This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
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Answer
R4 178 206 967.01
To calculate the capital buffer using the Kelly Criterion, we need the probabilities of gain and loss, and the absolute values of the gain and loss.
Step 1: Identify the probabilities and outcomes. The probability of default (loss) is given as . So, the probability of losing () is . The probability of not defaulting (gain) () is .
The net income or margin (gain, ) is R202.5 million. The maximum loss () is R4.125 billion, which is R4125 million.
Step 2: Apply the Kelly Criterion formula for optimal capital. The Kelly Criterion for determining the optimal capital () to maintain, given a probability of gaining and a probability of losing , is derived by maximizing the expected logarithm of wealth:
Step 3: Substitute the values into the formula.
Step 4: State the capital buffer. Rounding to two decimal places, the capital buffer should be R4178.21 million.
The capital buffer Ciskei Commercial Bank should maintain is .
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This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.