siamond wrote: ↑Sun Feb 24, 2019 8:32 pm
AlphaLess wrote: ↑Sun Feb 24, 2019 10:18 am
However, I would decompose the returns of the strategy in a different way:
1.1. Long 3x Long part of the treasury, short 3x short term rates aka LIBOR (times 60%),
1.2. Long 3x Stocks, short 3x short term rates LIBOR (times 40%),
2. Pay trading costs (by the ETF when rebalancing),
3.1. Pay financing spread (as short term rates at LIBOR are only accessible to certain participants) on treasury leg (x 60%),
3.2. Pay financing spread (as short term rates at LIBOR are only accessible to certain participants) on stock leg (x 40%),
4. Pay expense ratio (investor to ETF management).
Hm, I missed item #2 in this list. Staying with the UBT's example, I guess this would be a form of rebalancing towards their target market exposure (e.g. 80% regular index, 20% swaps & futures providing 120% index exposure). This is confirmed by the following extract from the ProShares annual report 2018 (page IV), and this is indeed not covered by the expense ratio.
Fees, Expenses, and Transaction Costs: Fees and expenses are listed in the financial statements of each Fund and may generally be higher, and thus have a more negative impact on Fund performance compared to many traditional index-based funds. Daily repositioning of each Fund’s portfolio to maintain exposure consistent with its investment objective, high levels of shareholder creation and redemption activity, and use of leverage may lead to commensurate increases in portfolio transactions and transaction costs, which negatively impact the daily NAV of each Fund. Transaction costs are not reflected in the Funds’ expense ratio. Transaction costs are generally higher for Funds whose indexes are more volatile, that seek to return a larger daily multiple of its index’s return, that seek to return an inverse or inverse multiple of its index’s return, that invest in foreign securities, and for Funds that hold or have exposure to assets that are comparatively less liquid than assets held by other Funds.
The fact that 'daily repositioning' transaction costs would be significantly higher if the index of reference is more volatile might (partly?) explain why our model overshoots for stock funds. I couldn't find any quantitative information about such transaction costs though. Any idea?
In 2009 and 2010, when leveraged funds were new, a lot of 'scientific' papers were published about the underlying dynamics of leveraged funds.
One set of papers shed light in the following dimension:
- approaching the end of day, when the index tracked by leveraged fund is up a lot (or down a lot), at the end of the day, the fund has to chase the price, and buy high while paying transaction costs, if you will (in case of down a lot, it would have to be selling low). This causes further market impact, pushing the price in the same direction MORE. However, the impact would probably reverse a bit. I am not sure if this type of price chasing is still market impactful these days.
Now, when you are implementing the 3x strategy 'on paper', then you obviously won't experience the slippage, but you would be subject to the market impact (say, the true price of the index SHOULD have been up 1.2%, if not for the leveraged rebalance, but with the leveraged rebalance, it is 1.3%, and the 0.1% will revert next morning).
Now, if some of the market impact reverses THE SAME day, then an 'on paper' strategy would also look good.
One way to capture ALL sources of slippage is to do the following:
- obtain DAILY returns of the tracking product (NOT the tracking index, but the product). E.g., for TMF, that would be TLT,
- obtain DAILY returns of the leveraged product,
- run a regression:
lev_ret ~ a + b * track_ret + eps.
The variables being estimated are "a" and "b".
Most likely, you will estimate "b" to be *SLIGHTLY* less than the leverage (e.g., 2.9 for a 3x fund), and "a" would be negative.
Then "a" would basically capture all sources of slippage:
- expense ratio,
- funding cost,
- trading costs,
I think you can probably make the regression better if you did this:
lev_ret ~ a + b * track_ret + c * st_ret + eps,
where st_ret are short term funding costs.
But the latter could be hard to obtain (and isolate).
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