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

i) 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.

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

iii) $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.

Hints:

Daily earnings at risk (DEAR)= position in US$ (if not in US$, need to use foreign exchange rate to change to US$) X price volatility

Price volatility=

1. For fixed income security = MD X adverse daily move, where MD = D /(1+R), MD is modified duration, D is duration, R is yield

2. For foreign exchange = adverse daily move

3. For equity = beta X adverse daily move, beta is 1 if portfolio follows stock market index

For 1,2,3, the adverse daily move = Z x standard deviation,

One-sided critical z-values

.80 .90 .95 .99 .999

0.84 1.28 1.65 2.33 3.09

Use one tail

N-day VAR = DEAR x N^0.5