Explaining and Forecasting Bond Risk Premiums

In examining the risk premiums for U.S. and German 10-year government bond yields, the authors found that the decline in bond risk premiums since the 1980s is associated with a decrease in global output variability and an increase in the power of 10-year government bonds to diversify portfolios. This article examines the dynamics of risk premiums for U.S. and German 10-year government bond yields and shows that the estimated patterns are associated with a decrease in the systematic component of risk.Using a no-arbitrage, essentially affine three-factor model and in line with the existing literature, we found that bond risk premiums have followed a downward trend since the 1980s: from 4.9 percent in 1981 to 1.2 percent in mid-2009 for the U.S. bond and from 3.3 percent to 1.1 percent for the German bond. We studied the relationship between the estimated government bond risk premiums and the risk associated with such securities in the context of fully integrated financial markets. Our basic conjecture is derived from modern portfolio theory (MPT): Holders of a financial asset can expect a premium over the risk-free asset only if they bear systematic risk, measured by the covariance between the asset returns and the returns of a global market portfolio. We estimated an error correction model (ECM) to analyze the co-movements between bond premiums (as implied by the affine model) and two variables: (1) the standard deviation of the world GDP growth rate and (2) the correlation between government bond returns and the returns of a portfolio diversified by asset class, geographic region, and currency. The use of variables that may be regarded as a single proxy for the MPT systematic risk allows us to interpret the ECM-fitted premiums as the fair values that investors require as remuneration for the risk of long-term government bonds.We show that the decrease in government bond premiums since the mid-1980s is mainly attributable to the reduction in the systematic component of risk and that the low premiums that prevailed until the third quarter of 2008 were broadly consistent with the perceived level of risk at the time.We also show that data from the most recent period—fourth quarter of 2008 to second quarter of 2009—reveal a dramatic gap between the level of premiums embedded in bond prices (those premiums remain extremely low) and the level of premiums that investors should require given their risk (such premiums have risen to historically high values). Although it is too early to say whether this fact constitutes evidence of a structural breakdown in the relationship we have estimated, our guess is that it is simply the result of investors shunning almost every asset class with an uncertain payoff in the aftermath of the Lehman Brothers bankruptcy. If so, as economic agents’ behavior returns to normal, most of the gap should narrow and disappear.We believe that these results are important for long-term investors. The lower the risk of government bonds, the lower the premium investors require (ex ante) to hold such securities, and the higher the price they are willing to pay. Over 1980–2005, a period seemingly marked by declining required bond premiums, (ex post) excess returns on government bonds were highly significant, especially when compared with the average values recorded over the 20th century.Of course, in order to answer the question about future bond risk premiums, one must explicitly express a view about the most plausible evolution of the current macroeconomic environment. To the extent that the great moderation of economic systems and the well-anchored inflation expectations we have experienced in the last two decades may be traced to structural changes that will persist even after the current crisis, investors may be confident that long-run bond risk premiums will remain low. Conversely, if financial markets have entered a completely new (and riskier) era and the past reduction in macroeconomic uncertainty has been merely the lucky upshot of fewer and smaller shocks hitting the economy, the outlook for long-term government bonds is gloomy.The main conclusion of this article is that investors’ expectations about long-term excess returns for 10-year government bonds will have to be significantly lower than the average values over the last two decades. Taking the current macroeconomic uncertainty into account, strategic investors should allow for an increase in (ex ante) bond risk premiums that may even depress bond prices. Investors will have to reconsider excess returns more in line with the average over a very long-term horizon, such as the last century.Note: The views expressed in this article are the authors’ own and do not necessarily reflect the views of the Bank of Italy.