November 7th, 2008Correlation Error With Leveraged ETF’s
This is a follow-up to an earlier post that mentioned correlation risk with leveraged ETF’s. Many people are surprised that there is not better correlation to the underlying with the leveraged ETF’s. To clarify that point, consider these facts:
- The Dow Jones ended today’s session at 8943.81, up 248.02 points, or 2.85%
- The Proshares Ultra 2X Dow ETF (symbol DDM) ended today’s session at 34.65, up 1.71 points, or 5.19%
- The Proshares Inverse Ultra 2X Dow ETF (symbol DXD) ended today’s session at 74.48, down 4.83 points, or 6.09%
Correlation risk is explicitly listed in the Proshares prospectus. If there were no correlation risk, then DDM and DXD would have moved exactly twice the percentage of the underlying Dow Jones average, or 5.7%. For today’s session, the inverse ultra came closer to that mark with a negative return of 6.09%. But on any given day, it is fairly random as to which of the Proshares Ultras come closer to their stated objective of returning twice the underlying. Because of the correlation risk, it may even be possible for the underlying index to go UP slightly for the day and the Ultra ETF to go DOWN.
Why don’t the leveraged ETF’s correlate perfectly? – This is a great question to answer, especially in light of even more leveraged ETF’s expected to hit the markets soon. I previously wrote about the Direxion 3X leveraged ETF’s, which also list correlation risk in their prospectus. Leveraged ETF’s can use a number of investment vehicles to target the 2X or 3X returns of an index. The Proshares prospectus lists the following:
- Futures contracts and options on futures contracts
- Swap agreements - In a standard “swap” transaction, two parties agree to exchange the returns (or differentials in rates of return) earned or realized on particular predetermined investments or instruments. The Funds are subject to credit or counterparty risk on the amount each Fund expects to receive from swap agreement counterparties. A swap counterparty default on its payment obligation to a Fund may cause the value of the Fund to decrease.
- Forward contracts – two-party contracts entered into with dealers or financial institutions where a purchase or sale of a specific quantity of a commodity, security, foreign currency or other financial instrument is agreed upon at a set price, with delivery and settlement at a specified future date.”
- Options on securities and Stock indexes and investments covering such positions
Consider for the moment that the new Direxion 3X ETF’s will use one or all of the same vehicles. Any of them would be capable of coming CLOSE to returning 3X the index, but all none would correlate perfectly. Let’s look at the possibility of using stock options only to simulate the leveraged ETF’s 3X exposure.
- Start with exactly $10,000 enough to buy 110 shares of the DIA (ETF that simulates the Dow Jones index) at today’s closing price of 90.13, and have ~$86 remaining (not counting commissions).
- The December 60 strike options have a closing ASK price for the day of $30.15. Purchasing 3 contracts of the December 60 would cost $9,045, leaving $955 remaining.
At the quoted price of the DIA December 60 strike, it has very little extrinsic value. This is because the 60 strike option on DIA is deep in the money by 30 strikes. The price movement of deep in the money options behave have very close to the price movement of the underlying stock. If DIA goes up 5% from 90.13 to 94.63, then the December 60 strikes will go from 30.15 to a minimum of 34.63 just to keep their intrinsic value in tact. A price change in the 60 strike to 34.63 result in a 14.86% change, just short of 3X leverage, and the first reason for correlation error.
The correlation risk so far is explainable due to the un-invested capital difference in the two plays – $955 for the option play and only $86 for the pure play ETF. Surely, you would say, the professional managers of Proshares, Rydex or Direxion leveraged ETF’s would not leave un-invested capital lying around. And you are probably right. But in our simple example, it’s not clear exactly what they would do with only $955. The most direct way for 3X leverage is with the 60 strike, but there are not enough funds remaining for an entire contract and partial contracts are not allowed. The other option is to purchase less expensive and less in the money contracts with the remaining funds. The December 84 strike contract on DIA goes for roughly the $955 remaining. But the price movement in the December 84 strike will not move at 3X the rate DIA. Additionally, because the December 84 strike is less in the money, it is necessary to pay additional time premium for the contract. That time premium will be lost by expiration. That is the second reason for correlation error.
Now consider what happens if DIA moves downward violently, to the 65-70 level. That changes the entire dynamic of the originally purchased deep in the money December 60 strikes. Instead of being deep in the money, they are now closer to at the money, and will inherit significant extrinsic value, or time premium that the underlying shares are not affected by. That is the fourth reason for correlation error.
If those three reasons were not enough evidence of correlation error, then let me add a few more.
- Spreads – The volatility in the market is causing significant increases in the BID/ASK spreads of options.
- Adjustments – The managers may need to consistently adjust the targeted strike prices that were initially chosen to simulate 3X leverage. All those adjustments require rolling contracts, and incurring additional spreads and commission costs.
- Expirations – As option expiration nears, it is necessary to roll those options forward, incurring additional spread and commission costs.
- Management fees – A 1% management fee would also add to correlation error.
- Volatility – changes in volatility have a significant impact on option pricing, especially at the money options.
Other Thoughts – First, let me be clear that the leveraged ETF prospecut’s do not disclose their specific strategy for targeting 2X or 3X returns. The example above is merely an example of a potential method for doing so. But regardless of the methods used, there is no doubt that significant correlation error does occur in the leveraged ETF’s. On top of that, there are also other signficant risks in owning leveraged ETF’s. Chief among those risks, in my opinion, is the counterparty risk. But for all their inefficiencies and risks, the leveraged ETF’s do provide a quick and convenient method for enhancing returns in the market. They are also quite useful for hedging your existing portfolio.