Using Affine Models of the Term Structure to Estimate Risk Premia

Abstract

This paper uses affine models of the term structure to provide historical estimates of risk premia. The foreign exchange and inflation risk premia can be modelled in the same way since the price level can be thought of as an exchange rate that transforms real prices to nominal prices. Affine models with three latent factors of the Cox, Ingersoll and Ross (1985) type are used, with a common factor between the two pricing kernels (state price vectors) to account for interdependence. In the case of foreign exchange risk premium two factors are used to model the domestic pricing kernel and two factors to model the foreign pricing kernel with a common factor between them. This specification can account for the forward premium anomaly, the tendency for high interest rate currencies to appreciate, which contradicts uncovered interest rate parity. In the case of inflation risk premium two factors are used to model the real pricing kernel and two factors to model the nominal pricing kernel with a common factor between them. The model distinguishes between expected and realised variables and therefore allows the estimation of expectational errors. The model also allows for time-varying market prices of risk and time-varying correlations between the two pricing kernels or between each of the pricing kernels and the foreign exchange rate or the price level. Another contribution, which has been ignored in the previous literature, is that the model is estimated using both bond yields and realised price level or foreign exchange rate changes. Fitting the later is necessary for the model to produce realistic patterns for the price level or foreign exchange rate changes. The results show that the foreign exchange risk premium fell substantially after 96, which is consistent with the large appreciation of sterling. Expectational errors were very large for the whole of the period studied, that is, from 93 to 99. Inflation risk premium was about 100 basis points for most of the period 87 to 97, but fell substantially since Bank independence in March 97, which may be the result of a higher credibility to the new UK monetary policy institutional framework. Inflation expectational errors also became smaller after the adoption of inflation targeting in UK in January 93. ∗ Bank of England, Threadneedle Street, London, EC2R 8AH, nikolaos.panigirtzoglou@bankofengland.co.uk . The views expressed are those of the author and do not necessarily reflect those of the Bank of England. The author thanks Nicola Anderson, Luca Benati, Roger Clews, Stephen Millard and seminar participants at the Bank of England for helpful comments.