Michael Bank has three assets, they are listed as below: 1. a zero-coupon bond with a maturity

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Question:

Michael Bank has three assets, they are listed as below:

1. a zero-coupon bond with a maturity of 8 years. The yield to maturity is 6.8%, while the market

value is $1,000,000. The standard deviation is 88 basis points.

2. Euro 1,200,000 exposure. The exchange rate is $0.83333/Euro. The standard deviation is 60 basis points.

3. $1,400,000 of equity. Beta is 1 and the adverse daily movement is 800 basis points.

(a) Calculate the values of Daily Earnings at Risk (DEAR) for these three assets separately by using a 5% one-tail probability (that is, the Z-value from the normal distribution table is 1.65).

(b) If the correlation coefficients between bond and foreign currency exposure, bond and equity, and foreign currency exposure and equity are 0.2, -0.3, and -0.01, respectively, calculate the DEAR for the aggregated portfolio. Provide brief explanation why the aggregated portfolio’s DEAR is different from the sum of the DEARs of the three assets.