The Nature of Volatility Across Financial Instruments

Agustín Shehadi Candela

We study the distribution of returns for 4,334 instruments across six asset classes — US equities, exchange-traded funds, US and Argentine fixed income, Argentine equities, and Argentine depositary receipts over foreign shares — using 9.2 million daily observations spanning ten years. Three findings organize the paper. First, the estimated tail index lies between 2 and 4 for every class: the variance exists everywhere and the fourth moment nowhere, which renders the F-test, the chi-squared variance test and the Jarque-Bera test inadmissible on this data. We report them alongside their robust counterparts to show the difference. Second, tail heaviness and volatility are distinct and differently ordered attributes: the two fixed-income classes have the lowest volatilities and the heaviest relative tails, while the most volatile class in the sample has the lightest. Argentine hard-dollar sovereigns dominate US equity on mean, volatility and Sharpe ratio simultaneously while carrying the panel's lowest tail index — a case in which the mean-variance ranking and the tail ranking point in opposite directions. Third, aggregation thins the tails monotonically but does not deliver normality by one month, and the mean reversion that would justify horizon-dependent allocation is modest where it exists (six-month variance ratios of 0.71-0.77 for equity-like classes) and absent in Argentine sovereigns. Accounting for the observed distribution rather than a Gaussian match reduces the optimal US equity allocation by 23% for a log-utility investor, and the welfare cost of the Gaussian assumption rises with risk aversion. We separate inference at the pooled and instrument levels throughout, and show that the two can disagree sharply: the comparison of US equity against Argentine fixed income yields p ≈ 10^-90 pooled and p = 0.42 across instruments. We argue the second is the defensible number, and draw the implications for how risk and horizon profiles should be constructed.

The Nature of Volatility Across Financial Instruments

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