Value-at-risk (VaR) of a portfolio investment is a statistic that measures the level of finan- cial risk within the portfolio over a specific time period. Consider an initial investment of AUDW, in a portfolio of two assets: Amazon (A) and Boeing (B). The weights attached to A and B are given by wa and ws. Further, assets A and B have expected returns denoted by Ha and UB and variances given by oand of respectively. For the portfolio simple return, Rp, we assume that Rp. N (up, op), where jp, and o are the expected return and variance of this portfolio. The a x 100% portfolio value-at-risk is given by VaRp,a = qapW, where a (0,1) and q,a is the a quantile of the distribution of Rp. This is defined as RP ha = uptaop, where qa is the a quantile of the standard normal distribution. 1. Show analytically whether, in general, the portfolio VaR is a weighted average of the individual asset VaRs, where the weights are given by wa and Wb. (6 pts) 2. Assume that the correlation coefficient between assets A and B is equal to unity, i.e. PAB 1. Do you reach the same conclusion as in Q2.1? Demonstrate your steps in arriving at your answer. Do you think that it is a good idea to approximate the portfolio VaR by the weighted average of the individual asset VaRs? Justify your answer. (6 pts) 3. Consider an initial investment of W. = AU D100,000, and an equally weighted port- folio P comprising of assets A and B. Verify your findings in Q2.1 and Q2.2 using 5% VaRs on A, B and P as well as the information in Table 2 below, when (a) PAB = 0.26 and (b) PAB 1.00 (note that q.05 = -1.645): Table 2 UB 0 % 0.212 0.156 0.0238 0.0187 Value-at-risk (VaR) of a portfolio investment is a statistic that measures the level of finan- cial risk within the portfolio over a specific time period. Consider an initial investment of AUDW, in a portfolio of two assets: Amazon (A) and Boeing (B). The weights attached to A and B are given by wa and ws. Further, assets A and B have expected returns denoted by Ha and UB and variances given by oand of respectively. For the portfolio simple return, Rp, we assume that Rp. N (up, op), where jp, and o are the expected return and variance of this portfolio. The a x 100% portfolio value-at-risk is given by VaRp,a = qapW, where a (0,1) and q,a is the a quantile of the distribution of Rp. This is defined as RP ha = uptaop, where qa is the a quantile of the standard normal distribution. 1. Show analytically whether, in general, the portfolio VaR is a weighted average of the individual asset VaRs, where the weights are given by wa and Wb. (6 pts) 2. Assume that the correlation coefficient between assets A and B is equal to unity, i.e. PAB 1. Do you reach the same conclusion as in Q2.1? Demonstrate your steps in arriving at your answer. Do you think that it is a good idea to approximate the portfolio VaR by the weighted average of the individual asset VaRs? Justify your answer. (6 pts) 3. Consider an initial investment of W. = AU D100,000, and an equally weighted port- folio P comprising of assets A and B. Verify your findings in Q2.1 and Q2.2 using 5% VaRs on A, B and P as well as the information in Table 2 below, when (a) PAB = 0.26 and (b) PAB 1.00 (note that q.05 = -1.645): Table 2 UB 0 % 0.212 0.156 0.0238 0.0187