Explanation:

To find the optimal addition, we must assess which choice minimizes portfolio volatility (and therefore Value at Risk, VaR) through better diversification benefits. Yamama Bank has a lower correlation with Grinold Bank (0 vs 0.8 for Fujarah Bank), which provides far better risk diversification.

Calculating with Yamama Bank added:

Total Portfolio Value = $700M + $300M = $1,000M
Weight of Grinold ( $w_G$ ) = 0.70
Weight of Yamama ( $w_Y$ ) = 0.30
Variance = $(w_G \cdot \sigma_G)^2 + (w_Y \cdot \sigma_Y)^2 + 2 \cdot w_G \cdot w_Y \cdot \sigma_G \cdot \sigma_Y \cdot \rho$
Variance = $(0.70 \cdot 0.12)^2 + (0.30 \cdot 0.12)^2 + 0 = 0.007056 + 0.001296 = 0.008352$
Portfolio Volatility ( $\sigma_p$ ) = $\sqrt{0.008352} \approx 0.091389$
Using the normal deviate for 99% confidence (approx. 2.33):
$VaR = Z \cdot \sigma_p \cdot Portfolio Value = 2.33 \cdot 0.091389 \cdot \`$ 1,000M \approx \ $212.94` \text{ million}$

Therefore, Yamama minimizes the risk effectively giving a VaR of $212.94 million.

Q.17 Anthony James has a portfolio with only a single position of `$700` million invested in shares of Grinold Bank. The manager is considering adding a `$300` million position in Shares of Fujarah Bank or Yamama Bank to the portfolio. The current volatility of Grinold is 12%. In addition, the shares of Fujarah Bank have a return volatility of 9% and a correlation with Grinold equal to 0.8, while the shares of Yamama Bank have a return volatility of 12% and a correlation with Grinold equal to zero.

Which of the two proposed additions will keep Anthony's risk budget at an optimal level at the 99% confidence level and what will be the portfolio's VAR?

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Last updated: July 5, 2026 at 07:12

Fujarah added; Varₚ: $195.72 million

Yamama added; Varₚ: $212.94 million

Fujarah added; Varₚ: $248.92 million

Yamama added; Varₚ: $414.54 million

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