Introduction to D-VaR Position Sizing (Part 1)
Position-sizing is the least exciting topic in trading. We all find ourselves too busy looking for the ultimate trading strategies or indicators to bother with spending time thinking about how much to bet. Contrary to what you might think, figuring out how much you should bet is not just a matter of determining your expected edge. Unlike casino games with defined odds, markets are uncertain and adjusting for the unexpected tail loss is just as important as adjusting for the expected size of your edge.
This concept is not new to hedge funds, and to those that trade for a living; They often think about risk first because their continued existence depends on staying in the game. For this sophisticated bunch, position-sizing, diversification, and hedging are the cornerstones of their risk management approach. Many of them are well aware that initial stop losses (in contrast to trailing stops which are very useful) are highly overrated as a means of managing risk–and if used improperly will increase your chances of going broke. This is because if they are placed too tight they will protect you from tail risk but expose you to more noise. If they are place too far the reverse is true– especially with unexpected gaps. The tradeoff is simple: death by one severe blow, or death by a thousand cuts. Finding the optimal balance is very difficult. Initial stops are not sufficient to manage risk by themselves and function much better when they are integrated with other risk management tools. In contrast, position sizing is very useful since you a) don’t face timing risk and b) can only lose what is invested–if you bet 5% of your portfolio no surprise gaps will lead you to losing more than you have bet.
To the best of my knowledge, I do not believe that this particular position-sizing method has been published somewhere before. However I do know that it is based on the well-known concept of “Value-at-Risk.” From Investopedia this is defined as follows http://www.investopedia.com/terms/v/var.asp:
A technique used to estimate the probability of portfolio losses based on the statistical analysis of historical price trends and volatilities.
VaR is commonly used by banks, security firms and companies that are involved in trading energy and other commodities. VaR is able to measure risk while it happens and is an important consideration when firms make trading or hedging decisions.
VAR Position- Sizing DJIA 1928-Present | |||||
Gross | worst daily | ||||
Sharpe | CAGR | SD | loss | ||
Buy and Hold | 0.24 | 4.5% | 18.4% | -22.6% | |
D-VAR 1% risk | 0.45 | 5.2% | 11.5% | -7.6% | |
D-VAR 1.5% risk | 0.41 | 6.9% | 16.7% | -11.4% |
Interesting idea David – I assume you’re doing this calculation and adjust position size on a rolling basis? Meaning, you calculate daily returns – I take it you are looking at all the returns available? So, if I’m 50 daily bars in from 1928, I’m looking at 50 bars of daily returns, and if I’m 300 daily bars from 1928, I use 300 daily bars? Or are you using a fixed lookback period?
Thanks!
hi damian, glad to hear from you. yes the position size is adjusted everyday on a rolling basis.
best
dv
to clarify further you are always taking a rolling 50-day sample, you are not learning from 1928 cumulatively.
best
dv
Hi David, how is this method superior to using a 50-day % ATR type of stop method which would also take into account any fat tail risk?
Excellent – thanks for the clarification. Very good idea btw. I take it, by the 5th percentile, you mean the bottom 20% of returns over the 50 days?
hi damian, thanks very much. in excel you would use “percentile, 5%”, in calculation terms this would be roughly the average of the lowest 2 and lowest 3 values.
dv
Value-at-Risk tends to be proportional to historical volatility, and S&P has published some research on “S&P 500 Risk Control Indices” (can Google this term) . JPMorgan is creating an investable product: http://apps.shareholder.com/sec/viewerContent.aspx?companyid=ONE&docid=7024905 .
hi quant, indeed this is true. one sees a direct relationship between the magnitude of the 5th percentile and HV.
dv
Hey DV and all, the summary stats here looks to me off based on my own experimentation. DV have you posted the spreadsheet anywhere? I would love to take a second look. Good work DV and good comments from the community!
K
Not sure this table will come out but here’s the results of my implementation of David’s idea back to 1901 (Pinnacle data). It seems to support David’s conclusions.
Cuml. Return Biggest Down Day
Decade Dow BH 1.00% 1.50% Decade Dow BH 1.00% 1.50%
1900s 46.97% 48.86% 63.03% 1900s -8.29% -5.71% -8.56%
1910s 47.78% 25.87% 34.99% 1910s -7.24% -6.31% -9.47%
1920s 131.73% 142.38% 260.09% 1920s -12.82% -4.06% -6.08%
1930s -39.54% 4.25% 2.89% 1930s -8.40% -4.27% -5.52%
1940s 31.71% 32.41% 44.71% 1940s -6.80% -6.48% -9.72%
1950s 240.58% 229.17% 434.87% 1950s -6.54% -6.82% -10.24%
1960s 19.42% 20.78% 21.07% 1960s -5.71% -3.88% -5.82%
1970s 3.38% 2.51% -2.85% 1970s -3.50% -3.12% -4.68%
1980s 239.35% 175.90% 317.94% 1980s -22.61% -7.58% -11.37%
1990s 317.59% 249.11% 461.61% 1990s -7.18% -4.96% -7.44%
2000s -9.30% 3.19% -1.16% 2000s -7.87% -5.09% -6.59%
Decades Bettered the Dow:15 7 14 8
Thanks Jerry, good work and thanks very much for sharing. Getting good data is always an issue and Pinnacle is a very good source. I’m glad someone was able to replicate the study conclusions. I will have to take a closer look shortly.
best,
david
Can D-Var position sizing be used for intraday futures trading. For example, last month we had about 100 turns, average time in trade was around 15 minutes.
Hi David, I was deep into position sizing research, aka learning, when I came across your intersting article. A few questions if I may:
1. I presume your DJI comparison tests were simulating daily trades (Close to Close) against buy and hold, in order to get a feel for the theory.
2. Do you think that finding the 5th Percentile of only the loss trades would be better; downwards volatility is usually worse than rising volatility.
3. The length of look back time affects the position size due to accuracy of the 5th percentile, in some cases make the positions very small nost of the time. How might you overcome this?
Thanks!
hi, yes it is close to close. the 5th percentile is the worst 5% of daily returns so that does address your good point. in this case the lookback is intermediate to be sensitive enough to adjust quickly to changes in tail risk. this allows greater leverage when tail risk is low. the leverage is indeed more conservative than a lot of methods, and this can be offset using a trend filter. good comments.
best
dv
hi dv.
do you have an email for a private chat on this?
hi there, dmvaradi@gmail.com
best
david