RDP 2008-09: A Term Structure Decomposition of the Australian Yield Curve 1. Introduction

The relationship between the level of interest rates across different maturities is known as the term structure of interest rates. The term structure can be used to assess the financial markets' expectations for the future path of monetary policy. For example, the pure expectations hypothesis (which ignores the possible existence of term premia) asserts that market participants' expectations of future short-term interest rates are simply given by forward rates as observed in the market.^[1]

The term structure of interest rates is often presented as a yield curve, which plots the yields to maturity of bonds with varying terms to maturity. Typically, the yield curve is presented for risk-free interest rates. In Australia, Australian Government bonds are normally used, since these are considered to have essentially zero probability of default and hence the yields do not incorporate any credit risk premia. However, the yield curve does not give a direct reading of interest rate expectations for two reasons. First, the yield to maturity of a bond is affected by the bond's coupon rate; the higher the coupon rate, the less important will be the payment at maturity as a share of the bond's total income stream and hence the yield to maturity will be affected more by short-term expectations of monetary policy relative to longer-term expectations. Second, if investors are risk-averse and the future path of interest rates is uncertain, then long-term interest rates will incorporate a term premium as compensation for investing in the face of this uncertainty.

If these two components of long-term yields can be stripped away, the resulting curve would provide a better indication of the markets' expectations of the future path of short-term interest rates, specifically the overnight interest rate used by the Reserve Bank of Australia as the instrument for monetary policy.

To abstract from the first of these complications, it is possible to use a set of yields on coupon bonds – that is physical government bonds – to estimate a set of yields on (hypothetical) zero-coupon bonds, which are bonds that do not make any periodic interest payments. There are a number of established methods to do this, which give broadly similar results.

The most direct method to abstract from the second complication – that is, to estimate expected future short rates separate from term premia – would be to use analysts' forecasts of future monetary policy decisions, as these give a direct reading on cash rate expectations. However, this method suffers from a number of drawbacks, chief among these being that analysts' expectations may not always be reflected in market pricing, and typically extend over only a relatively short horizon. An alternative is to specify and estimate a model of how expected future short rates and term premia evolve over time. The fact that these two elements are time-varying and are confounded in their effect on bond prices makes the choice of model crucial. The approach we employ is to combine these two methods, using data on analysts' forecasts within the model-based approach to aid separate identification of expected future short rates and term premia. Nevertheless, the central role of the assumed model (along with the computational complexities of fitting the model to data) means that it is prudent to treat the results of such a term structure model with some caution – a different model may generate different results.

Despite these caveats, the importance of the shape of the yield curve and expectations of future interest rates in understanding economic and financial market developments make the separation of yields into term premia and expectations a worthwhile exercise. To this end we employ an affine term structure model of zero-coupon yields that has been used widely in the literature and currently appears to be the best available candidate for such work.^[2]

The remainder of this paper is set out as follows. Section 2 provides a brief overview of the affine term structure model, the literature on affine term structure models, and their development. Section 3 details the term structure model that we employ, while Section 4 discusses how we use estimated zero-coupon yield data, along with analysts' forecasts of future interest rates, as the inputs into the estimation procedure for our model. Section 5 gives the results of our estimation over two sample periods, with the output of most interest being the expected future short rates and term premia produced. Finally, Section 6 concludes. More technical detail regarding zero-coupon yield curve estimation from data on coupon-bearing Australian Government bonds, as well as the affine term structure model and its implementation, are provided in the appendices.

Footnotes

By forward rate we mean an overnight interest rate which is observed in the market now but does not apply until some time in the future. [1]

An affine term structure model represents interest rates as being a linear combination of a small set of factors and parameters. See, for example, Duffee (2002) and Dai and Singleton (2002) for discussion of competing term structure models. [2]