This is an “Average” correlation derived from the Basket IV formula. The “Basket IV” can be derived from the actual market prices of the Index option. In the term on the right, you get the correlation of every existing pair of stock component. If you replace these corr(i,j) terms by only one term CORR assuming they are the same, then you can extract this in front of the equation, and because you can calculate all other terms from the market (such as implied vols for each components), you may therefore derived this “Implied COrrelation” coeficient CORR.
This is the view that the market has about future realised correlation of the whole basket.
This tends to change with time. For example during a bad bear market the correlation increases as all stock tend to move together downward more or less. The opposite is true in a bull market.
Correlation term strucure applies to the equity basket products with an analogy to volatility. For instance, the 2Y correlation computed with the methodology you have chosen can not apply to a multi-underlyings 5Y properly as you will underestimate its level.
From a theoretical point of view, this reveals the market point of view on the right correlation input to match the prices. At this point it recalls the implied volatility frame, isn’t it ?
Another way to approach it is to consider the correlation parameter as the best prediction of the future realized one. So if you calibrate it with a statistical approach, I think you would prefer to take a long historical series to calibrate a 5Y deal and a shorter one for a 2Y.
This study proposes an innovative methodology for backing-out implied correlation measures from index options. This index reflects the market view of the future level of the market portfolio diversification. 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.