I crawled the SEC reports to bring you these wonderful plots.

Exhibit 1: percentage of common stock holdings compared to the AUM:

Technically data back to 2005 is available, but I only went back to 2009 due to time constraints. The X axis on the plot represents the date the report was uploaded to the SEC, which does not necessarily match the date the holdings were measured.

Leveraged ETF's hold a portion of common stock, a portion of futures contracts and a portion of swap contracts. I ignored the futures contracts. I estimate that 2x ETF's have 72% common stock holdings and 3x ETF's have 58% common stock holdings. All inverse ETF's have 0% common stock holdings.

Why does this matter? A 2x ETF has 72% common stock holdings and 128% swap contracts. An 3x ETF has 58% common stock holdings and 242% swap contracts. An inverse 2x ETF has -200% swap contracts. The amount of swap contracts determine how many times the swap contract spread is paid.

Exhibit 2 weighted swap rate of proshares S&P500 over time:

There is no data prior to 2014 because the old annual reports don't contain that information. The X axis on the plot represents the date on which the swap rate was recorded (the reports explicitly state that this is the swap rate as of date X). Nowadays the swaps settle on the S&P index, but some older swaps settle on the SPDR S&P500 ETEF or some MSCI S&P500 ETF, which have additional costs (I didn't look further into this).

Exhibit 3 & 4: weighted swap rate of proshares S&P500 relative to the overnight LIBOR:

There are some oddballs, but in general:

The swap spread for 3x LETF's is about 0.04% to 0.05% higher than the swap spread for 2x LETF.

The swap spread for inverse LETF is around 0.2% lower than the swap spread for normal LETF.

The swap spread for large cap is around 0.4%.

The swap spread for mid cap is less than large cap.

The swap spread for small cap is less than mid cap. Any suggestions as to why this is the case?

Using this information we can compile a new equation for LETF:

Code: Select all

`(S&P500 - rf) * leverage = (LETF - rf) + (leverage - common_stock) * swap_spread`

Here rf is the overnight libor as a proxy for the risk free rate (I did not investigate other proxy's). Leverage is 2 or 3. Common stock is the amount of common stock holdings (.72 for 2x LETF, .58 for 3x LETF. Zero for inverse ETF's). Swap spread is the difference between the risk free rate and the rate on the swap contract, which can be observed on exhibit 3 & 4.

For Ultra S&P500, we find that (leverage - common_stock) * swap_spread is equal to (2 - .72) * .38% = 0.4864%. Siamond used a curve fitting method to arrive at the figure 0.5%.

For UltraPro S&P500, we find that (leverage - common stock) * swap_spread is equal to (2 - .58) * .42% = 1.0164%. Siamond used a curve fitting method to arrive at the figure 1%.

We still have to look into simulating LETF's with daily math and taking a closer look at the equations for inverse ETF's, but I think the friction cost mystery is solved.

Edit: it is worth noting that some of the 2x and 3x ETF's, such as ProShares Ultra MSCI Emerging Markets (2x), have no common stock holdings and are built entirely with swaps, sometimes below market rates.