The retail banking business of BankGamma has an expected P & L of $50 million...

To calculate the overall RAROC after acquiring the new business:

Expected P&L (Profit and Loss): $50 million+$50 million=$100 million\$50 \, \text{million} + \$50 \, \text{million} = \$100 \, \text{million}$50million+$50million=$100million

VaR (Value at Risk): Assuming diversification benefits are not considered, the total VaR would be $100 million+$150 million=$250 million\$100 \, \text{million} + \$150 \, \text{million} = \$250 \, \text{million}$100million+$150million=$250million

RAROC Calculation: \frac{\text{Expected P&L}}{\text{VaR}} = \frac{100 \, \text{million}}{250 \, \text{million}} = 0.4 or 40%

Thus, the closest answer from the provided options is 33.3%.