Term Structure of Expected Stock Returns

In the financial literature and media, we often encounter the concept of term structure, such as the term structure of volatility and the term structure of interest rates. Reference [1] introduced the concept of term structure of expected stock returns.

Essentially, the authors utilize options data to first calculate a risk-neutral PDF using the Black-Scholes model. Then, the risk-neutral PDF is risk-adjusted to arrive at the "real" probabilities. To do this, the author assumes power utility preferences for the investors. This approach allows us to obtain the real-world PDF and derive the option-implied expected returns. The paper pointed out,

This paper has proposed a new method to derive the term structure of expected stock returns. Using option prices, a forward‐looking term structure was derived, which we call the “equity curve”. We described how the shape of the equity curve has empirically evolved and analysed its predictive power for future stock returns. Three main results have emerged from the analysis of the US stock market over the period between 1997 and 2017. First, a higher level of the equity curve is associated with higher future stock returns. Second, the slope of the equity curve is also related to future stock returns in a theoretically expected manner. A positive slope (i.e., short‐term expected stock returns are lower than long‐term returns) is followed by future realised returns which are lower in the short term (1 month) than in the long term (1 quarter or 1 year). Third, a steeper slope (either positive or negative) is associated with a larger absolute difference between short‐term and long‐term returns. Thereby, the method used to derive the equity curve from option prices has economically and statistically reasonable properties.

This paper proposed an important concept that should be incorporated into modern portfolio management.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Olaf Stotz, The Equity Curve and Its Relation to Future Stock Returns, J. Risk Financial Manag. 2020, 13, 19

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