Measuring market risk of fixed income securities
The general formula to obtain the present value of a fixed income security given a yield curve is: 
, where T is the time until maturity of the security, CFt is the cash flow of the security at time t, and yt is the discount rate of a cash flow to be received at time t. The market price of the bond will converge to its par value as time passes, even if its yield to maturity remains constant. This price change is expected, hence it is not considered a risk. Market risk arises from the changes in interest rates, which causes reinvestment risk and liquidation risk. The first affects the rate at which coupon payments can be reinvested, and the second impacts the market price of the bond.
The market price impact of interest rate change is measured by examining the price of the bond as a function of its yield to maturity (y): 
. Since 
, the percentage change of the price caused by a 
change in yield is expressed as: 
, the second order approximation...
