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I apologize if similar question has been already asked.

I have to find optimal weights $w_F,_I,_M$ for the assets $F, I, M$ in the portfolio.

$E(r_F) = 0.03$

$σ_F = 0$

$E(r_I) = 0.2325$

$σ_I = 0.5$

$E(r_M) = 0.12$

$σ_M = 0.2$

$ρ_I,_M = 0.9$

After computing the $σ_p^2$, I get: $0.0225 =0.25w_I^2 + 0.04w_M^2 + 0.18w_I,_M $

So I also know that $ w_I + w_M + w_F = 1 $, but I can't get optimal values nevertheless. Any ideas?

Svit
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  • You could do it in two steps. (1) There are 2 risky assets, these define an efficient frontier. (2)The third asset is a risk free asset. Find the tangent from this asset to the efficient frontier. The point of tangency is the unique OCRA (optimal combination of risky assets) – Alex C Aug 28 '19 at 16:10
  • I've seen this requires calculating all possible weight combinations in Excel. I have to do it on exam, so is there another way? – Svit Aug 28 '19 at 16:45

1 Answers1

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I recommend having a look at this pdf, it outlines how to determine optimal weightings for n risky assets with linear algebra methods. The crux of the problem is that you must solve for the partial derivatives with respect to each weight, for 0 with the constraint of the sum of the weights = 1. This can be solved as a constrained optimisation problem / linear programming problem. Or, if you're looking for a quick answer, the pdf outlines a simple matrix operation to find the optimal weightings.

Hope this helps

Xenarc
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