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Unformatted text preview: squares of the price volatilities of the assets, are known. For the oﬀdiagonal 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 worstcase 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 worstcase risk with the risk obtained when...
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 Fall '13
 F.Borrelli
 The Aeneid

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