What Are the Mean, Standard Deviation and the Sharpe Ratio of A Leveraged EFT and Comparison to the Non-Leveraged One

A leveraged ETF can move in price 2 tims or 3 times the regular ETF. For example, SPXL's price change 3 times of SPY daily in theory. I want to know if a 2 times leveraged ETF has 2 times the mean and 2 times the standard deviation of the regular ETF. I also want to find its Sharpe ratio compared to the 1 time ETF.

Why do I want to know the Sharpe ratio?

I found the lower the Sharpe ratio, the riskier the portfolio, so I want to kwow if it's worth the risk to invest in leveraged ETF.

Suggested Readings:

• How Sharpe Ratio Affects Retirement Fundsflucturation
• Visualizing Stock Price Movement With Different Return Per Unit of RIsk (Sharpe Ratio)

Simulator

Enter the following data for the regular, 1X Bull Market ETF

Daily Risk Free Rate: %
Daily Mean Return: %
Daily Return Standard Deviation: %
Terms:

• 1X Bull Sharpe Ratio: 0
• 2X Bull Sharpe Ratio: 0
• 3X Bull Sharpe Ratio: 0
• 1X Bull Mean Daily Return: 0%
• 2X Bull Mean Daily Return: 0%
• 3X Bull Mean Daily Return: 0%
• 1X Bull Daily Return Standard Deviation: 0%
• 2X Bull Daily Return Standard Deviation: 0%
• 3X Bull Daily Return Standard Deviation: 0%

I found that when the risk free rate is 0%, all leverage ETFs have that same Sharp ratio, so I build this chart to see how the risk free rates impact their sharpe ratio.

The results is the higher the risk free rate the better higher the Sharpe ratio. With the Fed raising rates, it may be a good time to increase 2x bull or 3x bull market ETF such as SPXL positions.