Consider a portfolio consisting of 10,000 shares of Apple stock and 5,000 shares of T-Mobile stock....

 

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Consider a portfolio consisting of 10,000 shares of Apple stock and 5,000 shares of T-Mobile stock. Apple's current share price is $125 and T-Mobile's current share price $140. Assume that Apple's annual volatility is 25%, T-Mobile's annual volatility is 30%, and that the correlation between both stock prices's daily returns is 0.4. (a) Compute the 10-day 99% value-at-risk of the stock portfolio. (b) Compute the 10-day 99% expected shortfall of the stock portfolio. (c) Quantify the benefit of diversification in the portfolio with respect to the value-at-risk computed in (a). What is the reason for this effect? Remark: Assume 252 trading days per year. Moreover, for the standard normal distribution recall that the 99%-quantile is given by 2.3263. Consider a portfolio consisting of 10,000 shares of Apple stock and 5,000 shares of T-Mobile stock. Apple's current share price is $125 and T-Mobile's current share price $140. Assume that Apple's annual volatility is 25%, T-Mobile's annual volatility is 30%, and that the correlation between both stock prices's daily returns is 0.4. (a) Compute the 10-day 99% value-at-risk of the stock portfolio. (b) Compute the 10-day 99% expected shortfall of the stock portfolio. (c) Quantify the benefit of diversification in the portfolio with respect to the value-at-risk computed in (a). What is the reason for this effect? Remark: Assume 252 trading days per year. Moreover, for the standard normal distribution recall that the 99%-quantile is given by 2.3263.

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To compute the valueatrisk and expected shortfall of the stock portfolio we need to first compute the portfolios mean return and standard deviation Th... View the full answer