In algorithmic trading, we need to compare different strategies. How do we evaluate the historical performance of different algorithms? This short article will discuss in detail [Sharpe Ratio]
Every strategy can be scored using the Sharpe Ratio. It not only measures the return of the strategy, but also touches on the risk and volatility of the strategy. The Sharpe ratio is designed to calculate "risk-adjusted return," which is investment return after measuring risk.
The Sharpe ratio plays an important role in evaluating investment performance. It was published by William F. Sharpe, an American economist and Nobel laureate in economics. To build your own quantitative trading program, you must learn to use the Sharpe Ratio to screen trading strategies.
Excess returns are calculated by subtracting the benchmark return from the strategy's return. For example, if I have a currency trading strategy, my benchmark could be Bitcoin. Assuming my strategy returns 23% annually and Bitcoin returns 20% annually, the excess return is 3%.
The standard deviation of excess returns, or standard deviation, can be calculated from a series of excess returns series.
It can be seen that the greater the fluctuation in the return of the strategy, the larger the standard deviation of excess returns will be and the Sharpe ratio will be lowered. That is, if two strategies have the same excess return, the more "stable" one will have a higher Sharpe ratio.
Generally speaking, the higher the Sharpe ratio, the more attractive the strategy. A Sharpe ratio higher than 1 is acceptable. 2 or more is better, 3 or more is the only winning strategy. A Sharpe ratio below 1 can be interpreted as a loss in market returns. i.e. your benchmark is better than your strategy.
It is important to note that the Sharpe ratio assumes that the average return on an investment is normally distributed. In a normal distribution, most returns are distributed symmetrically around the mean, with fewer returns at the tails of the curve.
Unfortunately, the normal distribution does not represent the real world very well. In the short term, investment returns do not follow a normal distribution. Market volatility ranges from high to low, while the return distribution is concentrated at the tail. This may reduce the validity of standard deviation as a measure of risk.
When the standard deviation does not accurately represent the risk taken, the result may be a Sharpe ratio that is higher or lower than it should be.
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In summary, the Sharpe ratio is used to assess the efficiency of a strategy. A basic quantitative trading system will have a basket of trading strategies, and each strategy will then calculate its Sharpe ratio based on historical performance (this procedure is called backtesting, strategy backtesting).
Knowing the Sharpe ratio for each strategy, we can further calculate how to allocate positions. The mathematical model for optimal position allocation based on the Sharpe ratio was published in the 1950s and is called the Kelly criterion (the editor will introduce it in the next thread).
A basket of trading strategies + calculating the Sharpe ratio + using the Kelly formula to determine the bet amount = the skeleton of a quantitative trading system!