THE PURPOSE OF THIS CHAPTER

In this chapter we look at the risks to which bonds are exposed. Risk comes from not knowing for certain how things will pan out. Therefore saying that we are going to look at the risks to which bonds are exposed is the same as saying that we are going to consider those stochastic drivers that affect the prices of bonds.

The price of bonds is also affected by non-stochastic quantities, such as the residual time tomaturity, or their coupons.However, these deterministic quantities are perfectly known, and investors demand no ‘uncertainty compensation’. We are interested in the risks to which a bond is exposed, because it is for risk, and for risk only, that investors can ask compensation.

This chapter is therefore important for two different but related reasons. The first is rather obvious: if we want to pursue a structural approach to yield curve modelling, a clear understanding of the nature of the risks to which bonds are exposed is essential. For instance, if we speak of risk premia, it is important to understand what risk investors get compensated for taking, and why the bearing of certain risks should command a greater or smaller compensation than the bearing of others.

The second reason for looking at the ultimate sources of risk in some detail is a bit subtler.We may or we may not choose as state variables the risk factors. It may seem reasonable to do so, but sometimes considerations such as analytical tractability, or availability of empirical knowledge, will point in the direction of state variables other than the ‘ultimate’ risk factors that drive the yield curve. Using these ‘convenient coordinates’ is fine, as long as we understand clearly which risk factors ‘really’ drive the yield curve, and the nature of the ‘mapping’ from these ‘true’ risks to our chosen state variables.

We shall see in this chapter that the risks to which a (perfectly liquid and creditworthy) bond is exposed are inflation and real-rate risk. In order to understand the compensation that investors can expect for bearing these risks, we give a first ‘informal’ presentation in Section 4.3 of risk-neutral and real-world expectations.