Final answer:
To calculate the five-day VaR and ES of Bank of Victoria's stock portfolio, use the standard deviation of the portfolio calculated using the market portfolio's standard deviation and beta. The five-day VaR in the 99th percentile is approximately -$13.04 million, and the ES is approximately -$26.087 million.
Step-by-step explanation:
To calculate the five-day VaR and ES of Bank of Victoria's stock portfolio, we need to first estimate the portfolio's standard deviation (σp) using the market portfolio's standard deviation (σm) and the portfolio's beta. Since the beta of the portfolio approximates the market portfolio, we can use the market portfolio's standard deviation as an estimate for the portfolio's standard deviation.
Given that the market portfolio's standard deviation is 2.25 percent and the portfolio's market value is $250 million, we can calculate the standard deviation of the portfolio (σp) as follows:
σp = β * σm = 1 * 2.25% = 2.25%
Now that we have the standard deviation of the portfolio, we can calculate the five-day VaR and ES using adverse rate changes in the 99th percentile. The formula for VaR is:
VaR = σp * Z * V
where σp is the standard deviation of the portfolio, Z is the z-score corresponding to the desired confidence level (1 - 0.99 = 0.01), and V is the value of the portfolio.
The formula for ES is:
ES = VaR * (1 / (1 - 0.99))
Substituting the values, we get:
VaR = 2.25% * -2.33 * $250 million = -$13.04 million
ES = -$13.04 million * (1 / (1 - 0.99)) = -$26.087 million