Return vs. Leverage


an indicator that is used - and will certainly be observed by most subscribers here - is annual return. In particularly, it comes up in the portfoliomaker (nice tool by the way).

However, there are a lot of gambling systems around here. This makes the number easy to manipulate: leverage your system higher. If it works good (if not, you do not need to care anyway) it will look pretty fantastic even compared to other systems, which make exactly the same trading, albeit with a different leverage!

For this reason, I would find it very interesting, if there would be something like a leverage-neutral profit number (like profit vs. money-at-risk), but I am not an expert for these metrics. So any comment welcome.

I understand this very difficult with the large number of instruments traded here, but well… it would be a way forward…


Fully agree. Return alone should not be shown anywhere. What you should be looking at is annual return / max dd (Calmar ratio). Of course in young systems also Calmar can be misleading if the system has not yet experienced real losing periods.


yes, the Calmar ratio is one important measure.

But this is NOT what I meant, as it expresses only profit vs. risk.

Thus, it is good to compare different strategies for their risk appetite. This is not I mean here (though it is also important). What I am interested in is in particular to counter the effects of leverage.

Probably this is then more aptly described as: profit / money-used

(not money-at-risk, which I wrote earlier.)

What money used means is different for different instruments,

e.g., for futures it is margin, for stocks it is the money the stock.

Basically I want to abstract from the money in the C2-account which is not used. Because, if one account has $100.000 another $20.000 and they trade both with the same strategy (assumed, it fits within the 20.000) then they will have strongly different annual return…

although they are doing essentially the same thing.

And yes, the Calmar ratio is also important :wink:



"Probably this is then more aptly described as: profit / money-used

(not money-at-risk, which I wrote earlier.) What money used means is different for different instruments, e.g., for futures it is margin, for stocks it is the money the stock."

Klaus, I cannot agree with this for a futures definition. Margin is a terrible indicator of money used, especially the day trading margins. In fact, you should probably allow at LEAST 3-4 times REGULAR (not DAY) margin for futures.

Otherwise, the "Risk of Ruin" will suddenly become the most statistic. RoR is not IF, it is WHEN it will happen to practically every trader (especially including those who think it wil not be them)

Hi Index,

you are right in terms of: risk of an instrument. But this is not what I am interested here. (I agree, however, these are also very important numbers)

Please do not confuse the two things: I just want to have a leverage-free indicator. Just as well you could use: defined value of the future (i.e., eur(mini) = 125000 USD.

(then numbers are always larger than account size, but this would be still be fine).

(For example: you say: 3-4 times margin - I agree. But one supplier of a system may use 3, the other 4 - as a result the instruments will look dissimilar, even if they are identical)


Klaus -

I believe you are saying you want the total $ value of the instrument being traded, right? So, for example, if you trades 1 ES contracts, its value right now is ($50 * 850 = $42,500). If you traded this with an account of say $30,000, your leverage would be 1.4 to 1 (that is, you are holding 1.4 dollars in ES value for every dollar in your account).

I think that would be a good statistic to show. I have seen some "systems" with 30 to 1 leverage. They typically shoot up, and then fall straight down.


Thanks Kevin,

right. Showing total value of instrument would probably be a way to achieve what I am looking for (leverage-corrected-return).

I am exactly concerned about the overleveraged systems that kill themselves - and about the lack of comparability of systems that comes from these differences.


(1+APR)^(1/leverage factor)

(1+DD)^(1/leverage factor) will return the system to 1:1 ratios.

Be mindful that futures contracts are dependent on both the portfolio size, and the amount of dollar’s per point to get an accurate amount of leverage.

@Beau - and where do I get the "leverage factor" from?

A somewhat different approach, I have seen over at futures truth is that they normalize trades relative to margin used (we all know this is not a good risk measure, but it helps for relative comparison) and they do explicitly evaluate them as if no reinvesting would happen. (Countering effects of different scaling strategies.) - AT least they claim so.

Actually this would also be a good candidate for different possible charts. This is particularly the case when it comes to the "portfoliomaker".


I’m pretty old fashioned about systems. When I go to pick what I’m going to trade, I only pick one instrument, be it ETFs, Futures, options, or single stocks. Some ETF’s are higher leverage instruments than others. When you get into futures position sizing you can actually turn an unprofitable system into a winning system by overleveraging trades on winners and deleveraging on losers. The effect is either a big win or an overwhelming loss that decreases the numer of cars the system can buy that will make the system unattractive to current C2 users.

If you wanted to take a system down to 1:1 from, say 4:1 if they were trading QID and QLD at 192% of margin the way I do, you can take (1+APR)^(1/Leverage Factor). The key point to keep in mind is that the leverage factor is, as it’s used on, merely a normalization factor. When you go to compare other 1:1 systems, you’ll need to adjust the leverage factor to be comparable to the drawdowns of other 1:1 leverage systems. The point is, that even leverage by itself doesn’t tell the whole story unless you have some point of reference to compare to.

When you do it for options, you can take a percentage change in security over percentage change in portfolio and that would be your leverage factor. For example, say, I have a futures contract that makes 0.5% on the S&P, or about 4 points. Well, if that four points increased my portfolio by 20%, we’re talking about a leverage factor of 20/0.5 or 40:1. Leverage is always something people take out of context. Leverage by itself isn’t bad if used properly. It just needs to be in the context of the total portfolio, which, as it is used on and from what has been explained to me is their measure of single contract system profitability. There’s other ways to do it, but, in the context of [LINKSYSTEM_25716110] what’s different about the backtest and the real results is that relatively speaking the system started during a less robust period than what it had had in the beginning. Couple that with the leverage factor I use and you get an APR that’s below it’s long term rate, but as long as DD is in line this will still work at higher leveraged levels of capital. It just takes time to see how long it will be before the system lives up to it’s backtest, either for my system, or for any other vendor with a backtest that robust.

So, to summarize, the easiest way to get a leverage factor is to examine how much the percentage change in the most recent trade increased the entire portfolio by which percentage. Leveraged ETF’s might be a special case for this if you wanted to take it from the context of the 1:1 leveraged instrument from 2:1 leveraged instrument, but this overly complicates the simple way that most people would understand, which is just ( percentage change in portfolio )/ ( percentage change in trade ). By this measure you’ll get to see that there are too many futures systems on this site that have no reasonable basis for taking on this much risk, and, even if they have been profitable, you’ll find that the risk of ruin is significantly higher b/c it is a matter of goosing a curve rather than any indication of trading acumen.

Another way which is probably more tedious is to take the notional value of the contracts, multiply them by their point value, and divide into the equity curve.

For example, at 60 contracts, 866 points per contract, $50/point, the notional value comes to $2.598 million. Then, all you’ll need to see is the current portfolio value. So if the portfolio is $200,000, then the leverage factor is 12.99 or about 13:1. You’ll then need to decide based on the systems APR if you’re going to trade half as much, which will get it down to (1+13)^(0.5) for a factor of 3.74. Do this for the Drawdown as well and you’ll have a better idea about how to properly scale such a system. There are several ways of doing it, and the special cases apply to Futures, Options, and some ETF’s. The rest will usually be below 2:1 leverage and will follow that percent change in portfolio over percent change in security factor. It is then up to you to decide how to “compare” the calculated leverage factor in the context of its competitors.

So, using the 12.99:1 leveraged system, if there’s a system you find with the lower DD and lower APR after a reasonable period of time using lower leverage factors, you can say that that system is more efficient. And, if the system has less DD, you can use excel with goal seek to find the “normalization” factor that makes the system comparable to the other one. In this case, the higher leveraged system with higher APR’s and DD’s is not as efficient as the system with lower APR’s and DD’s if when you solve for the leverage factor that makes the system’s DD identical you find that the higher APR system actually had lower risk adjusted returns, we can say that that system isn’t as good as the system with lower leverage. It’s because we’ve found that the returns are only due to leverage, rather than trading prowess. Solving for the DD leverage factor that gets the higher DD higher APR system or even lower APR system down to the same DD values will allow you to say absolutely rather one system is better than the other.

It’s quite complicated, but really this stuff isn’t even covered in textbooks or even in the CFA curriculum, so, if it’s confusing, just think about it for awhile. All you’re trying to do with the “leverage factor” is make system DD’s comparable then taking that leverage factor to the APR and seeing which is higher. This will tell you who the better trader really is. The last point to remember is that this also assumes the system started around the same time. This doesn’t work in reverse, but a system younger than another with less DD and higher APR is comparable. It does not have the same ramifications in reverse to say an older system with more DD and Less APR is better b/c the two time periods are different. Mainly this is a better context for comparing the younger system to the older system, but we could just conclude that the older system with more DD and Less APR is not beneifical, but, in the end, it will come down to ease of use of the service and profitability.

Dear Beau,

it is clear it can be done. The initial discussion was simply about having this as part of the statistics here on the website (this is what the forum is about: proposals for features).

You can reverse engineer these numbers from the actual trading behavior of a system. And actually you have to, as without having a leverage-neutral return indicator, the comparison of systems on this website is not very meaningful. (or at least very hard)



I agree. But what we really get to is the Calmar Ratio of APR to DD. The leverage factor is more of a normalization factor. So when we see system1 with 35% APR and DD of 10% and system2 with 7% DD and 25% APR, when we solve for the factor that makes (1+DD system 2)^x=(1+.07)^x=(1+DD system1)=(1+.1), then x=1.4080. This implies that if you employed a higher degree of leverage with the system, then system 2 actually has a higher Calmar Ratio at 1.25^(leverage factor obtained from equating the system’s DD’s with each other based on a normalization factor)=1.25^1.4080=1.3691 and we conclude system2 is actually the better system that can “leveraged up” by a factor of 1.4080. So if it’s position size was 100% of equity on the ETF or security it trades, all you would have to do is trade 1.4080 times the current position size to 140.8% of equity.

It really comes down to the Calmar Ratio, and this type of analysis is a bit too customized to have on the site. There have been previous discussions on this subject that all ended with nothing happening b/c it’s too complicated and there’s some subjective estimation involved to make it useful for everyone.

In the end, I find excel is fairly useful for solving for the Normalized Calmar Ratios described above.