David is managing a hedge fund that invests in global assets. He is responsible for two portfolios: Chinese stock portfolio and UK stock portfolio, currently valued at $40 million each. The Chinese stock portfolio is expected to make a 10% return with a standard deviation of 20% next year. In the meantime, UK stock portfolio has an expected return of 6%.Suppose that both portfolios returns are normally distributed. (PLEASE SHOW WORK)

(a) Calculate a 95% confidence interval (a range that 95% of the time that the return is in that range) for the value of the Chinese stock portfolio.

(b) Provide the VaR of 10% for the Chinese stock portfolio.

(c) If the VaR10% for the UK stock portfolio is the same as the Chinese stock portfolio, what is the standard deviation of the UK stock portfolio?

(d) Davids boss thinks that these two numbers are quite concerning! But David argues that since the portfolio returns of Chinese and UK stocks are almost uncorrelated, these two numbers look normal. Prove his point by estimating the VaR10% for the combined position and compare it with the sum of the individual portfolio positions.

Hint: the sum of two normally distributed random variables will yield a random variable that is also normally distributed. The mean of the new variable equals to wa*E(Ra)+wb*E(Rb) and variance is wa2a2+wb2b2+2*wa*wb**a*b, is the correlation between a and b.