St. Michael's Bank has the following three assets.

1. a 16-year zero-coupon bond has a yield to maturity is 6.8%, while the market value is $1,200,000. The standard deviation of this zero-coupon bond is 68 basis points.
2. Euro 1,200,000 exposure. The exchange rate is $0.68/Euro. The standard deviation is 88 basis points.
3. $130,000 of equity. Beta is 1 and the adverse daily movement is 86 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 0.1, 0.6, and 0.8 respectively, calculate the DEAR for the aggregated portfolio. Provide a brief explanation why the aggregated portfolio's DEAR is different from the sum of the DEARs of the three assets.