What is the S&P 500 Sharpe Ratio?

What is the S&P 500 Sharpe Ratio?

The S&P 500 Sharpe Ratio is about -2.7% at the time of writing this article in July 2022. But this means nothing if you do not understand what the Sharpe Ratio is, and how this can be used to evaluate ETFs such as the S&P 500.

The Sharpe Ratio was named after its creator, William Sharpe, after being discovered in the mid '60s. The Sharpe Ratio is a value which tries to determine the relationship of risk and returns for an index or mutual fund. Specifically, the Sharpe Ratio describes how much additional return is yielded for increased volatility. It is incredibly popular because of how simple it is to understand; in short, a higher value is better

Although the Sharpe Ratio can be applied to all index funds and mutual funds, for the sake of this article we will only be looking at the S&P 500 Sharpe Ratio due to its popularity and general accessibility.

What is the S&P 500 Sharpe Ratio-William Sharpe

S&P 500 Sharpe Ratio and Volatility

When investing in anything, it is important to gather as much information as possible beforehand, especially with regards to volatility. Because the Sharpe Ratio provides information on how much return is generated with increased risk, it addresses possible changes as volatility shifts

This allows for the analysis of which ETF may be best for you, based on your risk management strategy, and additional factors.

If you know that you are in a particularly high volatility period, such as when the S&P 500, for example, is buying large amounts of a new company, or selling off large quantities of one that it already included, then you will be able to extrapolate what the possible additional compensation for this increased risk is, and decide whether it is a good time to buy into the stock, or to sell some off and balance out your portfolio elsewhere. 

What is the S&P 500 Sharpe Ratio-ETF

Calculating the S&P 500 Sharpe Ratio

Risk-Free Rate of Return

In order to calculate the S&P 500 Sharpe Ratio, or that of any other ETF, it is important to calculate the risk-free rate of return.

In order to determine what this is, the shortest dated government Treasury Bill is used. This value, also known as the Treasury Rate, or Treasury yield, is the current interest rate that an investor can earn on debt securities that have been issued by the Treasury. 

This value is considered to be the maximum risk-free rate of return that any investor can get. At the time of writing this article, the 6 month U.S. Treasury Bill Rate is approximately 2.86%.

Standard Deviation

The Standard Deviation as well as the overall growth of the ETF is required to calculate the Sharpe Ratio. This information is generally readily available on free platforms as well as in the reports issued quarterly.

Of course, it is important to note that the Standard Deviation as well as the growth of the stock will vary, depending on the timeframe that you are looking at.

This time frame should be reasonable when considering your investment strategy, and how long you intend to hold the ETF. At the time of writing this article, the standard deviation of the S&P 500 over a six-month period has been approximately 3.8%, while the growth has been about -7.4%

What is the S&P 500 Sharpe Ratio-SP 500 index annual Sharpe Ratio

Calculating the S&P 500 Sharpe Ratio

Calculating the S&P 500 Sharpe Ratio over the past six months is easy now that we have determined the values.

First, we must determine excess yield, so the yield above and beyond what was guaranteed by the U.S. Treasury Bill. This is simply the yield of the S&P 500, minus the risk-free yield. Then this needs to be divided by the standard deviation. 

In this case the values are as follows. [(-7.4 - 2.86) / 3.8] = -2.7%

Unfortunately, due to the current conditions the Sharpe Ratio is negative. This does not give any indication as to the risk/reward ratio. However, over a much longer period, the value changes to a positive, and can be used to determine how much excess reward is brought on by the excess risk of investing in an ETF instead of the Treasury Bill.

Problem with the S&P 500 Sharpe Ratio

The calculations of the S&P 500 Sharpe Ratio, and the Sharpe Ratio in general, is that it relies heavily on Standard Distribution. Standard Distribution is only very effective when normal distribution takes place, such as in the illustration below. 

What is the S&P 500 Sharpe Ratio-Problem with the S&P 500 Sharpe Ratio

In cases such as this, the standard deviation would be 1 on either side, as can be seen in the shaded area of the normal distribution graph. The problem is that, as risk increases, its relationship with additional profit does not always form a perfectly normal distribution. Instead, the relationship can be skewed one way or another, depending on a variety of factors. 

This means that the use of standard deviation would not be accurate, rendering the Sharpe Ratio severely inaccurate, and sometimes even misleading.

For this reason, it is important to observe the relationship between increased risk and reward in the S&P 500, ensuring that it is normally distributed, before taking the S&P 500 Sharpe Ratio into account. 

Should You Use the S&P 500 Sharpe Ratio?

The Sharpe Ratio can be extremely useful in determining whether or not to invest in terms of risk management. If the returns on one ETF appear higher, but the ETF is riskier overall, then it may not be the best decision for someone looking to just keep up with inflation or slightly above for a longer period of time. 

However, it is important to note that the Sharpe Ratio is not effective for every single ETF due to the difference in distribution. This can fluctuate all the time, but generally it seems that the S&P 500 risk:reward hovers near normal distribution, making the S&P 500 Sharpe Ratio viable most of the time. 

In order to increase the accuracy, it is recommended that the S&P 500 Sharpe Ratio is calculated using figures of no less than twelve months. This will minimize small fluctuations in distribution that might render the use of standard deviation inaccurate. 

As with all else though, it is important to note that risk exists with every trade, and to not invest more in the markets than you are willing to use. Do not rely on the S&P 500 Sharpe Ratio in isolation, but rather pair it with other variables before making your decision.

You might be also interested in What is SpotGamma? and What is Squeezemetrics?

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