# Determinants of the Yield Curve - a Model for the Relationship Between Risk and Yield

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## Abstract

This paper develops a model explaining the level and structure of bond yields and the yield curve based upon three principles. 1) Across different maturities along the yield curve, bond yields change with the proportional change in the risk or potential volatility of the bonds. 2) The incremental yield required as a bond's volatility increases by an infinitesimal amount is determined by the riskless interest rate. 3) The relationship between the yield of a bond and the riskless interest rate is governed by expectations of future riskless interest rates over the term of the bond. The model explains the entire spread of the yield curve based upon expectations of future short-term riskless interest rates and upon the potential volatility of default-free bonds. Expected future riskless rates are derived from market bond yields by the model. These expectations are unbiased predictors of actual future riskless interest rates and are somewhat more accurate than a commercial consensus forecast. Spreads between expected future riskless rates for three month and ten year maturities correlate more highly with future changes in real GDP than do the spreads between the three month and ten year yields themselves. The model produces weights so that paired barbell maturities more closely match a bullet maturity's yield than if the barbell maturities were weighted by duration, a widely used measure of potential volatility. Differences between the bullet and weighted barbell yields correlate significantly with future changes in yields. The model thus facilitates evaluation of current pricing and future expectations in the bond market.

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