Editing Equity premium puzzle (section)

=== Implied volatility ===

Graham and Harvey have estimated that, for the United States, the expected average premium during the period June 2000 to November 2006 ranged between 4.65 and 2.50.<ref>{{cite journal |title=The Equity Risk Premium in January 2007: Evidence from the Global CFO Outlook Survey |first1=John R. |last1=Graham |first2=Campbell R. |last2=Harvey |year=2007 |journal=Working Paper |ssrn=959703 }}</ref> They found a modest correlation of 0.62 between the 10-year equity premium and a measure of [[implied volatility]] (in this case [[VIX]], the Chicago Board Options Exchange [[volatility (finance)|Volatility]] Index).

Dennis, Mayhew & Stivers (2006) <ref>{{cite journal |title=Stock Returns, Implied Volatility Innovations, and the Asymmetric Volatility Phenomenon |first1=Patrick|last1=Dennis |first2=Stewart|last2=Mayhew |first3=Chris|last3=Stivers |journal=Journal of Financial Economics |date=2006 |volume=41 |issue=2 |pages=381–406 }}</ref> find that changes in implied volatility have an asymmetric effect on stock returns. They found that negative changes in implied volatility have a stronger impact on stock returns than positive changes in implied volatility. The authors argue that such an asymmetric volatility effect can be explained by the fact that investors are more concerned with downside risk than upside potential. That is, investors are more likely to react to negative news and expect negative changes in implied volatility to have a stronger impact on stock returns. The authors also find that changes in implied volatility can predict future stock returns. Stocks that experience negative changes in implied volatility have higher expected returns in the future. The authors state that this relationship is caused by the association between negative changes in implied volatility and market downturns.

Yan (2011) <ref>{{cite journal |title=Jump risk, stock returns, and slope of implied volatility smile |first=Shu |last=Yan |journal=Journal of Financial Economics |date=2011 |volume=99 |issue=1 |pages=216–233 |doi=10.1016/j.jfineco.2010.08.011 }}</ref> presents an explanation for the equity premium puzzle using the slope of the implied volatility smile. The implied volatility smile refers to the pattern of implied volatilities for options contracts with the same expiration date but different strike prices. The slope of the implied volatility smile reflects the market's expectations for future changes in the stock price, with a steeper slope indicating higher expected volatility.
The author shows that the slope of the implied volatility smile is a significant predictor of stock returns, even after controlling for traditional risk factors. Specifically, stocks with steeper implied volatility smiles (i.e., higher jump risk) have higher expected returns, consistent with the equity premium puzzle. The author argues that this relationship between the slope of the implied volatility smile and stock returns can be explained by investors' preference for jump risk. Jump risk refers to the risk of sudden, large movements in the stock price, which are not fully captured by traditional measures of volatility. Yan argues that investors are willing to accept lower average returns on stocks that have higher jump risk, because they expect to be compensated with higher returns during times of market stress.