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Suppose you have two highly correlated risky assets.

Correlation coefficient: 0.9

Volatility: Asset 1 price varies 2.5% /day Asset 2 price varies 5% / day

What can be done to do reduce the risk and increase the return?

Consider how to weigh each asset (ex. 50/50, 60/40, 80/20) and the possibility of leverage or shorting (if necessary).

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  • $\begingroup$ What have you tried so far? $\endgroup$
    – Kermittfrog
    May 4 at 6:00
  • $\begingroup$ Ive tried a simple portfolio of 50\50 but i feel more optimization is possible. $\endgroup$
    – Andrew Richmond
    May 4 at 11:46

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The variance of the linear combination of returns $(\omega_{1} \times ret_1 + \omega_2 \times ret_2) = $

$\omega_{1}^2 \times \sigma^2(ret_{1}) + \omega_2^2 \times \sigma^2(ret_{2}) + \omega_1 \times \omega_2 \times \rho_{1,2} \times \sigma(ret_{1}) \times \sigma(ret_{2})$.

You have the variances and the correlations and the standard deviations. So, you can put those in and take the derivative with respect to $\omega_1$ and $\omega_2$ to hopefully find the minimum.

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  • $\begingroup$ And what about weighting of the two assets and weather to apply leverage or shorting? $\endgroup$
    – Andrew Richmond
    May 4 at 21:59
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    $\begingroup$ The weights are the values of $\omega_1$ and $\omega_2$. But, with that correlation, my guess is that the result is going to be put most of your weight in the stock with the smaller variance But maybe it would short one of them in order to use the positive correlation ? This is why it's probably best to have some estimate of expected returns. This way you could trade off between the return and the variance. $\endgroup$
    – mark leeds
    May 5 at 3:50

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