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An asset A is expected to yield a $2\%$ return with a standard deviation of $1\%$, and another asset B is expected to yield a $1\%$ return with a standard deviation of $1\%$. Discuss how you would allocate your budget between the two assets if their correlation is $1$, $0$, or $-1$.

In case the correlation between A and B is $1$, I would say that A and B have almost the same Beta ( I don't know to which extent this is true ), and in that case they have almost the same systematic risk ( risk inherent to the entire market ), and since they have the same specific risk ( $1\%$ ), we can assume that they have the same overall risk. In that case B is not adding anything to our portfolio so I would put everything in A since it has a greater expected return.

In case the correlation is $-1$, I assume we need to do some hedging, but I don't really know how to compute the weights that I should allocate in my portfolio.

In case the correlation is $0$, I assume we could use Markowitz optimization for example to find the weigths.

Your help is appreciated

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  • $\begingroup$ In all three cases, we are likely thinking about maximizing some measure of risk adjusted return (such as Sharpe ratio), and probably assuming that if the weight in A is w, the weight in B is 1-w (ie that we are fully invested in the two assets). In a case like this, we can use ordinary calculus to find the optimal value of w. $\endgroup$
    – Rylan
    Commented Dec 11, 2023 at 7:57
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    $\begingroup$ Remind me, what was that equation again for the optimal combination of 2 risky assets ? ;) web.stanford.edu/~wfsharpe/mia/rr/mia_rr5.htm $\endgroup$
    – nbbo2
    Commented Dec 11, 2023 at 15:19

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