In Principal Components as a measure of systemic risk, the author Mark Kritzman defines absorption ratio (AR) as the fraction of the total variance of a set of asset returns explained or absorbed by a fixed number of eigenvectors. If the ratio is high, it means that the market is tight and vulnerable to negative shocks. If the ratio is low, it means that the market is less vulnerable to negative shocks.
I have implemented the calculation using Python and plotted the ratio (blue line) along with the MSCI ACWI index (orange line). As you can see, they move inversely with each other, which is expected.
The authors also define the following:
ΔAR = (AR15 day-AR1 year)/σ where
AR15 day which is 15-day simple moving average of AR,
AR1 year which is one-year simple moving average of AR
σ which is the standard deviation of one-year AR.
Then the authors calculate average annualized one-day, one-week, and one-month returns following a one-standard-deviation increase or decrease in the 15-day absorption ratio relative to the one-year absorption ratio.
Question 1) How is "a one-standard-deviation increase or decrease in the 15-day absorption ratio relative to the one-year absorption ratio" related to the equation above? Do they mean that ΔAR increases/decreases more than 1 from the previous day?
Answer (by pat) - Short on time, but they are referring to the level of the deltaAR indicator increasing or decreasing 1 unit. Think of it as an oscillating indicator that will typically oscillate between +/-1 during normal regimes, and greater than 1, when anticipating unusual market deviations (fragile).
The author says that "most significant stock market drawdowns were preceded by spikes in the absorption ratio" and "stock prices, on average, depreciate significantly following spikes in the absorption ratio".
Question 2) Can AR be used as a indicator of significant stock market drawdown in the near future? Someone in the industry told me that he personally thinks that the turbulence ratio (also developed by Kritzman) is a better indicator than AR
Question 3) I want to calculate how long, on average, it takes for the stock market to depreciate following a spike in AR. I want to know how many days, on average, it takes for the market to depreciate after the AR goes up. What are some statistical methodology to achieve this?
Thank you so much!