. In a large portfolio, we usually need to do a factor analysis to find some common factors such as market index, interest rates and so on, so we can reduce the risk analysis of a large portfolio to a low-dimensional problem about these common factors. For example, if we consider an equity portfolio, we can use the following Capital Asset Pricing Model (CAPM) as follows. ; = Qi + B;m + i (1) Here m represents the market return, i denotes the specific risk and i is independent from Rm, and j is also independent from ; for any i + j. Another standard assumption is i ~ N(0,01), normal random variable with mean 0 and variance oz. The distribution of m is not necessarily normal if we are concerned about the tailed risk. The standard deviation of m can be estimated from either historical data or the index option (as the implied volatility). (a) Calculate the standard deviation of ; in the last equation. (b) Consider a portfolio with two stocks, and each stock return is written in CAPM as follows (by ignoring the alpha coefficient) = 1.2m + i, , = 0.2m + a, (2) and Om = 0.3,01 = 02 = 0.01. (3) These standard deviations are quoted annually. Assume each stock position worths 10 millions. Calculate the maximum loss of the portfolio in one day with 99 percent confidence level. . In a large portfolio, we usually need to do a factor analysis to find some common factors such as market index, interest rates and so on, so we can reduce the risk analysis of a large portfolio to a low-dimensional problem about these common factors. For example, if we consider an equity portfolio, we can use the following Capital Asset Pricing Model (CAPM) as follows. ; = Qi + B;m + i (1) Here m represents the market return, i denotes the specific risk and i is independent from Rm, and j is also independent from ; for any i + j. Another standard assumption is i ~ N(0,01), normal random variable with mean 0 and variance oz. The distribution of m is not necessarily normal if we are concerned about the tailed risk. The standard deviation of m can be estimated from either historical data or the index option (as the implied volatility). (a) Calculate the standard deviation of ; in the last equation. (b) Consider a portfolio with two stocks, and each stock return is written in CAPM as follows (by ignoring the alpha coefficient) = 1.2m + i, , = 0.2m + a, (2) and Om = 0.3,01 = 02 = 0.01. (3) These standard deviations are quoted annually. Assume each stock position worths 10 millions. Calculate the maximum loss of the portfolio in one day with 99 percent confidence level