Rochester Savings Bank (RSB) uses DEAR to measure the daily market risk exposure of its bond holdings. RSB currently has $100mln worth of investments in bonds. The duration of its bond holdings is estimated to be 9 years. The current interest rate is 3%. Moreover, daily changes in the interest rate are assumed to be normally distributed with mean zero. RSB has just estimated that the daily loss on its bond holdings will be less than $1.45 million with 95% probability.

3a) What is the daily standard deviation of interest rate change?

Suppose now Five Star Bank faces the same interest rate environment (mean and standard deviation). But now it has $20m bond holdings with duration of 12 years.

3b) What is the estimated 5% DEAR for Five Star Bank? And the 5-day VAR (assume daily interest rate changes are i.i.d)?

RSB also holds a foreign currency of 10 million Swiss Francs (SF). The current exchange rate is 1SF = $1. The Swiss government is considering to impose a ceiling of 1 S = $0.9. This policy is estimated to have a 5% chance of being implemented in the following day. If not implemented, the market exchange rate of SF against dollar is estimated to either stay the same or to appreciate.

3c) What is the 5% DEAR from RSBs Swiss Franc position?