Due to the interplay between daily rebalancing and volatility, Leveraged Exchange Traded Funds\r\n(ETFs) may experience a cumulative return different from the product of their daily leverage ratio\r\nand the periodic index return. When the leveraged ETF�s return over a particular time frame minus\r\nthe leverage ratio of the ETF multiplied by the underlying index return is negative, we refer to it as\r\ndecay. The quantity of this decay is influenced by the daily leverage ratio, time, index return, and\r\nvolatility. This study quantifies the tradeoffs these variables have on decay, and derives maximum\r\nholding periods given an investor''s decay threshold under various volatility environments. While\r\nthe majority of studies suggest short holding periods for leveraged ETFs, this paper asserts that\r\nextended holding periods can be justified depending on volatility levels and an investor''s\r\nwillingness to accept a certain level of decay.\r\nFor decay thresholds of only -2% and low volatility levels, holding periods beyond 6 months can be\r\njustified for some leveraged funds. Empirically, forecasted decay over a 3-month period based on\r\nthe Russell 1000 and using a GARCH (1, 1) volatility estimate rarely underestimates actual decay.\r\nThrough 2007, the average justified holding period for all but the -3x fund generally exceeded 4\r\nmonths. During the financial crisis, justified holding periods decreased dramatically.
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