Portfolio managers A and B each manage $1,000,000 funds.Portfolio manager A has perfect foresight and the call option value of his perfect foresight is $180,000.Portfolio manager B is an imperfect forecaster and correctly predicts 60% of all bull markets and 70% of all bear markets.The value of portfolio manager B's imperfect forecasting ability is _________.

Question

Quizplus · Accepted Answer

Portfolio manager A's perfect foresight gives him an advantage over the market and his fund's return should be the risk-free rate plus the call option value, or $1,180,000.

Portfolio manager B's imperfect forecasting ability means that 30% of bull markets and 40% of bear markets are not correctly predicted. The expected value of the fund's return can be calculated as:

(0.6 * 1.1 + 0.4 * 0.9) * $1,000,000 = $1,020,000

The difference between the expected return of portfolio manager B and the risk-free rate is the value of his imperfect forecasting ability:

$1,020,000 - $1,000,000 = $20,000

Therefore, the value of portfolio manager B's imperfect forecasting ability is:

$20,000 / (0.6 + 0.3 + 0.4) * 0.3 = $54,000

The answer is C.

Portfolio Managers a and B Each Manage $1,000,000 Funds