Estimating Leveraged ETF Decay from Daily Price Changes

Summary

The note proposes estimating the decay of a leveraged exchange-traded fund using daily underlying price changes, leverage, dividends, and a time adjustment that accounts for calendar days. Its motivation is that a volatility-based decay estimate may overstate losses when the underlying has sizable intraday movement but closes near its prior level. Since leveraged funds reset their exposure daily, the author argues that close-to-close changes better match the reset interval than intraday volatility alone.

The document gives a proposed formula and definitions for its variables, but it does not derive the expression or test it against observed fund returns. The example contrasts a low net daily move with a higher volatility reading; it does not establish that the proposed calculation is more accurate. The time conversion and treatment of dividends are also not explained in enough detail to validate the estimate. It should therefore be read as a hypothesis about measuring daily-reset drag, not as a verified valuation method.

Key ideas

• Daily-reset leveraged funds respond to the underlying's close-to-close change across each reset interval.
• Intraday volatility may not imply decay when the underlying ends the day near its starting price.
• The proposed estimate combines leverage, daily price changes, dividend yield, and elapsed time.
• The note does not derive or empirically validate the proposed formula.

Tags

# Calculating the decay of a leveraged ETF


# Calculating the decay of a leveraged ETF












https://www.math.nyu.edu/faculty/avellane/thesis_Zhang.pdf

There is a formula given above but the immediate problem is that using the volatility for $\alpha$ tends to exaggerate decay since it's not uncommon for stocks to move very little despite the volatility being high. For example the SPX has a VIX of 12 despite the price barely changing .5% in a day.

The problem is that 3x ETFs reset daily, not inraday. This means you can tons of intraday volatility but if the prices keep ending unchanged, there will be no decay despite high volatility.

I think my version is more accurate:

$(\delta)^B(e^{(-dBt/360+o/2\ln(1-B^2p^2)-oB/2\ln(1-p^2))})$

t=o*7/5

o= number of trading days.

t=total number of days including weekends

B=leverage factor

d=dividend yield

p=daily price change

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.