How to measure risk

Such a vague question. There are various risks and you coul look at risks in a trader's perspective or market risk's perspective, such as stress testing, scenario analysis or measuring VaR. In trader's perspective, I'll give you an an example. A hedge is a sale of a package of state-contingent claims against a primary position which eliminates all the essential risk of that position. Only a sale of a security that is identical in all aspects to the primary position can eliminate all the risk. A hedge always leaves some risk unhedged Let us examine a very common hedge of a corporate with a government bond. An institutional trader purchases a 10-year 5% coupon bond issued by XYZ Corp. In an effort to eliminate interest rate risk, the trader simultaneously shorts a 10-year 4.5% coupon government bond. The size of the short is duration-matched to the principal amount of the corporate bond. This guarantees that for small parallel movements in the interest rates, the changes in the values of the two positions are identical but opposite in sign. If interest rates rise, the loss on the corporate bond holding will be offset by the gain on the shorted government bond. If interest rates decline, the gain on the corporate bond will be offset by the loss on the government bond. The trader, in effect, speculates that the credit spread on the corporate bond will decline. Irrespective of whether interest rates rise or fall, whenever the XYZ credit spread declines, the trader gains since the corporate bond’s price goes up more or goes down less than that of the government bond. Whenever the credit standing of XYZ worsens and the spread rises, the trader suffers a loss. The corporate bond is exposed over time to two dimen sions of risk: interest rates and corporate spread.

So we got rid of the interest rate risk, essentially by duration matching through this applies only of the interest rate moves in parallel but in effect, it's hedged, not perfectly hedged. You can measure the covariance to TRY to get a perfect hedge but essentially your second order risk is credit spreads now. So there are levels of risk, one is risker than the other and you can be expose to whatever you risk want to take on.