The pricing kernel puzzle concerns the locally increasing empirical pricing kernel, which is inconsistent with a risk-averse representative investor in a single period, single state variable setting. Some recent papers worry that the puzzle is caused simply by the mismatch of backward looking subjective and forward looking risk-neutral distributions of index returns. By using a novel test and forward looking information only, we generally confirm the existence of a u-shaped pricing kernel puzzle in the S&P 500 options data. The evidence is weaker for tests against an alternative with a risk-neutral investor and for longer horizons.

中文翻译：

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前瞻性数据中的定价核心难题

定价核心难题涉及局部增加的经验定价核心，它与单一时期，单一状态变量设置下的规避风险的代表性投资者不一致。最近的一些论文担心，这种困惑仅仅是由后向主观和前瞻性风险中性指数收益分布不匹配引起的。通过使用新颖的测试和仅具有前瞻性的信息，我们通常可以确认标准普尔500期权数据中存在u型定价内核之谜。对于针对风险中性投资者的替代方案进行测试以及更长的视野，证据不足。