Sharpe ratio. Protrader
The Sharpe ratio was named after its creator – William Sharpe, Nobel laureate in economics. The Sharpe ratio was designed to assess a portfolio of securities or other assets; in this article we will consider it in relation to the assessment of the trading systems.
The Sharpe ratio is a statistical indicator of the trading system, which is the ratio of average profitability for the period to the standard deviation of this profitability. From the definition it is clear that the Sharpe ratio takes into account not only a profit obtained by the trading system for a certain period, but also “spread” of the profitability in the form of the standard deviation. In this case, the standard deviation of the profitability is a measure of the risk. Thus, the Sharpe ratio is none other than the ratio of the profitability to the risk. The higher the Sharpe ratio, the more stable the expected profit. Exactly the stability of the profits is the most attractive for the traders. In most cases, the stability degree of obtaining the profit is more important than the absolute profit value. To illustrate the last thesis let’s consider the charts of the profitability of two hypothetical trading systems.
Pic.1. Profitability chart of the system #1.
Pic.2. Profitability chart of the system #2.
Calculation of the sharpe ratio
Where, R – profitability;
Rf – risk-free interest rate (benchmark);
E(R- Rf) – mathematical expectation of profitability;
σ – standard deviation of profitability.
According to the author's method of calculating, the profitability is resulted to annualized values. Methods of calculation which admit both relative and absolute values of profitability, such as interest rates or c onventional units are also often met.
It is important to note that a significant impact on the value of the Sharpe ratio has an indicator, which is not directly related to the considered trading system, namely the risk-free interest rate (Rf). Therefore, an important and controversial issue remains the selection of the benchmark. Benchmark is a certain standard of profitability, exceeding which the trading strategy becomes attractive in terms of investment. The selection of the profitability standard depends on the specifics of the estimated trading system. So, when trading on the stock market, a leading industry index is often chosen as a benchmark. For example, S&P 500 index is often selected as a benchmark for the US stock market. In other cases, it is possible to compare bank deposits or investments in government bonds with the conditional risk-free interest rate. Depending on the benchmark selection, the value of the Sharpe ratio can be changed over a fairly wide range, therefore this indicator has value only as a relative value when comparing the trading systems. Risk-free interest rate is often assumed equal to zero; this gives an opportunity to get away from the uncertainty associated with the benchmark selection and to compare the trading systems that are related to the different markets. When calculating the Sharpe ratio in the Protrader, the profitability of the benchmark is assumed to be zero, and the profitability is presented in absolute values, without resulting it to the annualized percentages.
Disadvantages of the sharpe ratio
- The ambiguity of the benchmark selection.
- The Sharpe ratio, as well as other statistical indicators, implicitly assumes that the historical indicators of the system have a predictive power. In other words, calculating the Sharpe ratio on the historical profitability and using it to compare the trading systems, the trader assumes that the future system indicators will be close to estimated. But due to the high uncertainty of the financial markets, obtaining the profit in the past does not guarantee this in the future.
- The Sharpe ratio assesses the stability of the profit receiving, but not the effectiveness of the investments. If the Sharpe ratio will be only the measure of the investment efficiency, then the most effective can be accepted the strategy with small, but constant profit. From this perspective, bank deposits have a huge effectiveness due to the stable capital gain and low volatility in profitability. For the correct assessment of the investment efficiency, the Sharpe ratio should be used in conjunction with other statistical indicators.
- When calculating the Sharpe ratio, the standard deviation of the profitability is a measure of risk. In this case, there is no difference between profit and losses. Risk is considered to be both positive and negative deviation of the profitability from the average value. That does not always make sense. Trading strategy risks with periodical relatively high profits are not differed from the strategy risks with periodic large losses.
- When calculating the Sharpe ratio, is assumed that the incoming data are subject to the normal distribution law. This is not always the case. Extreme events appear much more frequently in financial markets, than it assumes the normal distribution law.
Users of the “Protrader” terminal are able to use the Sharpe ratio to assess their current trading, as well as to compare test indicators of the trading systems in the “AlgoStudio”. To output a detailed report of the current trading on the selected trading account, you need to choose “Account -> Account performance”.
In the opened window you can see a detailed report of the trading on the selected trading account for a particular reporting period. The Sharpe ratio is included in the list of the standard statistical indicators.
The Sharpe ratio is included in the standard report in the “Algostudio”, which is available after testing the trading system.
Also the Sharpe ratio can be used as one of the statistical parameters when optimizing the trading systems. It can be included in the objective function or used when installing the limits of the optimization.
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