# Puzzler on construction of a 2-stock portfolio

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?

$X$ 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.