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and s-= [ 3. 3. (35pts) Consider a portfolio which consists of two assets. The returns of the assets are normally distributed with N(0.12.V0.15) and

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and s-= [ 3. 3. (35pts) Consider a portfolio which consists of two assets. The returns of the assets are normally distributed with N(0.12.V0.15) and N(0.1, 0.25). The value of portfolio today is $110 million. Sup- pose the time horizon is 15 days and the covariance matrices are given by Si- 0.15 0.2 0.15 0.0 0.2 0.25 0.0 0.25 a) Let the shares of assets be: 01= 0.55, 22=0.45 calculate VaR at 2% probability and for si? Show your calculations explicitly. b) Let the shares of assets be: 01=0.55, 2n=0.45 calculate the Value at Risk (VaR) at 1% probability for $2. c) Let the shares of assets be: x1=0.45, 12=0.55 calculate VaR at 2% probability and for std) Let the shares of assets be: x1=0.45, r=0.55 calculate the Value at Risk (VaR) at 1% probability for $. e) Let the shares of assets be: x1=0.55, #2=0.45 what is the probability that the end of year loss is more than $10 million for s'? f) Let the shares of assets be: x=0.45, 22=0.55 what is the probability that the end of year loss is more than $10 million for $2? and s-= [ 3. 3. (35pts) Consider a portfolio which consists of two assets. The returns of the assets are normally distributed with N(0.12.V0.15) and N(0.1, 0.25). The value of portfolio today is $110 million. Sup- pose the time horizon is 15 days and the covariance matrices are given by Si- 0.15 0.2 0.15 0.0 0.2 0.25 0.0 0.25 a) Let the shares of assets be: 01= 0.55, 22=0.45 calculate VaR at 2% probability and for si? Show your calculations explicitly. b) Let the shares of assets be: 01=0.55, 2n=0.45 calculate the Value at Risk (VaR) at 1% probability for $2. c) Let the shares of assets be: x1=0.45, 12=0.55 calculate VaR at 2% probability and for std) Let the shares of assets be: x1=0.45, r=0.55 calculate the Value at Risk (VaR) at 1% probability for $. e) Let the shares of assets be: x1=0.55, #2=0.45 what is the probability that the end of year loss is more than $10 million for s'? f) Let the shares of assets be: x=0.45, 22=0.55 what is the probability that the end of year loss is more than $10 million for $2

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