Unspanned Factors In Interest Rate Term Structure

The macro-finance model is usually constructed on the basis of the affine interest rate term structure model,and takes the macroeconomic factors as the pricing factors.When the market is complete,on the one hand,the traditional affine interest rate term structure model implies the assumption that the yield curve already contains all the information of the macroeconomic factors,that is,all the macroeconomic factors can be spanned by the yield curve.On the other hand,it also implies the assumption that the future interest rate and bond risk premium can be fully predicted with the information of the current yield curve.These two assumption are often inconsistent with the reality.For this paradox,Spanning Hypothesis has become a hot topic in the field of interest rate term structure.Through GMM test and bootstrap test,it is found that the macroeconomic variables,especially industrial value-added,can predict bond risk premium beyond the cross-section of yield curve.At the same time,industrial value-added does not only contain the information of cross-section of yield curve,but also contains other information that is not present on the cross-section of yield curve and is able to affect the time dynamic series of yield curve.It is usually named as the unspanned macro factor.The reason why the economic growth variable shows unspanned characteristics is that investors need risk compensation for the fluctuation of economic cycle in the process of holding treasury bond.On the basis of empirical test,we build a term structure model with unspanned factor to fit the spot yield of treasury bond,and find that the fitting precision is better than the traditional macro finance model,which shows the importance of introducing unspanned factor.Furthermore,we innovate the model and theory.First,based on the AFNS model,we set the industrial added value to be affected by three implicit Nelson-Sigel(NS)factors and implicit unspanned factors at the same time.Through the model,we extract four implicit state factors,including level,slope,curvature and unspanned factors,analyze the dynamic relationship between state factors.Then we discuss the unspanned factors from the measurement error,nonlinear model,monetary policy and economic significance.Secondly,on the basis of the macro-finance model,we set the inflation with measurable errors to be influenced fully with the state variable,and the industrial added value to be affected by both the pricing factor of the yield curve and the implicit unspanned factor.We find that the fitting precision and the prediction accuracy are high,which have good explanatory power.We use the model to decompose the nominal interest rate.It is found that the term premium and inflation expectation in the nominal interest rate have important impacts on the nominal interest rate and has obvious economic meaning.Based on the hidden information extracted from our model,we find that it has a good explanation for"Greenspan puzzle".The term spread is significantly affected by the short-term term premium and the long-term inflation expectation.The short-term term premium is relative to the investors’ requirements for risk compensation,and the long-term inflation expectation is about prediction for inflation.The differentiation between the shortterm and long-term term premium can be used to predict the term spread and macro-economy.When the term premium gap increases,the economy grows,and when the term premium gap decreases,the economy declines.The research has important reference significance for further expanding the research of interest rate term structure.