Thursday, June 19, 2008

Leverage Always Has a Cost

In yesterday’s post, I explained that Horizon BetaPro’s double exposure ETFs don’t give double the return of the index they are based on. One reason for this is the daily rebalancing of the doubled exposure as explained by Preet Banerjee in this post. Even without this daily rebalancing, the return would not be exactly double because leverage always comes with a cost.

The simplest way to get leverage is to borrow money. Instead of investing $10,000 in an index, you could borrow an additional $10,000, and invest $20,000 in the index. This way, you double your returns. Well, not quite double your returns. You have to pay interest on the borrowed $10,000.

This begs the question, is there any way to truly double your returns without paying any additional costs? We can show that the answer is no because it would create an arbitrage opportunity.

Arbitrage basically means a risk-free way to make money. Suppose that an investment exists that gives double the returns of an index. Then you could put just half your money in this investment to get the full return of the index. The other half of your money could collect interest in short-term government debt. Overall, you’re guaranteed to get better returns than the index whether the index goes up or down. If you simultaneously short the index, then you’re making free money by arbitrage.

So, whether you double your market exposure with borrowed money, stock options, or futures contracts, there will never be a way to guarantee double the return of the index.

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