Sharpe Ratio

You have two job offers.

The first pays a steady salary of $80,000 a year. The second is a commission job that also averages $80,000 a year, but some years it pays $130,000 and some years it pays $30,000. Same average pay. Which one do you take?

Most people answer the same way: it depends. If you have a mortgage, two kids, and no savings, the steady job is worth more to you even though the average is identical, because the bad years in the commission job could sink you. If you are 24, single, and living with roommates, the commission job might be fine, and you might even enjoy the upside.

Now sharpen the question. What if the commission job averaged $95,000 instead of $80,000? Now you are being paid something extra for putting up with the swings. Is $15,000 a year enough? That is exactly the question the Sharpe ratio was built to answer.

The common-sense version

The Sharpe ratio measures how much extra return you earned for each unit of risk you took. Higher is better. It answers the question "was the bumpiness worth it?"

It was introduced by William F. Sharpe in 1966 and refined by him in 1994, and it remains the most widely quoted risk-adjusted return figure in the industry. Nearly every fund report you will ever see includes it.

How it is calculated

The formula has three ingredients.

The first is the portfolio's return over the period you are measuring.

The second is the risk-free rate, which is the return you could have earned with essentially no risk, usually represented by a short-term U.S. Treasury bill. The logic is that you should only get credit for return above what you could have earned by doing nothing risky at all. A positive difference your investment return minus the risk-free rate is called excess return.

The third is the portfolio's standard deviation (this should sound familiar) over the same period.

Sharpe ratio equals (portfolio return minus risk-free rate) divided by standard deviation. In algebraic form, it looks like this :

Where the formula shows:

•  Expected return of the portfolio (or asset)

•  Risk-free rate of return

•  Excess return (or risk premium) of the portfolio over the risk-free benchmark

•  Standard deviation of the portfolio's excess return (measuring total volatility)

Lets run through an example. For this example, we’ll assume the risk-free rate is 3 percent.

Portfolio X returned 9 percent per year with a standard deviation of 15. Its excess return is 6 points. Divide by 15 and the Sharpe ratio is 0.40.

Portfolio Y returned 7 percent per year with a standard deviation of 8. Its excess return is 4 points. Divide by 8 and the Sharpe ratio is 0.50.

Even though portfolio X made more money, portfolio Y made more money per unit of risk, remember a higher Sharpe Ratio is better. If you could have taken Portfolio Y and simply dialed up the risk to match X, the math says you would have ended up with more than X delivered. That is the insight the ratio gives you: it lets you compare portfolios with different risk levels on a level playing field.

These numbers are hypothetical, and the risk-free rate changes constantly, so a real Sharpe ratio for the same portfolio would differ depending on when it was measured.

Reading the number

There is no official scale, but as a rough guide, a Sharpe ratio below zero means the portfolio did worse than a Treasury bill, which is not what we are shooting for. Something in the range of 0.3 to 0.7 is typical for diversified portfolios measured over long periods. A ratio above 1.0 sustained over many years is uncommon and worth a closer look, because it usually means either a very good period for that strategy, a short measurement window, or something in the data that deserves scrutiny.

That last point matters. The Sharpe ratio is only as honest as the period it covers. A fund that has existed for three good years can show a spectacular Sharpe ratio that says nothing about how it will behave in a bad one.

What it misses

Three things.

First, it inherits the blind spot of standard deviation. Upside surprises count against you just as much as downside surprises. A portfolio that occasionally has a spectacular year gets penalized for it. The next post introduces the fix.

Second, it assumes returns are roughly bell-shaped. Strategies that make small steady gains most of the time and then have a rare large loss can show a beautiful Sharpe ratio right up until the loss arrives. Some of the most famous blowups in financial history had excellent Sharpe ratios the year before.

Third, it says nothing about whether the return was enough. A Sharpe ratio of 0.8 on a portfolio that returned 4 percent is mathematically impressive and practically useless to someone who needs 7 percent to fund their retirement plan.

What this means for you

The Sharpe ratio is the first thing we look at when comparing two ways of building a portfolio, because it strips out the effect of simply taking more risk. If one approach has a meaningfully higher Sharpe ratio than another over a long enough period, it is doing something more efficient, and that is worth understanding.

But a higher Sharpe ratio is not automatically the right portfolio for you. Go back to the job example, someone who needs $95,000 a year to make their plan work cannot take the steady $80,000 job no matter how much better it looks on a risk-adjusted basis. They need the return, and their job is to take the risk that comes with it as intelligently as possible.

That is the difference between an efficient portfolio and a suitable one. The Sharpe ratio helps find efficiency, but your plan determines your suitability. In our practice, the ratio is a tool for choosing among the options that already meet a client's need, not a substitute for knowing what the need is.

Any opinions are those of Kirk McCarty and not necessarily those of Raymond James. Expressions of opinion are as of this date and are subject to change without notice. Raymond James and its advisors do not offer tax or legal advice. You should discuss any tax or legal matters with the appropriate professional. Investing involves risk and you may incur a profit or loss regardless of strategy selected, including diversification and asset allocation. Prior to making an investment decision, please consult with your financial advisor about your individual situation. Investing in oil or the energy sector involves special risks, including the potential adverse effects of state and federal regulation and may not be suitable for all investors.

Measuring the Bumps

Imagine packing for vacation and checking your favorite weather app only to find one piece of information, " This week, we’ll have an average temp of 75 degrees." Sounds pleasant, so you pack your favorite clothes for sunny and 75. When you get there, you get some more information and realize that the city is 45 degrees one day and 105 the next, and it has been that way all year. The forecast wasn’t wrong. The average really is 75. It’s pretty much useless because it doesn’t tell the full story and help you figure out what to wear.

What you actually need to know is how far the temperature tends to wander from that average. That is exactly what standard deviation measures, and it is one of the most used risk numbers in the financial world.

What is standard deviation?

Standard deviation is a measure of how spread out a set of numbers is around its average. A low standard deviation means the returns cluster tightly. A high standard deviation means there is more variation in returns.

Let’s revisit the two hypothetical portfolios from the last post. Portfolio A returned 8, 6, 10, 7, and 9 percent over five years. Portfolio B returned 25, -12, 30, -8, and 5 percent. Both averaged 8 percent. Portfolio A's standard deviation works out to about 1.6 percentage points. Portfolio B's works out to about 19 percentage points. That one number captures the difference between a smooth ride and a wild one, which the average completely hid.

These figures are hypothetical, but not impossible to find in the real world. From 2003 through 2007, the S&P 500 returned between 4.9 and 28.7 percent every single year, with a standard deviation of about 10. Over the very next five years, 2006 through 2010, the same index had a standard deviation of about 25, because 2008’s 37 percent loss sat in the middle of it. Aside from looking at the individual returns of each year, standard deviation is one of the best measures to help measure the investor experience over a period.

How it is calculated

If you don’t like math, skip ahead to the next section. Here are the steps, using Portfolio B.

First, find the average. For B, that is 8 percent.

Second, for each year, subtract the average and square the result. Year one: 25 minus 8 is 17, squared is 289. Year two: -12 minus 8 is -20, squared is 400. Squaring does two things: it turns every miss into a positive number, so the misses don’t cancel each other out, and it punishes big misses far more than small ones.

Third, average those squared numbers. In practice, analysts divide by one less than the number of observations when working from a sample, which is a technical adjustment you do not need to worry about. Either way, the result is called the variance.

Fourth, take the square root of the variance so the answer is back in the same units you started with, percentage points. That is the standard deviation.

Written out, the formula is: standard deviation equals the square root of the sum of (each return minus the average return) squared, divided by the number of returns minus one. For math folks, it looks like this:

s = √[ Σ(xᵢ − x̄)² / (n − 1) ]

The rule of thumb that makes it useful

Standard deviation is useful because of a pattern in how returns tend to spread out. If returns are roughly bell-shaped around their average, then about two-thirds of the time, a year's return will land within one standard deviation of the average. About 95 percent of the time, it will land within two.

So, if a portfolio has an average return of 7 percent and a standard deviation of 10 percentage points, the rule of thumb says that in a typical year you should expect something between -3 percent and +17 percent, and that a year outside the range of -13 to +27 percent would be rare.

This is what makes standard deviation so valuable to us. It turns "this fund is aggressive" into "in a bad year, this could reasonably be down 13 percent, and once in a long while worse than that." Often, investors aren’t able to really quantify what ‘aggressive’ or ‘conservative’ means, but we are able to better understand their tolerance for risk when we use metrics like standard deviation to give them real expectations backed by statistics.

What it misses

Standard deviation has two well-known blind spots, and the rest of this series exists largely because of them.

The first is that it treats an upside surprise exactly like a downside surprise. A year that comes in 20 points above average raises standard deviation by exactly as much as a year that comes in 20 points below. No investor feels those two years the same way. The next two posts deal with this.

The second is that real market returns are not perfectly bell-shaped. Extreme years, especially extreme bad years, happen more often than the bell curve predicts. The rule of thumb above says a three-standard-deviation year should happen about once every 370 years. Markets have produced them considerably more often than that. Standard deviation is a good place to start. It’s like the dough for a pizza. By itself, it’s not a pizza, and it doesn’t taste too great, but when you add the toppings, it becomes the most important ingredient and keeps everything together.

What this means for you

A portfolio's standard deviation over the last 20 years and over the last 3 years can be very different numbers, and the one that matters depends on the person. For someone who plans to draw on the account starting in two years, the recent, shorter-window figure and the worst single-year figure are what we focus on, because a long-run average will not pay next year's bills. For someone in their thirties adding to the account every month, we care more about the long-run figure and much less about any single year.

A standard deviation of 12 means little to most people. We try and do our best to communicate to clients what that means in plain English, "In a bad year, this portfolio could reasonably lose about $60,000 on a $500,000 balance, and you would still be within the normal range" is something any client can react to. If that sentence makes someone's stomach turn, we have learned something important before any money is at risk, and we adjust.

Standard deviation is the ruler. The next post introduces the first tool that uses that ruler to answer a better question: not just "how bumpy was it," but "was the bumpiness worth it?

Any opinions are those of Kirk McCarty and not necessarily those of Raymond James. Expressions of opinion are as of this date and are subject to change without notice. Raymond James and its advisors do not offer tax or legal advice. You should discuss any tax or legal matters with the appropriate professional. Investing involves risk and you may incur a profit or loss regardless of strategy selected, including diversification and asset allocation. Prior to making an investment decision, please consult with your financial advisor about your individual situation. Investing in oil or the energy sector involves special risks, including the potential adverse effects of state and federal regulation and may not be suitable for all investors.

Same Average, Different Ride

Two people leave Hattiesburg for Nashville at the same time. Both arrive at the same time. If all you saw was the arrival time, you would imagine they probably had the same trip.

The first driver set the cruise control and held a steady speed the whole way. No stops, no aggressive driving, not a ton of risk.  The second driver spent the trip alternating between 95 miles per hour and 35, sometimes because of traffic, sometimes because of a heavy foot. When all was said and done, they had the same average speed and same arrival time, but riders in both cars experienced very different trips.

Investing has the same problems. The number most people look at, the average return, is the arrival time. It tells you where the portfolio ended up. It tells you almost nothing about what the trip there looked like.

Here is a hypothetical example. Imagine two portfolios that each start with $100,000 and are held for five years.

Both portfolios averaged exactly 8% per year on average, so they of course should end up in the same spot at the end of the period. Portfolio A ends the five years at roughly $146,900. Portfolio B ends at roughly $138,100. Same average, about $8,800 less, and the only difference is how bumpy the road was.

Why the bumpy road costs you money

This isn’t creative math just to prove a point. Portfolio B is not a remarkably unique stretch either to exaggerate volatility and add in years of negative returns. If we looked back at every five-calendar-year period of the S&P 500 over the last 100 years, about one in five contained exactly two down years, and one in three contained two or more. An investor can reasonably expect to live through at least one of these cycles during their working and retired lives.

When a portfolio loses 12%, it needs to gain more than 12% just to get back to where it started. Lose 12 percent on $100,000 and you have $88,000. Gain 12% on $88,000 and you have $98,560, not $100,000. Every loss makes the next gain work harder, and the bigger the swings, the bigger that penalty grows.

Investors sometimes call this volatility drag. The plain-English version is that big swings quietly eat part of your return even when the simple average tells a different story. In our example, Portfolio B's simple average is really 8%, just like Portfolio A, but the actual compounded growth rate works out to about 6.7% per year, not 8%. Portfolio A's works out to essentially 8%, because it barely had any swings to drag on it.

It gets worse when you are taking money out

Now make one slight change and suppose the person who owns each portfolio is retired and withdraws $6,000 at the end of every year to live on. This represents a withdrawal rate of roughly 6% throughout the period, which is within reason.

With those withdrawals, Portfolio A ends the five years at about $111,500. Portfolio B ends at about $105,900.

Now let’s assume Portfolio B's exact same five returns, but reorder them so the two losing years come first: -12%, -8%, then +5%, +25%, +30%. The average is still 8%. The compounded growth without withdrawals is still identical, about $138,100.

With the $6,000 annual withdrawals, however, that reordered portfolio ends at about $94,900. Roughly $16,600 less than the steady portfolio, and the only thing that changed was the order of the years. We call this sequence of returns risk. The risk fuels nearly every decision that we make around portfolio construction.

A retiree that is in the distribution phase of their portfolio and a 30-year-old saver cannot be handed the same portfolio and told to treat market fluctuations similarly. When a portfolio enters the distribution phase (retirement), a bad year is no longer an opportunity to consider buying shares at a lower price. Instead, a bad year can permanently shrink the base that every future good year builds on. For a portfolio that is still accumulating, negative years can be key years of adding to positions at a lower price or buying companies at a discount to their fair market value. This only works, however, if you have a plan in place to do just that, and you execute it.

What the industry does about this

The financial world has spent decades building tools to measure the ride and not just the destination. They go by names like standard deviation, Sharpe ratio, Sortino ratio, maximum drawdown, and beta. Each one answers a slightly different question:

• How big are the swings? (standard deviation)

• How much return did I get for the swings I put up with? (Sharpe ratio)

• What if I only count the swings that went against me? (Sortino ratio)

• What was the worst stretch, peak to bottom, and how long did it take to recover? (maximum drawdown and recovery time)

• How much of my ride was just the overall market's ride? (beta)

In this series, we’ll look at what these fancy words and calculations look like in real life.  We’ll do our best to give common sense examples of what the metric is trying to tell us, the actual formula, what it is good at, and what it misses. No single metric is "the answer." They are all parts to a system that, when maintained properly, helps us, help you get to where you’re going as efficiently as possible.

What this means for you

The point of measuring risk is not to avoid it. Risk is what you are paid to take. The point is to take the kind and the amount of risk that fits your situation.

For someone drawing income from a portfolio, we care a great deal about the size and timing of the down years, because those are the years that do lasting damage. Protecting against market loss is far more important in this stage than trying to keep up with every bull market. For someone who is decades from needing the money and adding to it regularly, a bumpy ride is far more tolerable, and the bigger risk is being too cautious for too long. This doesn’t mean we throw caution to the wind for the next 20 years, it means that we take advantage of volatility in the accumulation phase and set rules in place for when it is time to de-risk.

Which ride is right for you depends on where you are going, how soon you need to get there, and who is in the car with you.

Any opinions are those of Kirk McCarty and not necessarily those of Raymond James. Expressions of opinion are as of this date and are subject to change without notice. Raymond James and its advisors do not offer tax or legal advice. You should discuss any tax or legal matters with the appropriate professional. Investing involves risk and you may incur a profit or loss regardless of strategy selected, including diversification and asset allocation. Prior to making an investment decision, please consult with your financial advisor about your individual situation. Investing in oil or the energy sector involves special risks, including the potential adverse effects of state and federal regulation and may not be suitable for all investors.