When running an algorithmic trading strategy, the most common valuation metric used is the annualized return. However, there are many drawbacks to using this metric alone. The calculation of the return of a particular strategy is not entirely clear. On the other hand, if there are two strategies that have the same returns, how do we know which strategy is more risky? And what does it mean to take more risk? In finance, we are very concerned with the range of returns between volatility and retracement. If a strategy has significantly higher returns, it is less attractive to us, even if its historical returns are similar to other strategies. The use of the Sharpe ratio indicator has been promoted for comparing different strategies and assessing the risk of each strategy.
William Forsyth was a Nobel Prize-winning economist. He helped develop the Capital Asset Pricing Model (CAPM) and developed the Sharpe ratio (updated in 1994) in 1966.
Sharpe ratio is defined by the following equation:
where Ra is the marginal return of the strategy or investment, and Rb is the marginal return of the appropriate benchmark. This ratio is the ratio of the average excess return of the investment or strategy to the standard deviation of that return. Thus, when the volatility of the return is relatively small, the strategy or investment will have a relatively large Sharpe ratio for the same return.
In trading strategies, the annualized Sharpe ratio is often cited. This ratio takes into account the length of time between trades. Assuming a strategy has N trading ranges in a year, the annualized Sharpe ratio of the strategy is calculated using the following formula:
It is important to note that the Sharpe ratio must be calculated based on the type of time interval considered. For example, if a strategy operates on a day trading basis, N = 252 because there are 252 trading days in a year, and Ra and Rb must also be daily earnings. Similarly, for a strategy that operates on an hourly basis, N = 252 * 6.5 = 1638, because there are only 6.5 trading hours per day.
In the formula for calculating the Sharpe ratio, reference points are mentioned. The reference points are used as a criterion to evaluate whether the strategy is worth considering. For example, a simple long-term strategy for investing in large stocks should be able to outperform the S&P 500 index, or at least be able to balance it out under smaller fluctuations.
How to choose a benchmark is sometimes unclear. For example, can an exchange-traded index fund be used as a benchmark for the performance of an independent listed company or the S&P 500? Why not the Russell 3000? Is a hedge fund a benchmark for a market index or another hedge fund?
To give a specific example. For market-neutral strategies, there is a somewhat complicated consideration of whether a risk-free rate or zero should be used as a benchmark. Because the strategy is market-neutral, the market indicator itself is not suitable for use as a benchmark. The correct choice is not to deduct the risk-free rate.
Although the Sharpe ratio is very important in quantitative finance, it also faces some limitations of its own.
First, the Sharpe ratio is a retrospective; it merely explains the distribution and fluctuations of historical returns, not those pointing to the future; an implicit assumption is that the past and future are equivalent when judging by the Sharpe ratio; however, this is not necessarily the case, especially when market systems change.
Second, the calculation of the Sharpe ratio assumes that the distribution of returns is fairly even. Unfortunately, markets are often biased. The distribution of returns is often fat-tailed, so the probability of extreme events occurring is greater than predicted by the fair-tailed distribution.
Some strategies are weak in their resistance to this type of risk. For example, selling a put option. Over time, selling a put option produces a flat option premium, which results in low volatility in earnings, and a yield that is well above the benchmark, resulting in a high Sharpe ratio. However, it does not take into account that the option will be redeemed, which will result in a sudden significant pullback or even a plateau in the stock curve.
Although for some people, this is commonly talked about. It is more practical to include transaction costs when calculating the Sharpe ratio. In many real-world examples, some trading strategies have a high Sharpe ratio, but when the actual costs are taken into account, they become low Sharpe ratio and low yield strategies. This means that net income must be taken into account when calculating the gain beyond the benchmark.
A more practical consideration is that you should ignore those with an annualized Sharpe ratio of less than 1 (after deducing transaction costs). Quantitative hedge funds tend to ignore those with an annualized Sharpe ratio of less than 2. I know of a well-known hedge fund that doesn't even use a Sharpe ratio of less than 3. As a retail investor, if you have a strategy with an annualized Sharpe ratio greater than 2, that's fine.
Sharpe ratios often increase with increasing frequency of trading. Some high-frequency trading strategies will have high single-digit Sharpe ratios, some can even be double-digit Sharpe ratios. Because these strategies can yield better daily, monthly returns, while rarely suffering greater risk, yield fluctuations are small, resulting in high Sharpe ratios.
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