The optimal addition keeps the VaR at the lowest point. The new portfolio value will be \`1,000$ million ($700`M Grinold + `$300M new position). The weights are $w_G = 0.7$ and $w_{new} = 0.3$. Using the normal VaR formula at $99`\%$ ($Z = 2.33$): $VaR = 2.33 \times \sigma_p \times \text{Portfolio Value}$.

For Fujarah: $\sigma_p = \sqrt{(0.7 \times 0.12)^2 + (0.3 \times 0.09)^2 + 2 \times 0.7 \times 0.3 \times 0.12 \times 0.09 \times 0.8} = \sqrt{0.007056 + 0.000729 + 0.0036288} = \sqrt{0.0114138} = 10.6835\%$ VaR = 2.33 \times 0.106835 \times \`1,000\text{M} = \$248.92`\text{M}$.

For Yamama: $\sigma_p = \sqrt{(0.7 \times 0.12)^2 + (0.3 \times 0.12)^2 + 2 \times 0.7 \times 0.3 \times 0.12 \times 0.12 \times 0} = \sqrt{0.007056 + 0.001296 + 0} = \sqrt{0.008352} = 9.1389\%$ VaR = 2.33 \times 0.091389 \times \`1,000\text{M} = \$212.94`\text{M}$.

Since Yamama gives a lower VaR (`$212.94` million), it keeps the risk budget at an optimal level.