Hi all, Hoping someone can help me out with something thatâs been vexing me for some time. Basically, Iâm wondering how to figure out how much portfolio exposure one would generally need to generate a certain yearly return. I know there are tons of caveats here, but itâs pretty obvious that the odds of generating a 10% yearly return on $100mm dollars with a one lot of e-miniâs are pretty slim. I size positions using the âPercent Volatilityâ method: X% Vol Postion = (X%*Trading Capital)/($Value of an average dayâs range) $ Value of a Dayâs Range = 21-day Average True Range x $Value per point So, for example, if the average range in ten year note futures was 1 point, I was trading $100mm, and I wanted a 2% vol position, I would need to buy (.02*100mm)/$1000 = 2000 lots. To keep it simple letâs just pretend for now Iâm only running one position. So if Iâm tasked with making saying 12% a year, while maintaining a Sharpe ratio of 1.5, and Bondâs have a historical volatility of X, what formula would I use to determine what %Vol position I would need, on average, to make these numbers? Thanks so much! - MD
There is something I do not understand : haven't you figured out your position sizing, risk-adjusted returns, from previous trading experience. Surely, you did not jump from zero trading to 100m in one go. Just in case that's the case, the investor is an idiot who deserves to lose his money.
If you assume realized vol = historic vol, then 68% of the time the return on the asset will be +- that #. So if hist vol of bonds is 12% annualized, your expected ret will be between -12% and 12% (assuming no carry). If those bonds earned 4% a year, your expected return will be -8% to 16% within the 1st standard deviation range. A bit oversimplified, but that's what you're looking for. If you are managing 100k, if realized vol = implied vol on S&P at ~12%, all you need is 100k of S&P to most likely hit your goal on 16% of the time [1- (50% (mean) + 34% (1 std dev)) ]. Increase your leverage to move the result's place on the distribution. By the way, that example assumes no dividend carry for simplicity. To factor in dividend, just shift the distribution (so it increases your odds from 16% of the time to a higher probability on the same leverage).
You can solve this as a "constrained optimization problem" using Excel Solver. You can setup Excel solver as follows: Objective Function: Maximize probability of hitting target return (12%) By Changing Cells: Portfolio Volatility Under The Following Constraints: 1) Sharpe Ratio = 1.5 2) Target Return = 12% 3) Mean Return = 0 Of course, this all assumes that the market returns are normally distributed, when in fact, market returns are often non-normal. (i.e. leptokurtosis) -- <a href="http://www.optionstack.com"> Options analyzer </a>