How Term Premia Relate to Expected Bond Returns
Summary
The document raises a conceptual question about whether bond term premia should be understood like equity risk premia. It contrasts an equity risk premium expressed as the difference between a stock’s physical-measure expected return and the risk-free rate with the common description of term premia through yields. The author is unsure how a yield-based measure reflects compensation for bearing duration risk, since yields describe bond prices rather than directly stating expected excess returns.
No answer or derivation is included, so the text does not resolve the relationship or provide empirical evidence. Its value is as a framing of the distinction between expected return compensation and yield or price levels, and as a prompt to examine how bond pricing connects the two. Readers should treat the author’s definitions as a question rather than a settled explanation; the document also briefly points to volatility risk premia as another comparison between physical and risk-neutral descriptions.
Key ideas
- The author contrasts an equity premium framed as expected excess return with term premia commonly expressed through yields.
- The central question is how a yield-based measure represents compensation for bearing bond duration risk.
- Bond yields are functions of prices, which motivates the author’s concern about connecting price levels to expected returns.
- The document poses the issue but supplies no answer, derivation, or empirical evidence.
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Full text
# Bond Risk Premium (Term Premia) vs. Equity Risk Premium # Bond Risk Premium (Term Premia) vs. Equity Risk Premium I'm generally a bit confused about risk premia, especially when we talk about term premia. My understanding is term premia is the equivalent of the equity risk premium for bonds, which describes the excess expected returns demanded for bonds (or more broadly interest rate derivatives) for being exposed to duration risk. My confusion comes from how it is defined. For equity risk premia, if we were to somehow magically know the underlying (real/physical measure) stochastic process for some stock with drift $\mu_t$, we would say the equity risk premia is $\mu_t-r_t$, referring to the difference between the "real" expected return per unit time and the "risk neutral" expected return per unit time. This is a discussion about the difference in returns that is caused by risk preferences. However, while this exact same quantity would exist for bonds, we instead define term premia in terms of yields, which is a function of prices: that is, term permia seems to have nothing to do with excess returns and instead is just about the absolute "level/number" of the price. I think this more broadly connects to some minor beginner-level confusions between how risk premia is really about expected returns, but somehow this also has something to do with the absolute "level/number" of prices being lower than they should be if investors were risk neutral? Other risk premia like volatility risk premia seem to also fall under the umbrella of there is a difference between some realized trait of the dynamics and the implied risk neutral trait of the dynamics ($\sigma$) -- which again have to do with returns (in this case the randomness of it).
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.