This index reflects the market view of the future level of the market portfolio diversification. This study proposes an innovative methodology for backing-out implied correlation measures from index options.The methodology is applied to the Dow Jones Industrial Average index and the statistical properties and the dynamics of the proposed implied correlation measure are examined. The evidence of this study indicates that the implied correlation index fluctuates substantially over time and displays strong dynamic dependence. Moreover, there is a systematic tendency for the implied correlation index to increase when the market index returns decrease and/or the market volatility increases indicating limited diversification when it is needed most. Finally, the forecast performance of the implied correlation index is assessed. Although the implied correlation index is a biased forecast of realized correlation, it has a high explanatory power and it is orthogonal to the information set compared to a historical forecast. Take the Dow (30 members). Theoretically we can back out an average pairwise correlation from the vol of the index option and the vols of options on the 30 members – given the weights and assuming ATM strike and same time to maturity etc…
(the basket vol if you like where the DOW is the basket)
define the vector M = [V1.sqrt(w1), V2.sqrt(w2),…….V30.sqrt(w30)] and R as the correlation matrix, then MRM’ (matrix multiplication) will give you the basket Variance.
Now correlation term structure would point to using different correls when comparing the above with different maturities (also you can think of correlation Skew when strikes are move away from ATM)
Well based on the above you may decide that the timing is right for a “Short Correlation” trade where you buy straddles on every single components and sell in the correct proportion a straddles on the basket. Such timing may be right if the correlation CORR is today 0.8 and that as measured over a number of previous periods CORR remains bounded between two values say 0.25 and 0.8.
During a crash however the correlation will go to 1 (or not far off) as all stock will fall together in a nicely buit painfull synchronous fashion