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Taleb (2007 p103) says “rare events aren’t fairly valued, and that the rarer the function, the greater undervalued it’ll be in price”. There is a huge body of literature on skewness across various asset and markets classes. Evidence of skewness in assets has existed for more than three decades (Beedles, 1979; Alles and Kling, 1994; Chen, Hong and Stein, 1999) to mention a few.
More recently, Harvey and Siddique (2000) suggested that traders require payment for negative skew and expected come back increases with negative skewness. Their results demonstrated skewness is present in asset prices and a prices model incorporating skewness helps describe expected returns in property beyond beta, size and reserve to market. They concluded, “systematic skewness is economically important and commands a risk premium, typically, of 3.per season 60 percent.” As mentioned above Harvey (2000) found that nearly all developed markets have negative skew. Damodaran (1985) was the first ever to highlight that negative skewness can derive from the distribution of bad and the good news from companies.
Companies’ release more very good news than bad news and bad news tends to be released in clumps. Hong and Stein (1999) proposed another reason for skewness. Analysing the implications of brief sale constraints they developed the following intuition. As the price tag on a share falls more info is revealed; specifically the purchase price of which market participants with differing valuations see value. Their differing views weren’t available to the market due to short sale constraints previously. This led to Chen, Hong and Stein (1999), to check whether shares which investors disagree more about as shown by increases in turnover, have higher skewness. Chen, Hong and Stein (1999) documented three major conclusions in their research into conditional skewness in stock prices.
While the existence of skewness is well recorded the reason why for the skewness are less certain. Alles (2004) using simulated data concluded a combination of Alles and Kling (1994) hypothesis produced from Kahneman and Tversky’s (1979) potential customer theory together with Brown, Harlow, and Tinic’s (1988) “uncertain information hypothesis” (UIH) can explain negative skewness. Importantly their finding also demonstrated a straightforward version of the geometric arbitrary walk model cannot create negative skewness.
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Financial theory says that rational investors should prefer positive skew; however, evidence is available showing that traders also prefer negative skew. The longshot bias illustrated by the popularity of lotteries, gaming machines and researched in horse racing can be used to show investors’ preference for positive skew. Hodges, Tompkins and Ziemba (working paper), show that the longshot bias will exist in a few options markets, but I have found no evidence that a wide cross-section of investors ‘suffer’ from this bias.
The bias may be only the behaviour of risk enthusiasts. Harvey and Siddique (2000) found negative skew receives higher profits. They assumed that investors require payment for negative skew; however they did not prove that investors both correctly assessed and required payment for that skew. The surplus returns could be market inefficiency at pricing improbable events. There is certainly evidence that features the inability of individuals to correctly evaluate probabilities. Behavioural financing suggests investors judgemental for numerous small wins and an individual large reduction over numerous small losses and a huge win.
A adversely skewed distribution provides the necessary environment for many small wins, as nearly all incidences are to the right. The good reasons for this can be explained by prospect theory, which hypothesises that traders receive decreasing praise for further increases. Lakonishok, Lee, Pearson and Poteshman (2007) mentioned protected call writing is the most popular option strategy.
Covered calls entail capping upside profits while dealing with downside risk, a negatively skewed strategy. Shefrin and Statman (1993) and Hoffman and Fisher (2010), found framing and risk aversion can describe investors’ predilection for covered writes. Kahneman and Tversky’s (1984) suggested one method to reconcile a co-preference for positive and negative skew.