A pension fund manager has chosen a portfolio consisting of the risk-free asset, with annual return 3% (annual compounding), and two risky assets. The holding period return can be expressed by the following factor model:

with the following parameters:

All factors are normally distributed with the following parameters:

Each specific risk factor is uncorrelated with the other factors, whereas the correlation coefficient between the two systematic factors is 0.68 . The portfolio weight of the risk-free asset is \(40 \%\), and the rest of the portfolio is equally allocated to the risky assets. The manager receives a bonus depending on the realized annual return: if it is at least \(9 \%\), the bonus is \(€ 200,000\); if the return exceeds \(12 \%\), she will receive additional \(€ 100,000\). What is the expected value of the bonus earned by the manager?

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i = i + iF + Bi2 F2 + Ei, i = a, b,