Tristan Yates

Understanding Levered ETFs and Geometric Returns

Leveraged ETFs have a monster cost of capital built in that you can calculate by doubling the SPY return and subtracting the SSO return - it's about 7.1%. FYI I'm writing an article for Trading Markets on their 2008 performance and what investors can learn from it in terms of managing portfolios.

The Case Against Leveraged ETFs

Thanks for the comment and questions. This is exactly why I publish.

msangelbates: It sounds like an interesting trading strategy, though I'm skeptical on the predictive power of SMA lines. The article is aimed more at people who are considering holding these at long term investments, as for example, Bill Donahue from the Street has suggested. Email me and we can talk more in-depth - I'm writing another article on momentum vs mean reversion and have some papers you may be interested in. [e-mail].

But as a trader, you likely have access to better index-linked products anyway, like index and ETF futures and options, which is what I personally use. In a low-volatility market I can leverage the index 5x+ times with a capped 20% downside risk using an in-the-money LEAP call. Why even consider a leveraged ETF then?

david: I used Yahoo adjusted-close prices, which include the effects of dividends. I think SSO keeps the dividends and uses them to pay interest costs, and that adds to the lag.

qftz: You may not be using dividend adjusted prices. On close 6/21, adjusted for dividends, SPY was 123.97 and SSO was 68.32. At yesterday's close, SPY was 152.42 and SSO was 97.67. Gain for SPY is +22.9%, SSO is +43.0%. See the 6.1% lag in the nine month period? (43.0 / (2 x 22.9)). If our fund really doubled the return, we would have expected to make +45.8%.

Note that this math differs from the article because we have some additional days, and I did the straight gain here rather than taking the individual daily SPY prices, doubling them, and comparing them to SSO.

The Case Against Leveraged ETFs

I'll expand on the example. Today the closing futures price for the S&P 500 for June is 1518.80. But today's closing S&P price is 1512.75. The difference is 0.4%. In other words, the S&P 500 has to go up 0.4% by June closing, about 30 days away, just so you can break even. That's "how they get you", or in financial terms, how they build the cost of capital into the investment.

Let's say you have $100k to invest and you want to create a 2X S&P 500 index fund. You buy index futures on $200k worth of the index. Every month, you settle and buy more futures. A year later, the index has gone up 10%. Your gains are 20%, or $20,000 right? Not quite. The futures cost you 0.4% x 2 x $100,000 per month, or 4.8% of $200,000 = $9600 for the year. You end up with only $10,400 in gains.

But, because it only takes 5% margin to own a future, you were able to keep $90,000 worth of cash in your account all year earning interest. Invested at 5%, you get an extra $4,500. So your gains are $14,900, or about 15% of your investment. Which is what we'd expect given basic leverage formulas: $2 x 10% - $1 x 5% = 15%.

This is what I mean when I say money costs money. An interest rate is built into any financial derivative you buy, and any leveraged investor has to exceed that cost of capital before they start making money.

The Case Against Leveraged ETFs

Exactly - the financial derivatives they use has a built in cost of capital and the investment gains are reduced by exactly that amount.

For example, today the closing futures price for the S&P 500 for June is 1518.80. But today's S&P price is 1512.75. The difference represents a cost of interest, and if you calculate that cost on an annual basis, you'll get something close to 5%. Or the fund might just buy a swap - at settlement date they exchange the gains in the S&P 500 for the accumulated interest on a short-term bond that pays 5%. It all amounts to the same thing.

I agree that's its confusing, and I did struggle with that section for a while, trying to do a better job of explaining it.

Leveraged ETFs: A Value Destruction Trap?

Thanks for your comment. When you review the prospectus of one of these funds it mentions that a +10% daily rise in the fund followed by a -10% drop will result in a -4% total drop rather than -1% if you owned the index. That validates the share buying/selling computations that we used in the model.

I agree with you that they most likely do use a combination of index futures and T-bills, but when the futures go up, your leverage ratio will go down and when the futures go down, your leverage ratio will go back up, and you're still stuck rebalancing - either buying more futures or selling more futures. The effect is the same.

However, you're correct that we don't know the exact cost of debt. We just used the broker rate of options, which is about 5% right now, and yes, having money in T-bills could make that cheaper. But there is also high expense ratio too that we didn't model.

Anyway, check out the UOPIX chart also and see what you think.

Leveraged ETFs: A Value Destruction Trap?

A reader just let me know about an older ProShares mutual fund that tracked the NASDAQ with constant leverage.
The ticker is UOPIX, and the long-term chart is pretty scary and illustrates the constant leverage trap very well. And if you're thinking of profiting from the constant value trap by shorting the leveraged long, the chart shows that it would likely be successful eventually, but it that it could be a very wild ride.

As for David's brain teaser - is it better to be long the leveraged short or short the leveraged long? Well, you could go quadruple short if you buy the leveraged short on 50% margin. How does that sound?