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S. Delikouras and M. Linn: The Risk-Return Trade-off Puzzle: Backward- versus Forward-Looking Expected Returns

May 2, 2025

The positive relation between risk and expected returns lies at the core of financial theory. Empirically, this relation is negative. We verify that the risk-return relation holds in expectation using regressions of option-based expected returns on option-based variances. This relation breaks down when in these risk-return regressions, we replace option-based expected returns with realized or fitted returns from predictive regressions. To the contrary, the positive relation is preserved when we replace option-based variances with realized or fitted variances. We conclude that the risk-return tradeoff is true in expectation, and that empirically it breaks down due to realized returns not realized variances.

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