# What is the Sharpe Ratio?

In 1966, William Sharpe would create a revolutionary concept in the field of investments: the Sharpe Ratio. With it, investors are able to effectively determine the return of an investment when compared to its risk. This means that they can better understand and evaluate the efficiency of an investment and then add the risk to the equation.

This Sharpe ratio, since its creation, continues to be among the most popular risk/return measures in the world of finance. Much of this popularity stems from the ratio’s overall simplicity. Its credibility would only increase further in 1990 when Sharpe would win a Nobel Memorial Prize in Economic Sciences. This was to reward him for his work on the capital asset pricing model (CAPM).

So, what makes this ratio so special in the eyes of investors?

## What is meant by Sharpe Ratio?

Basically, the ‘Sharpe ratio’ is a method for determining how much return one can achieve per each unit of risk. It is a useful technique to – and is computable by – all forms of capital market participants for performance evaluation. These groups range from conventional day traders to long-term buy-and-hold investors.

Evaluating the overall performance of traders and investors is not technically a matter of determining their return in general. In actuality, it is their return proportionate to their risk.

The ratio is the average return one earns in excess of the risk-free rate per volatility unit or total risk. By subtracting the risk-free rate from the mean return, the investor can better isolate certain profits. Specifically, those that associate with risk-taking activities. Generally speaking, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return will be.

When it comes to risk-free investments, a notable example would be U.S. government treasury bonds or bills. Admittedly, there are some disagreements concerning two factors:

1. Whether the rate of return on the shortest maturity treasury bill needs to be applied to the calculation, or
2. Whether the risk-free instrument must closely match the length of time in which an investor expects to hold the equity investments.

In fact, the main issue of the Sharpe ratio is that investments without a normal distribution of returns accentuate it. We will go over additional limitations later.

## Formula

The standard formula for calculating the Sharpe ratio is the following:

#### Sharpe Ratio = (Rp – Rf) / σp

To be technical, one determines the ratio by subtracting the risk-free rate (Rf) from the return of the portfolio (Rp). Then you divide the result from the standard deviation of the portfolio’s excess return (σp). It is important to note that the risk-free rate of return is usually a user-based input. Oftentimes, this is the equivalent of a bond that is safe and risk-free.

With all of this in mind, there is a question that stems from this. What would one consider to be a good Sharpe ratio? To elaborate, what would be indicative of a high degree of a likely return for a relatively low-risk amount?

• Any Sharpe ratio surpassing 1.0 ranges from acceptable to good by investors.
• Ratios that exceed 2.0 are very good.
• A ratio of 3.0 or anything surpassing that is excellent.
• A ratio falling below 1.0 is sub-optimal.

## Diversification & Portfolios

Modern Portfolio Theory states that including assets to a diverse portfolio that has low correlations can decrease portfolio risk. Moreover, it can do so without sacrificing return.

The ‘diversification’ method diminishes risk by way of allocating investments among various categories, like financial instruments and industries. Adding diversification could potentially increase the Sharpe ratio. This is especially true when you compare it to similar portfolios possessing a lower level of diversification. In order for this to be bona fide, investors need to accept the assumption that risk is equal to volatility. This is not entirely without merit, though it may be too narrow to apply to all investments.

The Sharpe ratio can also help evaluate a portfolio’s previous performance (ex-post) where actual returns are utilized in the formula. Alternatively, an investor can utilize anticipated portfolio performance and the expected risk-free rate to calculate a likely Sharpe ratio (ex-ante).

The ratio can aid in explaining the components of a portfolio’s excess returns. Whether they be because of smart investment decisions or the outcome of one too many risks. One portfolio or fund can benefit from higher returns than its peers. However, it is only a solid investment if those higher returns do not come with an abundance of additional risk.

To put simply, the greater a portfolio’s Sharpe ratio, the better its risk-adjusted performance will be. Should the analysis lead to a negative Sharpe ratio, it means one of two things. Either the risk-free rate surpasses the portfolio’s return or the portfolio’s return will likely be negative. Whatever the case may be, a negative Sharpe ratio will not convey any valuable meaning.

## Sortino & Treynor: what’s the difference?

There are two notable variations of the Sharpe ratio: the Sortino ratio and the Treynor ratio. The former differentiates damaging volatility from total overall volatility. The latter determines the total amount of excess return for each unit of risk that a portfolio takes on.

Sortino removes the effects of upward price movements on standard deviation. Doing so allows it to concentrate on the distribution of returns that fall below the target or mandatory return. In addition, the Sortino ratio replaces the risk-free rate with the necessary return in the formula’s numerator. Thus, it makes the formula the return of the portfolio considerably less the mandatory return. Moreover, dividing it by the distribution of returns below the target or obligatory return.

Now, regarding the Treynor ratio, it uses a portfolio’s beta or correlation the portfolio has with the whole market. The primary goal of the Treynor ratio is to figure out if an investor is receiving compensation. Specifically, for taking additional risk above the inherent risk of the market as a whole. The Treynor ratio formula is the return of the portfolio less than the risk-free rate and dividing it by the portfolio’s beta.

## The relation with crypto

If you are familiar with crypto trading, it should come as no surprise that there is a lot of risk and volatility in the practice. Cryptocurrency price fluctuation has a tendency of being quite extensive. Determining how much risk one can take on or off the table is crucial concerning making trade decisions and strategy. With the Sharpe ratio being a considerably handy tool for risk-adjusted return examinations, more crypto traders are adopting it. With it, they are able to gain a much better understanding of how much risk they should take.

Unlike large-cap coins such as Bitcoin and Ethereum, which are comparatively more stable, a lot of cryptocurrencies are quite risky. To elaborate, plenty of newer cryptos lack the same stability as Bitcoin and Ethereum largely due to them having less liquid markets. This applies to such digital currencies as 0x, OmiseGo, NEO, and Dash. While the Sharpe ratio cannot rectify this instability, it can still help with the unforeseen nature of where the prices will go.

When it comes to cryptocurrency trading, there is only one “risk-free” rate of return. That is by loaning your existing cryptocurrency pools to an exchange for funding their liquidity requirements. Moreover, with the payouts on average of 1% per annum and denominated in the cryptocurrency being loaned.

For instance, let’s assume you are lending Litecoin. In this particular case, you will be receiving 1% interest on that Litecoin. However, even loaning your cryptocurrency out to an exchange is not exactly “risk-free.” This is largely due to the exchange counterparty risk or the risk of hacking.

A majority of cryptocurrency exchanges permit traders to access their APIs (application programming interfaces). Therefore, traders can use the Sharpe ratio – preferably over short time periods – for risk-reward ratio calculation pertaining to a specific trade.

Over short periods of time, the Sharpe ratio can function as a tool for risk management. One that will determine whether or not an automated trade should or should not be made. What’s more, if it’s possible to incorporate it as part of an existing trading algorithm. Doing so will guarantee that automated cryptocurrency trading is within a trader’s risk management policies.

This does not mean that it is flawless, however, because one cannot accurately predict Black Swan-type events. Especially not in cryptocurrency trading.

## Limitations

As you may recall, there was a brief mention of the main limitation of the Sharpe ratio earlier. That being it is possible to accentuate it by way of investments that do not have a common return distribution. However, as per the earlier implication, there is more ground to cover when it comes to the constraints.

The Sharpe ratio utilizes the standard deviation of returns in the denominator as its proxy of total portfolio risk. This basically makes the assumption that returns undergo conventional distribution. A normal distribution of data is a lot similar to the act of rolling a pair of dice. It is common knowledge that over the course of various rolls, the most common result will be 7. Moreover, the least common results from rolling a pair of dice will be both 2 and 12.

However, returns in the financial markets typically steer from the average. This is mostly due to a large number of unpredictable drops or spikes in prices. Furthermore, the standard deviation presumes that price movements in either direction are going to be equally risky.

It is easy for portfolio managers to manipulate the Sharpe ratio. Especially if those managers want to boost their evident risk-adjusted returns history. This is possible by way of expanding the measurement interval. The outcome will be a lower volatility estimate. For example, the annual standard deviation of daily returns typically exceeds that of weekly returns. This is, in turn, considerably higher than that of monthly returns.

There is another way to select the data that will go on to distort the risk-adjusted returns. That being choosing a specific period for the analysis with the best potential Sharpe ratio. This is in lieu of an impartial period of look-back.

## Conclusion

One should evaluate both risks and rewards together when they are thinking about the best investment choices. In fact, this is the focal point that the Modern Portfolio Theory presents. When it comes to defining risk, it is the standard deviation or variance that takes rewards from investors. With that in mind, you should always address the risks along with the rewards when you are deciding on investments.

It is important to remember, though, that this ratio does not offer much valuable information regarding price movement and prediction. Instead, it is a supportive tool that helps evaluate the risk/return in a portfolio. This is vital for participants in cryptocurrency markets, which is where investors will frequently encounter unpredictable volatility.

All in all, the Sharpe ratio is an excellent tool for helping you determine the best investment choice. It will aid in finding a choice that delivers the highest returns while at the same time taking risks into consideration.