Risk States and the Term Premium on Long-Duration Bonds

Summary

The document poses an asset-pricing question about why long-duration bonds typically earn positive excess returns. It frames the issue through the covariance between an asset’s return and the stochastic discount factor: positive expected excess returns are associated with bonds performing poorly in states investors value most. The central task is to identify those adverse states for long bonds and understand why investors require compensation for holding them.

Inflation and real-rate risk are proposed as possible explanations, but the discussion does not resolve the question. It asks whether inflation alone can account for the premium and whether that account implies zero excess returns for inflation-protected bonds, despite longer-duration TIPS having higher yields than short-duration TIPS. No empirical evidence, model derivation, or answer is supplied, so the document is best read as a conceptual prompt about term premia, risk compensation, and the distinction between nominal and real bond exposure.

Key ideas

• The question links positive bond excess returns to covariance with the stochastic discount factor.
• Long-duration bonds may underperform in states that investors consider especially adverse.
• Inflation and real-rate risk are raised as possible sources of bond risk premia.
• The discussion asks why inflation-protected bonds may still exhibit a term structure of yields.
• No empirical or theoretical resolution is provided.

Tags

# Why do bonds have excess returns?


# Why do bonds have excess returns?












As I understand it, an asset has positive excess returns if and only if it has negative covariance with the stochastic discount factor $M$. That is, it must underperform in states that investors fear.

Long duration bonds typically have positive excess returns (i.e. term premium is usually positive). So what exactly are the bad states in which long bonds underperform?

Is it solely inflation (real rate risk)? If so, wouldn't TIPS have zero excess returns since they return the same real rates in all states? Under that explanation, it doesn't seem to make sense that long duration TIPS have higher yields than short TIPS.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.