Trying to understand my risk (Kelly/Sharpe/ROR/Drawdown Questions)

Discussion in 'Strategy Development' started by MustPlayOptions, Jun 10, 2006.

  1. Hi Everyone,

    This is my first post here as I’ve just recently discovered this site and I'm new to much of this so please forgive in advance any rambling or unclear statements. If I'm unclear about anything I'll try and clarify if asked. All answers/responses are greatly appreciated. The post turned out to be much longer than I thought (4 pages in Word) so will be broken up.

    So I came up with a tiny little system that in backtesting over 5 years and in actual use over the last 1.5 years has been performing well. It rarely trades so it's really nothing to write home about but I'm using it to learn about systems. It's option based and designed to catch volatility using diagonal calendars that are entered based on very strict criteria. Since it's diagonal calendar option based, it brings up a couple of questions about risk. In addition to those questions I have others as well as below.

    I've also been trying to read a lot about money management here and elsewhere. Before that though, I was pretty happy with my analysis of the strategy and comfortable with the risks. I had looked at risk almost strictly from a risk-of-ruin standpoint because I think drawdown is inadequate.

    The reason I say this is because if you have a volatile strategy that just never happens to have several losers in a row on backtesting - you won't see a drawdown that could ruin you. The other problem I have with drawdown is that I can see how having multiple open positions might mask a large drawdown if losses coincided with simultaneous gains. With ROR the potential masking effect isn’t there. By concentrating on risk of ruin I feel you can be more assured of not losing all of your capital.

    The two questions that come up are:

    1) What exactly is considered “at-risk” during a trade?
    2) If I’m wrong about my comparison between ROR and drawdowns – why?

    Since the trade is calendar based - there is an amount of capital required to open the trade, but in actuality if the underlying moved an extreme amount – you could lose the initial capital plus the difference in strikes. I chose to use the latter for my %Return values to be conservative.

    Another amount that could be considered “at-risk” would be based on the exit criteria. The trade is supposed to be exited on the first day that the trade loses 2k or before it gets too close to expiration. In actuality – the biggest loss was a little over 3k, but it would be extremely unlikely to lose everything since a stock would need to lose >50% in one day of it’s value just to lose the initial capital (not including the extra 5k).

    I know this is very possible, even if unlikely, and in fact periods of high anticipated volatility (not including earnings which is an exclusion), usually are partial setups for the trade. So while possible, it’s very unlikely that the entire “at-risk” amount is truly at risk.

    This question can be extrapolated to stock trades as well. Let’s say a system trades Google and used 1000 shares at a cost of $400. If the system being used theoretically exited with a stop-loss of 2k which would imply realistic loss “max” of 6k, but was at risk of a 8-10% or more loss (approximate historical max loss on Google) – it’s nearly impossible for the value of the position to go to 0 - it would require Google going bankrupt overnight without any warning – and even then it would be worth maybe a dollar ;). It’s not unheard of though for stocks to lose 50% of their value in a day.

    So in this case what would be “at-risk”? Would it be the full $400k, $200k, $40-$50k or 6k? Given what happened when the CFO misspoke and it plummeted 30 points in 2s, I would be tempted to say the 40-50k, but being more conservative I would probably say 200k. I’m curious to hear what everyone else thinks. At first glance this may not seem to matter because the %Return would of course be based on the full 400k, but if you are using margin for the plays – then the amount at risk is very relevant. I think it’s also very important because, to me, the amount “at-risk” could really be considered the actual “bet size” when looking at position size.

    If you consider your bet size to be the “at-risk” amount, then the amount of capital required increases dramatically compared to if you only look at the average max loss and even the historical max loss.
  2. Now back to the option strategy – it has the following characteristics (some are rounded for clarity):

    Avg EV: 731
    Avg At Risk (Cost + 5k): $14,500
    Max At Risk (Cost + 5k): $40,500
    Avg Return (from at-risk): 5%
    %Winners: 77%
    %Losers: 23%
    Avg Win: 1,400
    Avg Loss: -1,544
    Max Win: 3,400
    Max Loss: -3,200
    Max Drawdown: -3,600

    Std Dev: 1,480
    Sharpe: 0.49
    Kelly Fraction: 52%

    ROR with BR 7,000: 0.95%
    ROR with BR 30,500: 0.0000002%

    99% Confidence Interval of Returns: 130-1,300
    p-value (looking at returns vs 0): 0.0021

    Note that the ROR here is not a trip ROR but a lifetime ROR. Trip ROR would be smaller. Position size is always based on 10 contracts per leg as smaller positions would lose too much from commissions/slippage. Backtesting was done by hand over 5 years.

    Initially – I didn’t look at the Sharpe or Kelly fractions at all but they raised some questions I’ll get to when I did. I calculated the last 2 values to see if the strategy was performing better than chance and based on these values it is. After reading more on this site, I have yet to see anyone look at a trading system from this statistical approach and that Martingales (e.g. the edge test) are sometimes used but more often it seems to be equity curves. You theoretically could have a positive equity curve but not a statistically significant edge and I’m trying to learn more about Martingales and the edge test as I understand it is based on comparitive random sampling.

    Now I’ll get to the other questions. First let’s look at some key values:

    Avg At Risk (Cost + 5k): $14,500
    Max At Risk (Cost + 5k): $40,500

    ROR with BR 7,000: 0.95%
    ROR with BR 30,500: 0.0000002%

    The first thing that you’ll notice is that the chance of Ruin is small with only a 7k bank. If you leveraged enough to have the full 30.5k cash at hand to be able to open any position that comes up – you still have a very small chance (1%) of losing everything.

    Looking at the Sharpe and Kelly values though, you would never have guessed that the above paragraph was true. Based on the Sharpe value, the risk/reward ratio is not that great. Based on Kelly – you should only put at risk 52% of your capital. If you have only a 7k bankroll, then you would open a position with no more than $3,650 at risk which would actually not even cover the 5k diagonal part and if you ignored that then you would only be placing 50% of the possible trades. If you wanted to be able to Kelly bet the “at-risk” amount you would actually need a $77,900 bankroll. This would reduce your rate of return significantly. Looking at return per trade % based on bankroll it would decrease it from 10.4% with the 7k bankroll to 0.9% per trade. Even if you used a 30.5k bankroll which would take a lifetime to ruin, the return is reduced to 2.4%.

    Most posts I’ve read have said that Kelly betting is high if not way too high, and yet even by borrowing 335% of your bankroll to augment it – your risk is still less than 1% of losing all of your bankroll - ever. Kelly betting is supposed to maximize the log of your bankroll’s growth rate, and yet if you follow ROR instead, your bankroll would grow much more in this case. Even if you started with the more conservative 30.5k.

    Now I know not all systems work forever and there could be a total breakdown of the system, but still the two methods of looking at risk: ROR vs. Kelly seem to give very contradictory results. So finally my next questions:

    3) What am I missing? I.e. Why aren’t people using ROR calculations directly instead of or in conjunction with fixed fractions or proportional betting?

    4) Why is the suggested bankroll for ROR so different and “more aggressive” and yet statistically very safe? I.e. Is there more risk than what the ROR calculation is implying?

    5) How should the “at-risk” amount come into play with position sizing?

    This last question arises because neither ROR nor Kelly take this value into account. With the example of the 7k bankroll and even the 30.5k bankroll – you could lose the entire bankroll in one trade even if it is statistically very unlikely given the stops and percent move required to do so. That would obviously be a disaster and important to avoid but any investing is risk so how important is it to consider this when other signs – in this case ROR, but with expensive stocks it may be others - suggest that the “at-risk” amount could be set aside from consideration.

    I’ve been thinking a lot recently about the money management side of trading systems because hopefully someday I’ll find another strategy that will work. I still have to read about the “Turtle” money management system, but I got stuck on these questions first. I’m trying to get a feel for how the allocations for the various strategies will work – especially if one is infrequently traded compared to another reason why the “at-risk” questions are important to me.

    Thanks to anyone who actually made it through this post and thanks again in advance to anyone who takes the time to answer.

  3. Thank you :)

    This is definitely related to my questions and it looks like I have a whole new subject to read about now.

    I'm still curious to see if anyone else looks at ROR instead of historical drawdowns as a measure of the potential risk to capital and if that's used by anyone when determining how much bankroll is needed for a strategy, or how big of a position per trade to take.

    Thanks again,
  4. It seems some might have a (mis)concept(ion) of applying the same for each trade based on total capital. However, I guess some other traders would consider using a reasonable fraction of kelly for each additional trade, and each additional trade is based on the Reducing Balance of capital after total existing trades. Just 2 cents.
  5. Value at Risk example with above data:

    So if I'm using the Var-Covar and I understand it correctly, then I would expect my 99% confidence max drawdown to be:

    Max Drawdown (99% Confidence): 731 - 2.33*1,480 = -2,717

    Is that correct?

    In my data 4.5% of the trades had losses greater than that so that probably implies that the returns are not normally distributed - correct?

    So now that I have a name for what I was looking at - the next thing I'll need to look at is the VaR implementation aspect since that's the other subject of my questions.

    It's not clear that many people are actually using the VaR for position sizing though and it's more like you said that the position sizing seems to be mostly determined by the Bankroll size.

    Maybe I'm just misunderstanding but it seems to me that VaR could (should?) be a significant factor in determining necessary bankrolls or position sizes for a strategy.

    Kelly as far as I can tell is unrelated to VaR and the Sharpe isn't really directly related/proportional.

    Sorry for the rambling but is anyone using VaR as a consideration in their strategy allocation and position sizing?

  6. I also would like to learn the input and comments from others here. You're welcome to let us know your progress/ findings anytime. Bye.
  7. The other interesting thing to note BTW is that let's say we decided to use the Var/Covar method of VaR measurement or even the max drawdown to determine our core bankroll for this strategy (but we had as much leverage as needed to open positions). (The historical VaR in this case is the same as the max drawdown btw).

    Let's also say we are comfortable with a 99% chance that we won't lose everything.

    Both max drawdown and VaR suggest that a bankroll of <$4,000 should do the trick. If you calculate the ROR however of a $4k bankroll then your ROR is actually 7%!

    So at least in this case it seems that VaR and Max Drawdown are inadequate.

    I guess I'll have to do more research now that I have some terms to use to see if there's more information about using ROR and VaR for position sizing/portfolio managing.

    None of these seem to take into account the "worst day possible" information either which is interesting and a little scary.

    I'm still very interested in hearing any comments/suggestions.

  8. So in this case are they reducing the balance of capital based on the cost of the open trades or the value-at-risk of the open trades?

    Maybe that's where it's coming into play...

    Thanks for your replies,