&P 500, so just looking at percentage returns isn't a fair comparison. How can we solve this problem? With math, of course!
Allow me to introduce you to a very cool risk-adjusted performance metric, the Modigliani Risk-Adjusted Performance measure or M^{2} (it was invented by Nobel-prize winner Franco Modigliani and his granddaughter, Leah Modigliani -- two Modiglianis, get it? I know, I know, it's actually embarrassing).
So What Do I Do?
M^{2 }is based on the Sharpe Ratio, which you might have heard of already. The Sharpe Ratio also gives you a risk-adjusted performance measure, but it's dimensionless, meaning it has no units.
That not only sounds a little weird, it's a bit tough to interpret. If your portfolio has a Sharpe Ratio of 0.8 and your buddy's is 0.6, you know that yours is "better" -- but how much better is it, really?
M^{2} solves this problem by putting risk-adjusted performance in terms we can all understand: percentage points. If your M^{2} is 5.8% and your friend's is 5.2%, you know you did 0.6% better than he or she did. This makes gloating much easier.
How Do I Do It?
First, you need a portfolio to analyze and a benchmark. The benchmark can be a real one, like the S&P 500, or it can be subjective, like another portfolio. You'll want to get as much data as you can -- monthly returns over five years is pretty great.
To make your calculations, you'll need the following:
Thing You Need |
More Details |
---|---|
Excel or a similar program |
You probably don't want to crunch these numbers with a calculator |
Your portfolio's total returns |
You can export the raw data into Excel to calculate a total return for the whole period. Or maybe you have this number already! |
Your benchmark's total returns |
Again, you can export the raw data. You might just be able to get the number depending on what you use as a benchmark. |
Your portfolio's standard deviation |
Take your data and use the Excel formula to calculate. |
Your benchmark's standard deviation |
Same as above (unless you have this number from another source). |
A risk-free asset's total returns |
The 10-year Treasury is a popular one -- again, export the data to get an aggregate number if you need to. |
A risk-free asset's average total returns |
Same as above. |
A cup of coffee |
This part should be obvious. |
One important detail: Make sure all the numbers come from the same period of time! Your fearless and yet humble author has been known to make such blunders. This is where the coffee comes in.
Step One: Sharpe Ratio
The first thing you want to do is find your portfolio's total returns and your risk-free asset's total returns. Next, use the appropriate spreadsheet formula to calculate the standard deviation of your total returns (this measures volatility).
Then, plug those numbers into this formula:
Step Two: Getting to M^{2}
To get to M^{2 }you just need two more numbers: the standard deviation of your benchmark and the average risk-free rate for the period. You can calculate them in Excel or find the data online, depending on what you're using as a benchmark.
Input these numbers into the formula below:
And... Now What?
After you compute M^{2} for your portfolio, the S&P 500, your neighbor's 401(k), and your mom's IRA, you can calm your enthusiasm and see how well you're doing. Is your M^{2 }way higher than the S&P 500? That's pretty great, because it means you're getting a lot of excess return by comparison -- adjusted for the risks in both portfolios.
Of course, M^{2} isn't by any means the end-all be-all of analysis, but it does give you another level of insight. It comes with its share of caveats (namely: it's for portfolios, not stocks; don't use bad data; and if your returns are very skewed, as opposed to looking like a bell curve, it might not be so accurate), but it's a nice tool for those days when you want to sit back and really see how things are going, and think about where you might want them to go next.
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