Sharpe ratio is one of the many terms that investors and day traders come across especially when screening for a trading strategy or investing in a mutual fund or an ETF. While the name can sound a bit intimidating, Sharpe ratio is actually a very simple yet important metric that covers one aspect of measuring returns, which is volatility.

The Sharpe ratio is a metric used to measure a fund or a portfolio’s risk-adjusted returns. When a portfolio or a fund has a higher Sharpe ratio, the better are the fund’s returns, relative to risk that the fund took on. Sharpe ratio is based on a standard deviation and as a result, it can be used to compare the risk-adjusted returns across all types of funds or portfolios.

Sharpe ratio was formulated by William Sharpe, who is a Nobel Laureate, under the Economic Sciences category. He also created the Capital Asset Pricing Model (CAPM). The Sharpe ratio was developed to measure the relative returns in excess of a proxy for risk-free and guaranteed investment, which is the 90-day Treasury bill to its standard deviation.

William Sharpe

William Sharpe first created the Sharpe ratio initially in 1966 in a paper entitled “Mutual Fund Performance” and was originally called reward-to-variability ratio. This was later revised in 1994 where William Sharpe acknowledged that the risk-free rate of return was the variance.

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In layman terms, Sharpe ratio simply tells you that to earn every one point of return from your investment; you would be risking "x” units. The “x” is of course the Sharpe ratio. Thus you can see that when you are comparing two funds or when you want to know which of your two investments truly gave you more returns in excess of the risk-free rate, the Sharpe ratio is a good metric to follow, provided that the time frame of the investment was the same.

Sharpe ratio evolved as part of the Modern Portfolio Theory or MPT which is a mean variance analysis. It is a mathematical framework used to assemble a portfolio of assets such that the expected returns are maximized for the given risk or variance.

The modern portfolio theory works on the basis that investors are always risk averse. Generally speaking when investors are presented with two options, they will always prefer a less risky investment over the other. However if the risk adjusted returns are higher, then investors are more likely to choose this second option. This is done by the help of Sharpe ratio which is an important metric in the modern portfolio theory. The MPT has its own pros and cons of course Harry Markowitz who was responsible for introducing the modern portfolio theory, alongside William Sharpe came under harsh criticism from other economists. Markowitz was also awarded the Nobel Prize for Economics and has come under fire from other renowned economists such as Nassim Taleb who dismiss the modern portfolio theory.

Anyways, to understand Sharpe ratio, let look at an example where Fund A and Fund B have both generated returns of 22%. But, fund A has a Sharpe ratio of 1.06 and fund B has a Sharpe ratio 0.98. Which of these two funds took offered higher returns when compensated for risk?

This is answered by Sharpe ratio, which tells you that Fund A took on less risk to achieve 22% returns, where as fund B took on more risk to take on the same returns. Obviously, when analyzing these two funds, Fund A is a better option compared to fund B.

Broadly speaking, when using Sharpe ratio it is important to understand that higher the standard deviation, higher the returns need to be in order to get a high Sharpe Ratio value. This also means that funds with a lower standard deviation can also achieve higher Sharpe ratio if they can keep up in maintaining a consistent rate of return from their investments in the funds.

An important distinction to make here is that a higher Sharpe ratio only measures the returns based on the risk taken and doesn’t give any insight into how volatile a fund is or was. Neither does Sharpe ratio account for absolute returns. Sharpe ratio is only used to identify whether the fund or a portfolio’s risk and return relationship is optimal or not. As to the question of what is an optimal value, it is relative to the assets that are being scrutinized.

## How is Sharpe ratio calculated?

Sharpe ratio is calculated by subtracting the 90-day Treasury bill (risk free) return from the fund’s returns. The result is then divided by the fund’s standard deviation. This resulting Sharpe ratio is expressed in percentage basis. Thus a 12% return with standard deviation of 0.08 and a T-bill return of 5% would result in (0.12-0.05)/0.08 = 0.87 which is the Sharpe ratio.

Or to express it differently, to achieve 1 point in returns, you would have to risk 0.87 units.

The Sharpe ratio is expressed mathematically as follows:

• Rp is the expected return on a fund or a portfolio
• Rf is the risk-free rate of return
• StdDev(Rp) is the portfolio's expected rate of return standard deviation(Rp)

## How to use the Sharpe ratio?

Sharpe ratio is used just about everywhere, from assessing exchange traded funds to mutual funds and even in evaluating a trading strategy to high frequency trading.

Sharpe ratios have more meaning than alpha. Alpha, in investing terms measures the active returns on a security, the performance of which is compared to a benchmark market index. Alpha is commonly used to gauge mutual funds and other such similar investment products and it is represented by a single number on a percentage basis. For example, an Alpha of 3% means that a mutual fund performed 3% better than the benchmark index returns and an Alpha of -2% means that the fund performed 2% worse than the market index that is used as the benchmark.

Standard deviation on the other hand measures the volatility of a fund’s return in absolute terms and does not use a benchmark index such as Alpha. In this context, Sharpe ratio is said to maintain consistency and offers more meaning to the question of risk/return.

It is because of this consistency that Sharpe ratio is often used to compare funds rather than alpha’s as a metric. This means that when comparing risk-adjusted returns you can also compare different assets such as a portfolio of stocks versus a portfolio of bonds.

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As an example, the picture below gives a rough idea on selecting the different funds from the screener. With the expense ratio being equal, and ignoring the total net assets, you can see that the WellsFargo:ST HY B (STYIX.O) has a Sharpe ratio of 1.49, which is the highest, meaning that this fund offers you better returns when adjusted for volatility and compared to other similar funds.

Mutual Funds and ETF Screener, with Sharpe ratio (Source - Reuters Funds Screener)

Despite its relevance, Sharpe ratio has a drawback too, in that it is expressed as a number. While a higher Sharpe ratio is preferred, the number doesn’t give any further information beyond comparison of the asset/fund or portfolio. For example a Sharpe ratio of 1.5 is good, but you wouldn’t know anything about the volatility. However, a Sharpe ratio can tell you a lot more if you compare the ratios especially between two funds.

So far we know that Sharpe ratio is consistent and the fact that is represented as a number (sometimes as a fraction) makes it easy to compare two funds or portfolios. Sharpe ratio goes beyond mere comparison as you can also compare the risk adjusted returns across different assets as well, such as stocks and bonds. In fact you can compare anything against the risk-free rate of return.

When a Sharpe ratio is high, the investor is getting more returns for taking on more risk, while a lower Sharpe ratio means that the investor is taking on more risk but the returns are not equally justified. In a way, Sharpe ratio can be used as a yardstick across portfolios and funds and shows you which are shouldering more risk to achieve the same returns. The most common use of Sharpe ratio among day traders is in evaluation a trading strategy (similar to how one would evaluate an ETF or a mutual fund to invest in).

Sharpe ratio as a metric to evaluate a trading strategy

## The limitations of using Sharpe ratio

The Sharpe ratio can be distorted if the portfolio or investments don’t have a normal distribution of returns. Illiquid investments can lower the overall portfolio’s standard deviation, which can be used at times knowingly to influence the Sharpe ratio figures.

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The Sharpe ratio is a backward looking variable, meaning that it only accounts for historical distribution of returns and volatility and doesn’t give any indication of the future. Changing market conditions can definitely influence the outcome of the Sharpe ratio, which is something to consider.

The issue on using the “risk-free” return is also a topic of debate. While the Treasury bills are often used as the benchmark, some algo developers also make use of the S&P500 index. For example, if you were focusing on ETF’s it makes more common sense to use the S&P500 benchmark returns than using the treasury markets. The deeper the question goes, the more questions come out as to what makes for a good benchmark risk free rate of return.

Sharpe ratio can also be reverse engineered and the number can be influenced by a number of variables such as volatility and leverage.

The time frame is one of the important factors when looking at Sharpe ratio. For example, you might have a same strategy but with different holding periods. With a change in the time frames, the returns and the standard deviation of returns change which can give a completely different Sharpe ratio. However this is adjusted by factoring in the Sharpe ratio on a daily basis for short term/scalping strategies while the Sharpe ratio for longer term strategies are usually annualized to get uniformity.

## Does Sharpe Ratio matter for day traders?

Sharpe ratio matters to day traders and swing traders when you are following a trading strategy. Sharpe ratio is primarily used in design of algorithmic trading and automated trading strategies. One of the applications of Sharpe ratio is that it can be applied to any market. So whether you are trading options or stocks or ETF’s or even futures, based on the returns you can always work backwards in determining the Sharpe ratio. You can then use this number to compare against other trading strategies or even funds to analyze the performance.

And if you are feeling adventurous, you could also look at stocks based on their Sharpe ratio.

Stock Screener based on Sharpe ratio

What is a good Sharpe ratio is a question that is most commonly asked by traders. However, Sharpe ratio, when taken in isolation is pointless. Most traders can be found often asking the question as to how to improve their Sharpe ratio which doesn’t really help unless there is another trader’s strategy to compare against. Even then, there is no definite answer as to what is the golden number, so to speak. The widely accepted notion is that a Sharpe ratio of 1 is good and anything strategy with a Sharpe ratio above 1 is definitely worth looking into. However, it is all about comparison and the relative performance, as the Sharpe ratio itself is built on the theory that when two investment opportunities are present, investors will choose a lower risk option, but will choose a higher risk investment provided the returns are compensated by higher returns.

In the very short term and from a day trader’s perspective, Sharpe ratio can be a useful tool as long as you are scalping the markets and not holding positions over a long period of time. Traders can use the Sharpe ratio to compare against other similar trading strategies to get an idea of the volatility and the returns. Note that due to the frequency of the trades made as a day trader compared to a swing trader, the Sharpe ratio will differ as the short term day trades have higher volatility.

While Sharpe ratio is widely used in the investment world, it also finds its use in a professional day trading environment. Many professional trading strategies and ones that are used in automated trading systems often contain extensive back testing and forward testing of the trading strategy in order to determine the metrics, which includes the Sharpe ratio as well. In fact if you were to buy a black box trading system, chances are that the trading strategy will provide you with the back testing results including some key metrics such as the Sharpe Ratio.

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