You expect a Sharpe of 12% unlevered, yes? Perhaps this is obvious, given you've returned nearly 100% on your starting capital.
Well Sharpe Ratio is return over risk; so it should not be affected by the amount of leverage you are using. With a 25% annualised vol target, and an expected Sharpe Ratio of 0.5, my expected return is 12.5% a year with the leverage I've got (I talked about leverage in another post; I think its a poor measure of risk). Yes I've made a lot more than that this year (350K on 300K starting capital), for two reasons: - I was running a higher than 25% annualised vol target, and with more capital at risk, for much of the year. - It's been an exceptionally good year. Even if I'd had the same vol target all I would have made around 57% on my starting capital.
Given that it's been such a great year, does that make you nervous that your 25% vol estimate might not be a good estimate (or that, say, its 95% confidence interval might be wider than you think?) In other words, what would be the probability of earning 150%, given you expected 12.5%?
To be precise I target 25% annualised daily vol. So its the daily vol I'm targeting, not the annual vol. Because of time series correlation, the two might not be the same. Also I get a new figure for daily vol every day, so its easier to know if its in line. I watch my daily vol like a hawk. My vol estimates are pretty good. I've never had a 3 sigma day, up or down. I'm very comfortable with that. A better test is to say what is the probability of making 56%, given a 25% sigma, since that abstracts away from the change in my risk target (to repeat 56% is what I would have made if I hadn't adjusted my risk target throughout the year). The answer depends on your underlying Sharpe Ratio, which is unknown. I use 0.5 as a conservative figure. But the backtest, using robust out of sample fitting, comes in at 0.9 Sharpe. If the true Sharpe Ratio is 0.5, then the chance of making 56% is around 4%. If the true Sharpe is 0.9, then the chance of making 56% is 10%. So what we have is eithier a one in 25 year return, or a one in 10 year return. (This assumes a normal distribution, which for annual returns is probably okay). So my true Sharpe is probably higher than 0.5, but I'm comfortable with this as a conservative lower bound.
Doesn't this provoke an interesting question. Is this risk profile really suitable for an individual? I can see a fund comprised of long term investments of a small % of liquid net worth tolerating multi year drawdowns or lackluster performance on a strategy which ought to outperform in the long run. Yet "in the long run, we're all dead." I think a strategy which either doesn't trade frequently enough or doesn't capture enough advantage per trade to recover to new equity highs quickly is very hard for an individual to cope with while those who can afford to take a longer term view may find it more valuable. Would be interested in your thoughts on this. I have always viewed trading as being on a continuum from insolvency to retirement. You haven't made it until you've taken your chips off the table for the last time. Although there are always some who are clearly a lot closer to making it than others. Have heard too many stories of blow ups, suicides, etc even amongst multi decade veterans. Flash crashes, errors in judgment, vice, human nature, complacency, or just old man vig. The successful traders I know all seem to have an undesirably high emotional exposure to their P&L - which persists well beyond the period of any initial doubts about whether they can make it in this business. There is the eternal trade off between having too much capital exposed - or the equally dangerous having too little exposed which then forces you to spend more time in the markets as you didn't capitalise on the opportunities available. It seems people are sensitive to risks to capital but not appropriately sensitive to risks to time. I would have liked to have realised this earlier in life. Speaking personally I have found a generalised anxiety arising in periods of poor strategy performance. It can affect how one views their overall competence and must be guarded against. In later years I determined that it was preferable to turn off the more marginal but still +EV strategies and keep the strategies which make higher and more consistent returns per contract traded. Somebody else can have the more marginal stuff because the cost in anxiety is not worth the increase in performance.* So one can end up with a strategy which trades less but is very very consistent. For you, it appears you are capturing an effect which requires long duration of market exposure and therefore this is not an option for you. Thanks for your contributions, always interesting to see how others are doing things. * - yet in making that trade off I am again exposed to more years in the market to achieve a goal - but otherwise "the game isn't worth the candle"