Consider a bond with $100m face value in a 5-year note selling with annual coupon payments of 6%. The term structure of spot interest rates is 5% flat to all maturities.

1. Compute the market value of the bond
2. Compute the duration D and modified duration MD of the bond
3. Now, assume that the term structure moves up by a s(Dy) = 1.6450.40% instantaneously at all maturities. This is a typical 95% VAR for the change in yield over a month. What is the change in value of the portfolio using duration mapping? Is this the local or full valuation method?
4. What is the change in the value of the portfolio using full repricing at the new yields? Is the difference with the previous answer large?
5. More generally, cash flow mapping would use movements in interest rates for different maturities, e.g., annual. If the volatility is constant across maturities and correlations all equal to one, how would you expect the answer to (c ) change? If correlations are below 1, would you expect a lower or higher VAR?