# III.5

# Portfolio Mapping

## III.5.1 INTRODUCTION

The first four chapters of this book covered the analysis of three broad categories of financial instrument: interest rate sensitive instruments, futures/forwards, options, and volatility swaps. We focused on the characteristics of the individual instruments and of the market in general but rarely discussed how to analyse large portfolios of these instruments. In this chapter we describe how to map large portfolios of financial instruments to their risk factors. Since the portfolio risk factors and their risk factor sensitivities are quite different in each case, we treat each of the main categories of instruments separately.

Interest rate sensitive instruments without embedded options include loans, cash and futures positions on fixed coupon bonds, floating rate notes, forward rate agreements (FRAs) and vanilla interest rate swaps. The positions on these instruments can be characterized by a *cash flow*, i.e. a series of cash payments {*C*_{T1}, …, *C*_{Tn}} at times *T*_{i} for *i* = 1,2, …, *n*. Large portfolios of similar types of instruments have cash flows that occur at numerous different times in the future. For this reason the market risk of such portfolios is usually analysed by mapping all the cash flows to a fixed, finite set of zero coupon yields at standard maturities such as 1 month, 2 months, and so on up to the maximum maturity of the instruments. Such a set of discount rates is a set of *risk factors* for the portfolio. To understand these ...