Backtesting Trading Signals: Hit Rate, Costs, and Return Calculation

# Computing the profits for a simple trading strategy (Backtest)


# Computing the profits for a simple trading strategy (Backtest)












I have developed a trading algorithm, surprisingly simple in nature (I did start off with grand plans of applying Machine Learning to this problem as I am a data scientist by trade).

I would place the code here, but I would like to do some appropriate backtesting before throwing it open for peer review. In any case, I am seeing accuracies of `predicted_trading_signal` compared with `perfect_insight` of $+80\%$ across many of the russell 2000 group, which as a data scientist, and a rational person seems too good to be true. To this end, I would like to know if this is an appropriate test

Here is some pseudocode:

```
# generate trading signal up onto data[i]
predicted_trading_signal = some_algo(data[:i])

# generate perfect insight signal
perfect_insight = another_algo(data[i], data[i+1])
# where data[i+1] is say the next day
if some_statistical_property_of_data > lambda:
    if  predicted_trading_signal == perfect_insight:
        correct+=1
    else:
        incorrect+=1

# after running over all windows of interest for a particular stock 
accuracy = 100.0* correct /float(correct + incorrect)
```

I wish I could be more concrete with the code!

- Is this a valid approach to computing accuracy

- is conditioning on information up until todays date and using the following days price typical in testing strategies without data leakage (a subtle problem to a naive person such as myself in trading)

- Is there a better approach?

My final question (hopefully this is considered part of the bigger question - I hate multiple questions in one post on mathstackexchange)

Can I determine the profit-loss calculation as $$ P_i = \text{trading_signal}_{i-1}\left(S_{i} - S_{i-1}\right)\cdot C_{i-i} $$

Here

- $C_{i-1}$ is the initial capital invested.

- $S_i$ stock price

- $\text{trading_signal}_{i-1}$ is initial trading signal

## Answer by Rehan (score 2, accepted)

https://quant.stackexchange.com/a/31969

To begin with, I'm assuming that your trading strategy gives output something of the kind - Buy, Sell, Neutral

While on a cursory glance, your calculation seems fine, here are a few things that you can look at

- Why does the perfect insight only look at the incremental change? Many trading ideas are path dependent - so re-check if your best suited action would have changed if you added history.

- The accuracy parameter, as I understand is the percentage of wins in the strategy trades. The more commonly used term for this is "hit ratio". However, the hit ratio is a misleading number. The hit ratio should always be look at, in conjunction with the "Average Winning Trade / Average Losing Trade" number. Only then can you arrive at the expected values. What can happen is that you have a strategy which has an 80% hit ratio, but your average win/average loss is 0.1, which would mean that overall, the strategy is generating negative returns.

- I see that you are using a statistical condition on the data - I hope that this accounts for the transaction costs - as in, the trade is called a win only if it is sufficiently higher than the entry price.

As for your query on Profit calculation, you have missed out on the dividing factor.

$P_i=trading\_signal_{i−1}.\frac{(S_i−S_{i−1})}{S_{i−1}}⋅C_{i−i}$