Research On Time-varying Volatility Risk Of Term Premiums In Bonds

This paper combines persistent volatilities of consumption growth and inflationwith Epstein-Zin recursive preferences using Long-Run Risks model with the yieldsdata of China’s bonds in different maturities. In the model estimated in the paper, therelationship between risk aversion and inter-temporal elasticity of substitution (IES) isnot flexible any more. Representative individual’s risk aversion to the same periodcan be departed from the inter-temporal alternative. Based on the recursivepreferences, individuals in this model hate future uncertainty but prefer include risksof next period into the consumption and investment decisions at the moment. Themodel in this paper emphasizes the time-varying volatility risk. This paper estimates amodel in which persistent fluctuations in expected consumption growth, expectedinflation, and their time-varying volatility determine asset price variation.According to the real nominal term structure data, investor doesn’t like highuncertainty and ask for the compensation of volatility risks to the uncertainty.Simultaneously, the time-varying volatility of term premiums comes from thecompensation of volatility risks. Investors hate sudden volatility risks not onlybecause inflation will decrease the payment of nominal bonds, but also becauseinflation is negative news for future consumption growth. Investors prefer the smoothconsumption curves, which means under the same conditions investors will decide toprefer the financial assets still with higher payment when the economy goes downaccording to their own risk aversion. In fact, when information of future turns out tobecome worse so that nominal bonds can’t attract people to hold, the payment ofnominal bonds will react to decrease precisely. Therefore, the premiums that investorswho are averse to risks ask for to compensate the risks are depend on how muchdegree the volatility is considered as the carrier of bad information. The volatilityrisks of inflation and consumption play a main role in explaining the time-varyingchanges of term premiums, which is consistent with empirical results (including thesurvey data). According to prospect theory, long-run interest rates equal to theweighted average of future expectations to short-run interest rates. In general,long-run and short-run interest rates change in the same direction. When short-runrates increase, long-run rates will follow to increase as well. But that makes adifference in China. It can be noticed that in China long-run interest rates are not sensitive to short-run rates’ volatility. The prospect theory doesn’t play a good role inthe financial market in China. As we can see, about2011, the differences betweenyields of different maturity becomes more departed from the prospect theory, thedifferences between long-run and short-run yields become more and more close.Generally speaking, long-run interest rates will react to short-run interest rates but itshows in a different way in China. These all indicate that in China, the risk premiumsof bonds are time-varying variables.This paper uses the time series data of both macro variation and nominal bondyields, and estimates long-run risks model by the method called likelihood estimationwith full information. By linking the estimation of volatility to the measurement ofterm premiums, it can be noticed that the compensation to volatility ofmacro-economic factor (the growth of consumption or inflation) is significant in theinterpretation of time-varying volatility risk of term premiums. And this finding issame as the experimental evidence from statistics model and measurement. However,it obviously differs from the researches that solely emphasize the importance ofvolatility risks of macro economy. This paper divides bond yields into stablecomponents and volatility components by using the method called the analysis ofmajor components. Thus, it can be noticed that the volatility components have thesimilar tendency of the growth of consumption. And by the subsequent parameterestimation, it also can be noticed that the way that can get a better parameter result isto introduce yields’ series of bonds with different maturity rather than just introducingmacro-economic variations. That demonstrates the preceding result is correct and thevolatility components can well explain the majority of term premiums. And it is a factthat both volatility of growth of consumption and volatility of inflation couldinfluence obviously volatility of bond yields and even the former is better. For thestable components, as what had been discussed by precursors previously, the inflationfactor is more predominant than the growth of consumption.This paper focuses on the aspect of estimation of time-varying volatility risksand tries to demonstrate the consequence matching to the parameter model by usingthe analysis of major components. The consequence is that both inflation andconsumption can interpret time premiums of bonds, but the influence of inflation ismore obvious. And it can be noticed that time volatility is determined by thecompensation of inflation and consumption volatility risks instead of one of them.Therefore, the macro-economic variation of volatility risks is a pivotal function forthe interpretation of time premiums changing with time.