Explanation:
Recall that:
Portfolio VaR = VaRₚ = ασₚW = α√(x′Σx)
The first step is to calculate the variance of the portfolio dollar returns. Let x be the dollar amounts allocated to each risk factor, in millions. We first calculate the product:
Σx = [0.065² 0 $4] [0.065² × $4 + 0 × $3] [$0.0169]
0 0.1² $3] [0 × $4 + 0.1² × $3] [$0.03]
Therefore, the portfolio value in dollar returns is:
σₚ²W² = x′Σx = [$4 $3] [$0.0169] = $4 × 0.0169 + $3 × 0.03 = 0.1576
[$0.03]
The dollar volatility is:
√0.1576 = $0.396989 million
With α = 1.65, the portfolio VaR is given as:
VaRₚ = 1.65 × $396989 = $655,032
Ultimate access to all questions.
No comments yet.
Q.3026 We are given a portfolio having two foreign currencies, namely the Australian Dollar (AUD) and the Sterling Pound (GBP). These two currencies are uncorrelated, with standard deviations against the dollar of 6.5% and 10%, respectively. The portfolio has USD 4 million invested in the AUD and USD 3 million invested in the GBP. Compute the portfolio VaR at the 95% confidence level, assuming that α = 1.65.
A
USD 675,218
B
USD 546,889
C
USD 655,032
D
USD 586,274