0
$\begingroup$

Lets say you get to choose any 2 stocks.

Is it possible that a portfolio can be built from the two stocks (long or short either, any weighting) that has a lower volatility (standard deviation of movements), and simultaneously higher percent return than either of the two underlying securities alone.

I want to say yes, but I think the answer is no. In the event of a correlation of -1 between A and B:

A: a stock with high stddev, and small positive return

B: a stock with same stddev, and small negative return

Long A short B = much higher returns, much higher stddev

Short A Long B = 0 return, 0 stddev

I currently have an infinite loop randomly building portfolios to test this at home. Bonus: Is it possible with a portfolio with more than 2 stocks in the portfolio?

$\endgroup$
1
$\begingroup$

$X$ and $Y$ perfectly correlated with same vol. So $X-Y$ has no volatility at all and for any $n$, $n(X-Y)$ has still no volatility.

If $r_X > r_Y$ are returns of $X$ and $Y$, then $n(X-Y)$ has return $n(r_X-r_Y)$ which can be as big as you want with $n$ big enough.

$\endgroup$
  • $\begingroup$ Something like this can happen accidentally in a large problem if your input data is crappy, and that is one reason why people sometimes put in a long only constraint before running the optimization. $\endgroup$ – noob2 Aug 31 '16 at 14:48
  • $\begingroup$ Sorry, I do not fully understand your solution. Are you making assumptions about the securities? n appears to be a multiplier here, which is not relevant to the problem. if it is a weight it should be (n)(x)-(1-n)(y). $\endgroup$ – will kinsman Aug 31 '16 at 15:34
  • $\begingroup$ Let A and B have same variance, correlation 0.9999. Return of A 10% a year, B 5% a year. Then for example let w1=1001 and w2=−1000. Then w1+w2=1 and you make approx 1000 times the difference in return between the two securities i.e. 50% a year. $\endgroup$ – noob2 Aug 31 '16 at 15:43
  • $\begingroup$ Understood, so the return can easily be higher, and as long as (A-B) has lower volatility then either A or B then the second condition is fulfilled, implying that it is possible. Thanks! $\endgroup$ – will kinsman Aug 31 '16 at 16:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.