Need a portfolio math geniuses help.

[mgdpublic]

Hi all,
Hoping someone can help me out with something that’s been vexing me for some time. Basically, I’m 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 it’s pretty obvious that the odds of generating a 10% yearly return on $100mm dollars with a one lot of e-mini’s are pretty slim.

I size positions using the “Percent Volatility” method:

X% Vol Postion = (X%*Trading Capital)/($Value of an average day’s range)

$ Value of a Day’s 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 let’s just pretend for now I’m only running one position. So if I’m tasked with making saying 12% a year, while maintaining a Sharpe ratio of 1.5, and Bond’s 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

 

[smallStops]

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.

 

[scriabinop23]

Hi all,
To keep it simple let’s just pretend for now I’m only running one position. So if I’m tasked with making saying 12% a year, while maintaining a Sharpe ratio of 1.5, and Bond’s 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

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).

 

[mgdpublic]

If you are managing 100k, if realized vol = ~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)) ].

Thanks for your answer. Would you mind walking me through this part?

 

[optstack]

Hi all,
Hoping someone can help me out with something that’s been vexing me for some time. Basically, I’m 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 it’s pretty obvious that the odds of generating a 10% yearly return on $100mm dollars with a one lot of e-mini’s are pretty slim.

I size positions using the “Percent Volatility” method:

X% Vol Postion = (X%*Trading Capital)/($Value of an average day’s range)

$ Value of a Day’s 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 let’s just pretend for now I’m only running one position. So if I’m tasked with making saying 12% a year, while maintaining a Sharpe ratio of 1.5, and Bond’s 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

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)

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