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Consider a portfolio which consists of two assets.The returns of the assets are normally distributed withN(0:12;p0:15)andN(0:1;p0:25). The value of portfolio today is $110 million .

Consider a portfolio which consists of two assets.The returns of the assets are normally distributed withN(0:12;p0:15)andN(0:1;p0:25). The value of portfolio today is $110 million . Sup-pose the time horizon is 15 days and the covariance matrices aregiven byS1=0:15 0:20:2 0:25andS2=0:15 0:00:0 0:25:a) Let the shares of assets be:x1= 0:55;x2= 0:45calculate VaR at2% probability and forS1? Show your calculations explicitly. b)Let the shares of assets be:x1= 0:55;x2= 0:45calculate the Value atRisk (VaR) at 1% probability forS2. c) Let the shares of assetsbe:x1= 0:45;x2= 0:55calculate VaR at 2% probability and forS1d)Let the shares of assets be:x1= 0:45;x2= 0:55calculate the Value atRisk (VaR) at 1% probability forS2. e) Let the shares of assetsbe: x1= 0:55;x2= 0:45 what is the probability that the end of yearloss is more than $10 million forS1? f) Let the shares of assets be: x1= 0:45;x2= 0:55 what is the probability that the end of year loss ismore than $10 million for S2?

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