Record highs of flagship indices ‘cluster’ together
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Following a month’s gap, the NSE Nifty hit an all-time high again on Monday, closing at 9,771.05 points. Likewise, the BSE Sensex hit a record by closing at 31,715.64. This was the second time this month that the Sensex closed at an all-time high, following three such occurrences in June, nine in May and three in April. Prior to this, the last time the Sensex had closed at a record high was way back in January 2015.
Looking at the figures, which show the closing levels of the Sensex and the Nifty over the past 10 years, a naive reader (or a certain kind of chartist) might assume that we are in the middle of yet another bull run. From a pure data analysis perspective, this is not an unreasonable assumption to make, for historically we have seen that record highs of the flagship indices “cluster” together.
With some analysis, however, it is clear that it is quite logical for record highs to cluster together, and that we can’t really predict how long this bull run will last. Most commonly used models of stock prices (and indices) assume that prices follow a “random walk”, which implies that market returns are normally distributed at whatever time scale you look at, and that returns in one time period are not correlated with returns in a non-overlapping time period. What this implies is that the closer the previous day’s closing level of an asset or an index is to the all-time high of the instrument, the more likely it is that it will end at an all-time high.
Trivially, if the market has closed at an all-time high today, all it needs to close at an all-time high tomorrow is to generate a positive return, and the likelihood of that happening is greater than 50% (because long-term returns of any stock index are positive). In other words, dates when markets close at a record price cluster!