Reasons for skew

Skew for equities is normally inverted

Unless there is a high likelihood of a significant jump upwards (eg, if there were a potential takeover event), equities normally have negative skew (low strike implied greater than high strike implied). There are many possible explanations for this, some of which are listed below:

  • Big jumps in spot tend to be down, rather than up. If there is a jump in the stock price, this is normally downwards as it is more common for an unexpectedly bad event to occur (bankruptcy, tsunami, terrorist attack, accident, loss or death of key personnel, etc) than an unexpectedly good event to occur (positive drivers are normally planned for).
  • Volatility is a measure of risk and leverage (hence risk) increases as equities decline. If we assume no change in the number of shares in issue or amount of debt, then as a company’s stock price declines its leverage (debt/equity) increases. Both leverage and volatility are a measure of risk and, hence, they are correlated, with volatility rising as equities fall.
  • Demand for protection and call overwriting. Typically, investors are interested in buying puts for protection, rather than selling them.

Diverse indices have higher skew

  • Put corrs tend to 100, but diverse index is on avg lower corr — also true for eq weight vs market cap index
  • As index skew is caused by both single-stock skew and implied correlation skew, a more diverse index should have a higher skew than a less diverse index (assuming there is no significant difference in the skew of the single-stock members). This is due to the fact that diverse indices have a lower ATM implied, but low strike implieds are in line with (higher) average single-stock implieds for both diverse and non-diverse indices.

    A related observation on implied correlation: Equal-weighted correlation is c5 points below market value-weighted

    Market value-weighted correlation swaps tends to trade c5 correlation points above realised correlation (a more sophisticated methodology is below). This level is c10 correlation points below the implied correlation of dispersion (as dispersion payout suffers from being short volga). In addition, the correlation levels for equal-weighted correlations tends to be c5 correlation points lower than for market value-weighted, due to the greater weight allocated to smaller – and hence less correlated – stocks.