Why are bonds so volatile?
Trading and Investing
Review of Raphael Douady’s Paper: “The Volatility of Low Rates”
Raphael Douady’s paper, “The Volatility of Low Rates,” scrutinizes the traditional risk models applied to fixed-income investments, particularly bonds. The paper challenges the conventional assumption that bond risk is directly proportional to interest rates. Moreover, a premise suggesting that interest rates follow a log-normal distribution.
As a result, this assumption leads to two main implications:
Firstly, nominal interest rates could never fall below zero! Secondly, bond volatility should dissipate as interest rates approach zero.
However, recent financial environments, such as those observed in Germany, demonstrate that interest rates can indeed turn negative, and bond volatility persists even at very low rates. Douady’s research aims to reassess the validity of traditional fixed-income modeling in light of these observations.
Analysis of Traditional Models and Real-World Observations
The paper delves into four decades of bond data, covering periods of both high inflation and low rates, to investigate whether the traditional modeling approach remains relevant. Douady posits that, even at low interest rates, bond risk remains proportional to the rate when increased by a factor of 1%. For instance, a shift from 1% to 0% interest rates results in halving the bond risk, contrary to the traditional model’s expectation of nullified risk. The research suggests that the volatility of interest rates behaves as if there is an implicit floor of -1% for rates, challenging the log-normal model that cannot accommodate negative rates or persistent volatility near zero.
Interest Rates: “Normal” vs. “Log-Normal” Post-Lehman Collapse
Following the 2008 financial crisis, markets experienced profound changes, notably in sovereign interest rates, which reached unprecedentedly low or even negative levels. The paper contrasts the log-normal modeling approach, which precludes such negative rates and vanishing volatility, with Heath, Jarrow, and Morton’s (HJM) “normal” model that assumes rate volatility is independent of rate levels.
Douady’s empirical investigation reveals that, while the log-normal volatility rule seemed reliable from the early 1980s until the subprime crisis, the post-crisis era with near-zero rates maintained “normal” volatility levels, thus defying the log-normal model.
Methodology and Findings
Douady’s study employs back-testing of bond data to discern market behaviors regarding the “real zero” level for interest rates and the corresponding volatility as rates decrease. The findings indicate that markets tacitly position this level close to -1%, consistent across different currencies and economic periods, from the 1990s in Switzerland and Japan to the post-2008 era in the USA and Europe.
The paper tests various models to account for observed behaviors, including the normal model with decay factors and a shifted log-normal model that adjusts volatility to be proportional to the rate plus 1%. It introduces an additional independent noise source with a standard deviation of 50 basis points per annum as the volatility floor. The results suggest that this adjusted log-normal model with noise provides a better fit for actual interest rate volatility across various economic configurations.
Conclusions?
Douady concludes that the best model to fit the volatility of interest rates is a hybrid: a log-normal model augmented with an independent noise source. This model accommodates rates falling to -1% and preserves a floor level of volatility near zero, which aligns more closely with empirical observations. The research findings call for a reevaluation of traditional fixed-income models, advocating for adjustments that reflect the realities of modern financial markets, where negative interest rates and low-rate volatility have become part of the landscape.
Critique
The paper provides a compelling argument and robust analysis that challenge long-held beliefs in fixed-income modeling. By integrating empirical data with theoretical scrutiny, Douady’s work makes a significant contribution to financial risk management literature. It highlights the necessity for financial models to evolve in response to changing market conditions and for practitioners to adopt more nuanced approaches in risk assessment and bond portfolio management.
