bv_cvxbook_extra_exercises

# We can invest in two stocks the rst stock doubles in

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Unformatted text preview: squares of the price volatilities of the assets, are known. For the oﬀ-diagonal entries of Σ, all we know is the sign (or, in some cases, nothing at all). For example, we might be given that Σ12 ≥ 0, Σ23 ≤ 0, etc. This means that we do not know the correlation between p1 and p2 , but we do know that they are nonnegatively correlated (i.e., the prices of assets 1 and 2 tend to rise or fall together). Compute σwc , the worst-case variance of the portfolio return, for the speciﬁc case x= 0.1 0.2 −0.05 0.1 , 0.2 + + ± + 0.1 − − , Σ= + − 0.3 + ± − + 0.1 where a “+” entry means that the element is nonnegative, a “−” means the entry is nonpositive, and “±” means we don’t know anything about the entry. (The negative value in x represents a short position : you sold stocks that you didn’t have, but must produce at the end of the investment period.) In addition to σwc , give the covariance matrix Σwc associated with the maximum risk. Compare the worst-case risk with the risk obtained when...
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