When we analyze and evaluate the performance of a financial asset or a trading system, we usually focus on the profits that it produces over a period of time and we forget a no less important question: what is its associated risk?

Undoubtedly, we want to have a winning trading system that generates profits, but we must not forget the star parameter: risk.

As you know and we have already explained in this blog, there are enough ratios to measure our trading strategies, but in this article I am going to talk about the Sharpe ratio.

Contents

## 1. Ratio or Sharpe Coefficient.

The Sharpe ratio was developed by Nobel Laureate William Sharpe and is one of the most widely used ratios to evaluate and compare financial assets or trading systems. To do this, it analyzes the performance of an investment taking into account the risk of that investment, which allows us to determine if the **profitability of our trading strategy is due to a really good system or, on the contrary, we have assumed a lot of risk.**

Calculating the Sharpe ratio is fairly straightforward and is defined as the annualized return of the trading system (fund, portfolio, etc.) minus the risk-free return and divided by the standard deviation or standard deviation. The formula is as follows:

Sharpe ratio = (r _{ p } – r _{ f } ) / σ _{ p }

Where:

r _{p} : average profitability of the financial asset.

r _{f} : average return on a risk-free portfolio of assets (risk-free return).

σ _{p} : standard deviation of the portfolio’s return.

In case you have any questions about what these three parameters are, here I will tell you in a simple way:

**Average return on the asset**: it is the expected return on the asset in the selected period, which can be: a day, a month or a year.**Risk-free return**: these are short-term public debt obligations (bonds, Treasury bills, etc.) from a geographical area similar to that of the asset we wish to evaluate. This is the minimum return that an investor can obtain in the market.**Standard deviation.**In short, the standard or standard deviation measures how much the returns deviate from their average.

## 2. Interpreting the Sharpe ratio.

As I have already mentioned in other posts, the most important thing when we use statistical metrics to evaluate a trading strategy is the correct interpretation and understanding of the values obtained.

Basically the value of this ratio can be classified into three possible scenarios:

- Ideally, the value of the Sharpe ratio is
**equal to or greater than 1.**The higher the Sharpe ratio, the better the return in relation to the risk that has been assumed when making the investment. - If the value is between 0 and 1, the strategy is not optimal, but it could be used.
- If the Sharpe ratio is less than 0, we should not use the strategy or portfolio that we are evaluating. The negative Sharpe ratio means that the risk-free asset is more profitable than the risky asset.

In addition to the interpretation of the numerical value of this ratio, in general terms the Sharpe coefficient allows us to:

- Compare the
**risk-**reward**ratio**between different investment opportunities. - Select the
**most attractive strategy**from the point of view of risk, with the same return.

## 3. Disadvantages or limitations of the Sharpe ratio.

As I have already told you before, there are no perfect metrics and each one has its limitations. In this sense, the Sharpe ratio is no exception and among the main disadvantages that it can mention are the following:

### 3.1. It does not distinguish between consecutive losses and intermittent losses.

The Sharpe ratio does not depend on the order of the sample and it is not the same to lose 10 consecutive times as alternately.

So that you understand it better, I explain it to you with an example: suppose that we evaluate two strategies during a year, both strategies had 6 months of gains and 6 months of losses. Strategy A had alternating gains while Strategy B had 6 months of losses and then 6 months of gain, as shown below.

My | Strategy A | Strategy B |

January -1000 2000 February -1000 -1000 March -1000 2000

April -1000 -1000 May -1000 2000 June -1000 -1000

July 2000 2000 August 2000 -1000 September 2000 2000

October 2000 -1000 November 2000 2000 December 2000 -1000

**Final Profit **

**6000 **

**6000 **

**Average Profit **

**500 **

**500 **

**Standard Deviation **

**1566.7 **

**1566.7**

**Simplified Sharpe **

**0.32 **

**0.32**

If we analyze both systems, we see that they both have the same mean profit and the same standard deviation, hence the same simplified Sharpe ratio. But if we look at the cumulative profit graph, it is not difficult to realize that strategy A has a more regular or stable cumulative profit curve than strategy B, therefore, I would choose to select strategy A over strategy B despite to have the same Sharpe coefficient.

### 3.2. It does not distinguish between positive or negative deviations (volatility).

Another weakness of using the Sharpe ratio is that when we use the standard deviation of return to calculate risk, it does not differentiate between bullish and bearish volatility. The volatility of a trading strategy allows us to measure or predict the performance of that strategy. So the **higher the volatility the expected returns will be more inconsistent.**

### 3.3. Relative value.

The Sharpe ratio is very useful only when **compared to another trading ****or investment ****strategy ****. **Let’s see an example so that you understand me better: Suppose we evaluate a strategy or portfolio and the Sharpe ratio is equal to 1, this value is quite good. Now we evaluate a second portfolio and its Sharpe ratio is equal to 3.5. Although the first strategy has a good Sharpe ratio, the second strategy has a better ratio and this makes it more attractive when choosing any of them under equal conditions.

## 4. Simplified Sharpe ratio.

On many occasions, instead of using the Sharpe ratio, according to the formula I described above, it is common to use a simpler version known as the simplified Sharpe ratio. The formula for its calculation is as follows:

**Simplified Sharpe ratio** = mathematical expectation / standard deviation

Because the Mathematical Expectation can be interpreted as the average profit (net profit / total number of operations), then we can rewrite the formula as follows:

**Simplified Sharpe Ratio** = Mean Profit / Standard Deviation

## 5. Example of evaluating a strategy using the Sharpe ratio.

Suppose we have investment strategy A, which has an annual return of 16% with a standard deviation of 9%. In addition, we have another investment strategy B with an annual return of 9% and a standard deviation of 3%. The benchmark risk-free return for these strategies will be Treasury bonds that yield 1%.

If we look only at returns, it is very easy to see that strategy A is better than strategy B. However, we do not know the risks that we have taken in strategy A to obtain that return. For this reason, we must adjust profitability based on risk and thus determine which strategy actually performed better. We achieve this using the Sharpe ratio.

Let’s calculate the Sharpe ratio for strategy A:

Sharpe ratio = (r _{ p } – r _{ f } ) / σ _{ p } = (16 – 1) / 9 = 1.67

Let’s calculate the Sharpe ratio for strategy A:

Sharpe ratio = (r _{ p } – r _{ f } ) / σ _{ p } = (9 – 1) / 3 = 2.67

If we analyze the results, we realize that, according to the Sharpe ratio, the strategy that achieved the best profitability according to the risk assumed was strategy B. For this reason, **we should not always let ourselves be dazzled by the returns of a strategy, we must analyze it from different points of view.**

## 6. Conclusion, is it useful?

Finally, to say that the Sharpe ratio can be used when we want to know the risk assumed when executing a certain strategy or investment, indicating whether the profitability obtained is due to an excess of risk. Getting to the point, it allows us to compare the effectiveness of the strategies.

If we are evaluating two trading strategies, the one with the highest Sharpe ratio is the best because it has a lower risk associated with it. The value of the Sharpe ratio of a strategy itself is not that important, what matters is its comparison with the value of the ratio of other strategies.

As I have mentioned in other posts, I do not recommend that you base your trading decisions on the results of a single indicator or metric and the Sharpe ratio is no exception, do not use it alone.

I personally consider that **the Sharpe ratio is nowhere near the best trading measures** you can consider. For example, if you apply a system with a lower stop loss and take profit compared to a broader one, the former will benefit the ratio, even if the latter has better statistics.

Also, the issue of disregarding positive volatility is a huge downside. Having the same weighting in positive positions and negative positions is a major limitation. We need realistic measurements that are a good X-ray of our trading. Which?

Relatively recently I made a video with the best ratios or ratios that I look at to consider an optimal trading system to start applying it. You have articles on this blog talking about each of these measures with practical examples and explanations.

And one more thing, when you compare different strategies or portfolios keep in mind that these portfolios belong to the **same category** , it does not make sense to compare radically different portfolios where the risks associated with each portfolio or strategy are more than evident.

Do not forget that any questions or information you want to share, you can do it through the comments.