Return rate assessment is the process of measuring the profitability and the risk of a trading algorithm over a specific time period. It can be used to answer the following questions:

• Is the return rate high or low, compared to which benchmark?

• Is the algorithm taking too much risk to increase its chances of making a profit?

• Is the algorithm profitable due to skill or luck?

Relative return rate

The relative return rate is the rate of return on a portfolio relative to a benchmark. The benchmark is selected depending on the nature of the algorithm. For example, a trading algorithm that trades underlying stocks may use the VN-Index benchmark, while a market-neutral algorithm may use the risk-free rate instead.

For example, algorithm A trades underlying stocks under a dominant beta strategy, while algorithm B trades on a market-neutral approach. During the same 1-year period (Jan 1, 2021, to Dec 31, 2021), both algorithms achieved a return rate of 20%.

In absolute terms, the two algorithms are equally profitable. However, in relative terms, there’s a big difference. It’s due to the two algorithms having different benchmarks. For algorithm A, the benchmark is the VN-Index, which actually increased by about 34% during the comparison period. For algorithm B, the benchmark is the 3% risk-free rate.

The two algorithms have equal absolute returns but different relative returns. Algorithm A has a worse result than the benchmark (20% - 34% = -14%), while algorithm B has a better result than the benchmark (20% - 3% = 17%). This difference is most evident in bad years in the market.

Sharpe ratio - return on risk

The main goal of investing is to maximize returns. However, the higher the return, the higher the risk. Therefore, when evaluating the rate of return, it’s necessary to consider the risk factor altogether.

The Sharpe ratio , named after the American economist William Sharpe, can solve this problem by dividing the return rate by the risk parameter. This allows for the evaluation of the investment performance on the basis of balancing between return and investment risk.

The formula for the Sharpe ratio is as follows:

Sharpe ratio = (R_p – R_f)÷σ_p

where:

–  R_p is the portfolio’s return

–  R_f is the risk-free return rate

– σ_p is the portfolio’s standard deviation, representing risks. The Sharpe scale rating threshold is as follows:

In the algorithm optimization stage, it’s necessary to consider whether additional profits are due to rational optimization or simply taking on higher risks. Instead of focusing on increasing the expected return, investors should focus on increasing the Sharpe ratio. A high expected return is good, but it’s only optimal if it doesn’t excessively increase the risk.

Skill or luck

Imagine two investors A and B randomly buy a stock and hold it for a year. Investor A’s stock price goes up many times while it’s the complete opposite for investor B. Does that mean investor A has better investment skills than investor B?

Sometimes, high profits are just a matter of luck. An algorithm that has a stable performance can still suffer big losses due to unforeseen events. On the other hand, an algorithm that has very high profits but has only a few trades may just be lucky rather than effective.

When an algorithm has enough trades, the random factors will cancel each other out. It’s important for algorithm traders to distinguish between luck and skill in their trading process. To achieve consistent returns and beat the average market over the long term, skill always matters more than luck.

However, the return rate is not the only aspect that needs to be considered to fully evaluate the algorithm’s performance. One aspect is the worst-case scenario when running the algorithm. What should be done when the losses exceed the acceptable limit? This issue will be discussed in the maximum drawdown (MDD) article.

Another aspect is how to use leverage effectively. When and how much leverage should the algorithm use? The formula to find the optimal leverage parameter will be presented in the article on the Kelly criterion.