Jan

16

IID, from Zubin Al Genubi

January 16, 2024 |

One main assumption in statistics is that samples are independent and not correlated. However, it seems apparent to almost every trader that the outcome for one day is related to yesterdays price action.

Andrew McCauley writes:

Your comments reminded me of something that Benoit Mandelbrot mentioned in his book The (Mis)Behavior of Markets: A Fractal View of Financial Turbulence:

Speaking mathematically, markets can exhibit dependence without correlation. The key to this paradox lies in the distinction between the size and the direction of price changes. Suppose that the direction is uncorrelated with the past: The fact that prices fell yesterday does not make them more likely to fall today. It remains possible for the absolute changes to be dependent: A 10 percent fall yesterday may well increase the odds of another 10 percent move today—but provide no advance way of telling whether it will be up or down. If so, the correlation vanishes, in spite of the strong dependence. Large price changes tend to be followed by more large changes, positive or negative. Small changes tend to be followed by more small changes. Volatility clusters.

Big Al offers:

Just felt like doing some tinkering, so here is a chart with two series: The upper series is the moving 20-day C-C % return of SPY adj, calibrated by the right hand axis. The lower series (left hand axis) is the 20-day rolling sum of the absolute value of the daily % changes. As expected, the lower, vol series tends to peak when the upper series is spiking downward, but the chart could provide some interesting trailheads for further research.


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