Question 1: The management of Border Bank has asked you to help with it with its market risk computations. It has compiled the given data on its financial assets:
A) $500 million of amortizing home mortgage loans with an average maturity of 15-years and an average loan rate of 5% (suppose annual end-of-the year payments). The present yield on comparable loans is 4%. The volatility of daily changes in yields is averaging 50 basis points. Note that you will require finding out the annual payment needed for the loans prior to computing their market value and value at risk.
B) $300 million of non-amortizing commercial loans with an average maturity of 4-years and an average lending rate of 7%. The present yield on comparable loans is 6%. The volatility of daily change in yields is averaging 40 basis points.
C) $200 million of corporate bonds with an average maturity of 10-years and an average coupon rate of 6%. The current yield on comparable bonds is 5%. The volatility of daily changes in yields is averaging 30 basis points.
By using a 99 percent confidence interval (2.33 standard deviations), what is the 1-day Value at Risk (Daily Earnings at Risk) for each kind of asset and what is the 1-day Value at Risk for the bank overall? What would be the 15-day Value at Risk for the bank? Note that you will first need to compute the market value and the modified duration for each kind of asset based on their expected cash flows before estimating their VaRs. For the overall bank VaR computations, suppose that the correlation between the amortizing mortgage loans and the commercial loans is 0.80, between the mortgage loans and the corporate bonds it is 0.70 and between the commercial loans and the corporate bonds is 0.60.