Optimal Leverage

Ticker

Start Date

End Date

Lower Leverage

Upper Leverage

Chart Loading...

Calculation of Optimal Leverage Curves

Leveraged ETFs are affected by the concept of volatility drag, which refers to the loss in returns caused by daily market volatility. This drag impacts all leveraged ETFs.

This paper^[1] presents a formula for the long-term compound annual growth rate of a leveraged ETF, which is approximated as:

R = k \mu - \ rac{0.5 k^2 \sigma^2}{1 + k \mu}

Here, $R$ represents the compound daily growth rate, $k$ denotes the ETF leverage, $\mu$ is the mean daily return of the benchmark, and $\sigma$ indicates the daily volatility of the benchmark.

References:
[1] Cooper, Tony, Alpha Generation and Risk Smoothing Using Managed Volatility (August 25, 2010). Available at SSRN: https://ssrn.com/abstract=1664823 or http://dx.doi.org/10.2139/ssrn.1664823

Calculation of Optimal Leverage Curves

Leveraged ETFs are affected by the concept of volatility drag, which refers to the loss in returns caused by daily market volatility. This drag impacts all leveraged ETFs.

This paper^[1] presents a formula for the long-term compound annual growth rate of a leveraged ETF, which is approximated as:

R = k \mu - \ rac{0.5 k^2 \sigma^2}{1 + k \mu}

Here,

R

represents the compound daily growth rate,

k

denotes the ETF leverage,

\mu

is the mean daily return of the benchmark, and

\sigma

indicates the daily volatility of the benchmark.