Complete Guide to the Sharpe Ratio

Ever heard of Newcomb’s paradox? 👽

An alien comes to you and presents you with two boxes. Box A always contains $1,000 and box B might contain $1,000,000 or $0. You could either take both boxes or just box A. At a glance, it might appear obvious you should take both boxes.

This is the kind of information you could get by just looking at the market, just looking at the return rates of certain investments.

There is, obviously, a caveat. A supercomputer predicted a week before which option you’d choose and pre-set the prize in box B. If it predicted you’d take both, box B is empty, if it guessed you’d only take that box, it contains $1,000,000. This prediction isn’t guaranteed to be right and it can’t be changed.

This kind of risk is what the Sharpe ratio uncovers. It can’t tell you exactly what is a winning or losing move but it goes a long way in letting you know just how financially dangerous your decisions are—and this is invaluable no matter your choice.

On one hand, not all risks are as obvious—in hindsight in this case though—as with Gregor MacGregor’s famous investment scam about an incredibly prosperous South American duchy that defrauded and killed numerous enthusiastic British investors in the 19th century.

On the other hand, playing it safe can also turn into a disaster as Ronald Wayne, the third co-founder of Apple could tell you—he got worried that Job’s debts would fall on him and sold his 10% for $800 back in the day. So, whether you decide to bet on MacGregor’s duchy, or skip that too-good-to-be-true leveraged ETF, the Sharpe ratio is your best first step for weighing in the pros and cons of each investment.

What is the Sharpe Ratio? 🤔

Just like an onion, the stock market has numerous layers and the Sharpe ratio is a popular tool for discerning some of the most important slices—risks and profitability. This metric was devised by William F. Sharpe—no relation to the famous Richard Sharpe—to make sure that those excellent returns you are looking at are really as good as they seem.

For example, it can help us figure out that the very famous ARKK ETF might not be so impressive as it has a Sharpe ratio of about 0.55. Just to get us started, this number isn’t terribly good and we’ll be going into a lot more detail about why it is so later down the track.

In a nutshell, this ratio looks at the returns of pretty much any investment vehicle—most often a fund or a stock—and compares it to a risk-free security to determine just how likely your great returns are to get swallowed by associated risks.

Ideally, there should be a correlation once you make this calculation. If your investments are twice as risky as a risk-free investment but offer only 20% better returns, they probably aren’t worth you sticking your neck out.

That’s the short explanation, but the longer version isn’t that much longer in all honesty.

Sharpe Ratio Formula 🧪

Simplicity is the key to the Sharpe ratio’s popularity. The formula is widely known and generally easy to get.

When you subtract the average returns of the best risk-free asset (RF) from the average return of your asset (Aa) and divide the result by the standard deviation of your asset (SDa), you get the Sharpe ratio of your measured asset (Sa). So:

Quite simple. This formula works no matter what you are valuating, from a single meme coin you are thinking to add to your portfolio to your entire investment into the market. But, just to be sure we are all on the same page, let’s take a closer look at these key elements.

Average Return of the Measured Asset (Aa) 💰

This metric is what will probably first draw your attention when investing. It might reel you in—perhaps like the often insane returns of certain types of ETFs—or put you off by being too low. Still, while it might appear simple, there are some key things to note about average returns. The first of these is that they are time-dependent. Returns can represent the year-to-date performance, earnings since inception, or anything in between.

Since the Sharpe ratio is so easy to calculate manually, and many of the leading available brokers can do the math for you, you should also decide on the average of interest by yourself.

The period you are looking at can vary greatly. For example, if you are hoping to take a long position with something like blue-chip stocks you might be interested in a 10-year average. On the other hand, a far shorter time frame would probably have far more use if you are day trading—which just might be the case as some worry that the practice is now easy to the point of being overall harmful.

Furthermore, as we’ve said, this measured asset is a rather ungrounded term as it can mean basically anything you are examining. It is worth remembering that, especially when holding a long position, your portfolio’s Sharpe ratio should increase with every new purchase.

The whole point of diversification under the modern portfolio theory is to make your investments less risky.

Average Risk-Free Return (RF) 💸

While it might not appear very likely, risk-free returns are probably the biggest apple of discord among these three elements. To begin with, there are no truly risk-free benchmarks available since everything on the market is subject to numerous factors—internal and external crises, changes in the political landscape, temporary scares and crazes, uncertain interest rates, and so forth.

Actually, treasury bonds which tend to be used as a benchmark for this metric have taken a hit in 2021 as their yields have seen a major decline amidst the aforementioned inflation uncertainty. That being said, risk-free numbers have to be taken somewhere with the ultimate choice coming down to you. So, whether you do choose treasury bonds or some other ‘safe’ option like blue-chip stocks, you should make sure they mimic the asset you are measuring as closely as possible.

Ideally, you want a benchmark that has existed on the same market as your measured asset in the same time frame—there is little point in comparing apples to oranges. However, not all agree that there is insurmountable value in this close-knit approach and simply using the most recent government treasury bill remains the industry standard.

Standard Deviation of Asset (SD) 📊

Put simply, standard deviation represents how far an asset’s prices are from their expected value. Standard deviation is another quaint part of the equation as it can affect its precision. A relatively small SD is unlikely to throw the Sharpe ratio off, but a high one might just throw the results into disarray.

Still, these extremes aren’t that common and standard deviation remains another useful and widespread tool. You should be able to get this metric for most companies either by googling or from your broker, but it is useful to know how it is calculated—especially since its equation isn’t as simple as the Sharpe ratios.

There are two main variants of the standard deviation—the regular kind and the sample version. In the world of finance, the sample standard deviation is often used.

Sample Standard Deviation Formula ➗

Here’s a nice and scary formula. Let’s use it as a jumping-off point.

So, let’s divvy up this scary formula into its building blocks:

• s — The ‘s’, also often given as a lower-case greek sigma (σ) is the standard deviation.

• N — ‘N’ represents the number of periods we are measuring. So, if we are going for a, for example, 7-day period, N would be 7.

• x̄ — ‘x̄’ serves as the mean here, the simple average for the N period.

• x_i — ‘x’ represents the value on any given period and the little ‘i’ next to it tells us that there should be a number indicating which period we are talking about. So, if we are looking at day 6 it would be x6.

• Σ — The upper-case sigma (Σ) tells us that we should add together all the squared subtractions of x̄s from X_is before going further.

Second to last, since we are looking at a sample standard deviation, we should divide the number we get by the total number of periods measured minus one.

Finally, we should find the square root of the number we’ve calculated.

So, let’s say we are doing this for a 7-day period where the relevant prices are: 10, 9, 11, 10, 11, 12, 11.

So, the next step is the squared subtractions. We’ll just write down the first one, but you can double-check us for the rest if you wish.

Adding all these calculations together gives us 5.68

Now, we should divide this result by N-1, or, in our case, 6 meaning that we are looking for the square root of 0.95 making our standard deviation 0.97.

What Does the Sharpe Ratio Tell You? 🧠

Since all the math going into the Sharpe ratio might make it seem a bit complicated, let’s reiterate—the main driver of its popularity is simplicity. By comparing the return rates of investments to volatility it lets us know that we are getting bang for our buck.

The idea is rather simple, you want to make sure that you are getting compensated for any additional risks you are taking. Generally speaking, a Sharpe ratio of 1, or above is considered good. If you see your portfolio’s ratio drop to, say, 0.5 with a new investment, you’d probably want to be sure that its return rate has also grown significantly.

One of the main things you can gauge from your Sharpe ratio is whether your returns reflect a good strategy, or overexposing yourself to risky trades.

On the other hand, when engaging in short positions, like binary options, a low Sharpe ratio could be your goalpost when selecting trades. The rationale here is that if you are betting on quick price changes with your binary options, a low ratio could help you pinpoint options with a desired level of volatility.

Once again, the Sharpe ratio tells you how risky and volatile a security is—what you do with that information is up to your strategy. Furthermore, you can apply this ratio to your existing portfolio looking into the past as a tool of analysis.

This could either give you cause to pat yourself on the back for your wise investments or ring the alarm bells to finally purge that pesky startup from your retirement fund as it is risky enough that it will probably cause you some major losses soon.

Another use for the Sharpe ratio is forward-looking—you could apply it to your hypothetical future portfolio after you make a certain purchase to decide if you should really go through with the trade.

Using the Sharpe Ratio in Investing 🪙

Since we have established that the stock market doesn’t happen in a vacuum, neither should the Sharpe ratio be used in isolation. Setting this to example, you might be looking to invest in a tech giant. Since it will take some time to get used to Facebook’s new name, and you are seeking an older household name than Tesla, consider Apple and Microsoft.

Photo Finish 📷

At a glance, Microsoft might be looking more and more appetizing—especially since it overtook Apple as the World’s most valuable stock—but it just doesn’t have that cool factor Apple always maintained.

Silly as it might sound, this isn’t trivial—Space X drives much hope and enthusiasm due to this coolness despite Musk stating that simply avoiding bankruptcy is still a big goal. To further muddy the waters, both Apple and Microsoft have impressive and comparable 5-year average return rates.

Apple stands at about 456.3%.

Microsoft at about 485.5%.

Ultimately, the Sharpe ratio gives us a hint at what is the safer bet: Microsoft with a ratio of around 2.09 as opposed to Apple’s 1.10.

An Obvious Advantage? 🔎

Sharpe ratio is also useful when it comes to funds with pretty much the exact same logic applying. So, let’s look at two popular ETFs: ARKK and SPY. ARKK is an exciting ETF that invests in numerous innovators and has had a really good run since its inception—one guided by the enthusiasm its coolness factor generates, some could say.

SPY is a mainstay—a big ETF that tracks one of the main indices, the S&P 500, of the stock market. So, let’s compare them. SPY has a 5-year average of about 17.51% and a Sharpe ratio of 2.50 while ARKK boasts an average of 48.65% for the same period while its ratio is around 0.55.

Unlike in the previous example, here we’d argue that SPY is the clear winner—ARKK’s higher returns aren’t significant enough to justify a Sharpe ratio that is five times lower. Furthermore, following Michael Burry’s shorting of the fund, the popular belief with some investors is that the future has more volatility in store for Cathie Wood’s ETF.

Sharpe Ratio and Passive Investing 💴

The popularity and versatility of the Sharpe ratio have made its availability inevitable. While it is obviously applicable for passive investing as it can be calculated for funds without active management, it also lends itself to an even more hands-off approach.

With this in mind, Acorns is just one of the many excellent Robo advisors that come with the feature that allows you to set a minimum and maximum Sharpe ratio of your portfolio. This option is great both for beginners and weathered veterans as it can greatly help you fully realize one of the main benefits of passive—and mainly index—investing: easy diversification.

Still, its value is likely only to grow—along with the need for vigilance with these investment vehicles—as their growing popularity is likely to attract ever more attention and potential for volatility. As The Times has argued, the smooth sailing of passive investing is unlikely to remain galeless forever.

What is a Good Sharpe Ratio 💡

The case of Apple vs Microsoft highlights what we’ve been saying about the vacuum—or a lack thereof. A ratio of 1.10 is good, but since there exists a similar company with slightly better returns with a ratio of above 2, it is the less-risky option.

Generally speaking, a Sharpe ratio of 1+ is considered good, 2+ is very good, and 3+ is downright excellent. Still, investments with lower ratios than this shouldn’t be dismissed right off the bat. You simply might be looking to invest in a new, shaky, yet promising field so a Sharpe ratio of 0.4 is your best bet if all other relevant competitors are at 0.3 or below.

The Problems with the Sharpe Ratio ⚠️

While this article so far might appear like a raving review, this tool is far from trouble-free. The first elephant in the room is that the market doesn’t always conform to Nobel laureates’ expectations, and while conclusions derived from the Sharpe ratio are more likely to be correct than not, they aren’t guaranteed.

This universal problem is compounded by the fact that this ratio draws its simplicity from mathematical elegance—standard deviation, a key component in the equation, is far from a perfect representation of actual price deviances.

Another issue, on its own and adding to the increasingly shaky tower of the Sharpe ratio is the fact that many of the numbers used when calculating it are somewhat arbitrary. What time frames are we choosing? What is our risk-free benchmark? How closely does our benchmark align with what we are measuring and how important this alignment is?

What is an okay Sharpe ratio given our chosen circumstances?

All of these questions come down to personal judgment calls—which at worst don’t even have guidelines determined by expert consensus.

Furthermore, this arbitrariness of the Sharpe ratio gives rise to some more insidious practices. Managers of various funds have been known to manipulate the various metrics that go into the equation to showcase less-than-honest performance in worst cases, practically ultimately tripping over their heels to get the wrong results.

Obviously, none of this means that the Sharpe ratio is bad, but it serves to highlight the need for a thorough technical and fundamental analysis before making any sales or purchases. It is far too easy to accidentally start gambling rather than investing when trading stocks.

The Variations of the Sharpe Ratio 🏛️

The Sharpe ratio has two main variations: the Sortino ratio named after Frank A. Sortino, and the Treynor ratio developed by Jack L. Treynor. Both of these metrics improve on certain shortcomings of the Sharpe ratio and can either be used to further the results of their parent ratio or to supplant it altogether.

The Sortino ratio replaces standard deviation with downside deviation removing the effects of positive unexpected changes from the end result. This means that this ratio is generally more competent at giving a portfolio’s risk-adjusted return rate—as positive deviations included in the Sharpe ratio are, in a way, a risk of making more money than expected.

The Treynor ratio takes the idea of bang for the buck—or buck for the risk—of the Sharpe ratio to the extreme. It takes the portfolio’s beta instead of standard deviation in its formula and tries to quantify just how lucrative any additional risk is. It is another ratio where the higher the number is, the better—but note that it can give negative results in which case it doesn’t carry much useful data. 

Conclusion 🎬

The Sharpe ratio is a very useful, very popular metric for a good reason. It can help any investor pierce through any frontline attempts of obfuscating the actual performance and worth of any possible investment. Its ability to be used in the analysis of your portfolio’s past performance to tell you what to keep, and what to cut loose is just another benefit.

However, as we’ve seen, it gives data that is both incomplete on its own and prone to be used for further obfuscation by malicious actors—usually hedge fund managers as it turns out—making it somewhat flawed. While its usefulness can’t be denied and it should remain in good graces with every investor, it should always be used in conjunction with other tools.

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