I have a day trading strategy. In the attached photo, you can see its performance trading Nasdaq futures. The top panel is the strategy's cumulative returns in dollars, net of commissions. It has led to a profit of ~$300K over about 24 years. So, I can divide 300K by 24 years by the required capital to get annual returns. Assuming a $20K average required capital during these 24 years, that would equal $300K/24/$20K or 62.5% return on capital. The bottom panel shows the same strategy performance but in percentage (blue line) (vs the Nasdaq returns (gray line)). For example, if Nasdaq went up by 2% in day and the strategy was long, this curve would go up by 2%. Cumulative percentage returns is about 400 at the end so that would be about 400%/24 or 17% annual returns (vs Nasdaq annual return of 250%/24 or 10.5%) The maximum draw-downs and their peak vs trough dates and magnitude are also annotated for each curve. I have a bunch of strategies like this and I am wondering if I should use the dollar curve or percentage curve to compare them. As you can see, the two curves have very different shapes and that's what confuses me. For this example, the dollar curve has a maximum draw-down of 20% (a whopping $49670) in 2021 but the percentage curve only a 9.21% in 2009. For the dollar curve, the magnitude of the ebbs and flows grows as time passes corresponding to the growth in the dollar value of a contract (I think). For example, a $1000 change in the curve at the beginning of the curve would amount to a large change while at the end a very small change given that the cumulative curve is around $300,000. But the percentage curve grows more uniformly. Also, the huge maximum draw-down in the dollar curve happens in 2021 but note how moderate the decline in the percentage curve is during that period. So, looking at the dollar curve, I would want to go investigate what the strategy did in 2021 to incur that big loss but according to the percentage curve, it was just a moderate decline. My initial sense is that the percentage change curve is a better metric for comparing strategies. However, different futures have different values and thus different capital requirements as well as commissions. For example, you'd need much more money to trade a Nasdaq contract than a Russell 2000 one. Using the percentage returns curve ignores this fact. So, in sum, what did I got right and wrong here? Which curve should I use to compare different strategies?
I think you didn’t translate, from $ to %, correctly. You need to z/a to get total return. Then (total return)^(1/n) to get the return per annum. a being the first balance, z being the last balance and n being the number of years. For example … you start with 20k and end up with 320k after 24yrs. Total return = 320k/20k = 16 Return per annum = 16^(1/24) = 1.122 Which means it yielded an average of 12% p.a. As per your max drawdown… it should be the same money wise and percent wise. With percents you start with 1 then … If you make 10% then do 1 * 1.1 = 1.1 If you lose 10% then you do 1 * 0.9 = 0.9 To compare 2 strategies its better to compare percents. The probability of win, loss and the average $win and $loss then you can run montecarlo simulation. Max draw down (as you’ve done) is also a handy measure. After it’s good to keep in mind real world constraints (as you said) such as margin, liquidity and other stuffs. This assume you do compound returns.
Thanks for the response. Where you said, "As per your max drawdown… it should be the same money wise and percent wise," are you sure about this? I mean I'm 99% sure my curves are correctly calculated but as you can see, max drawdowns are vastly different in terms of magnitude and time of occurance. Here's how the curves are calculated. Imagine the price of NQ goes up by 100 points from 10,000 to 10,100 and the strategy is long. The dollar curve is going to go up by 100 times $20 (which is NQ's point value) minus commissions (commissions are far too negligible to impact the shape of the curve) The percentage curve is going to go up by 1% ((10100-10000) / 10000). This simplicity is what makes me so certain that the curves are correctly calculated. If you are saying that the max drawdown should be the same, the above calculation has to be wrong. Is it?
Do you care to explain the need for log? It's typically done to make the returns more normal for parametric statistical tests but for my purposes, I think simple returns are appropriate. Will you take a look at the calculations attached and tell me why log is needed and how the calculations are wrong without it? The blue and orange columns correspond to the percentage and dollar curves discussed in my main post above. Thank you.
I dont know what you're trying to do but with logs you get continuous compounding built in, they are asymmteric, and can add them to know where you're at. it's easier so if you make 30% log(1.3) = .26 lose 30% log(.7) = -.35 or if you start at 100 make 30 then lose 30% add them and you're down 9.4% = .26+ -.35