About rebalancing leveraged ETFs, I’d like to make a cautionary note. The links above discuss rebalancing with 2X ETFs: I can’t find a paper looking at 3X ETFs and rebalancing.
What distinguishes leveraged ETFs from other types of leverage is the constant leverage. The leverage ratio is the ratio of total assets (debt and equity) to equity. With a margin loan, debt stays constant, but equity varies; therefore, the leverage ratio varies. With leveraged ETFs, that leverage ratio of total assets to equity stays constant.
Assume your portfolio is 100 shares of company A, and each share cost $1. Half of the shares were bought using borrowed money. Assume the value of company A shares go up 25% in the first day, and down 20% the next day. With a constant debt strategy, you’re back to where you started.
Let’s use the same scenario, but with a constant leverage strategy. On the first day, the portfolio increases in value to $125. Prior to rebalancing, your equity is $75 and your debt is $50. But with a constant leverage ratio, you want debt and equity to be the same. So you buy $25 of company A stock. Company A stock now costs $1.25, so you buy 20 shares at that price. After rebalancing at the end of the first day, you have $75 in equity and $75 in debt, with total assets of $150. On the second day, the value of company A stock goes down 20% to $1. Your total assets have decreased to $120. Prior to rebalancing on the second day, you have $45 in equity and $75 in debt. To get back to a leverage ratio of 2, you sell $30 of company A shares at $1 each. You now have 90 shares, which are worth $1 each. You have lost $10, unlike the constant debt strategy, where there was no gain or loss.
To maintain a constant leverage ratio, one rebalances, and that results in buying high and selling low. With a constant leverage strategy, you’re not exposed to margin calls, but the price you pay for that is the rebalancing cost.
The higher the volatility, the higher the rebalancing cost. When volatility is very low, the cost is minimal. But if volatility gets high enough, it will make a constant leverage strategy counterproductive.
http://www.iijournals.com/doi/abs/10.39 ... 11.1.4.066
I’m going to go into the above link in more detail. The following numbers use the CRSP value weighted index from January 1926 to December 2009. They ignore costs and taxes. The annualized rate of return of the index was 9.66%. If the index was levered 2X and the leverage was rebalanced daily, the annualized return was 16.71%. For 3X leverage, the return was 20.46%.
Before you decide to convert your portfolio to 3X leveraged ETFs, read this paragraph. The author doesn’t state whether the following results are with 2X or 3X leverage. He mentions a 99.8% loss during the 1929 market crash. From October 2007 to December 2008, there is a 93% loss. Entry and exit points matter.
He takes the same data base, and divides the return of each year into low volatility and high volatility categories. The dividing line is whether the monthly volatility (annualized) of the last year was more or less than 18.6%. He gives “average arithmetic annual returns based on rolling yearly periods”. For high volatility periods from 1926 to 2009, index, 2X and 3X returns were -1.4%, -2.3% and -3.7% respectively. For low volatility periods, the returns were 15.2%, 33.5% and 55.5%.
Volatility matters. However, returns also matter. The following uses the same assumptions as the last paragraph, but looks at data from 1990 to 1999. Even in the high volatility periods during this time, the respective returns were 12.2%, 21.7% and 27.3%. So higher returns can overcome high volatility.
The author also did a Monte Carlo simulation. The following assumes average annual returns of 6-12%, leverage rebalanced daily and ignores costs and taxes. With a 15% standard deviation, index, 2X and 3X returns are 9%, 16.2% and 21.2%. With a 20% standard deviation, the numbers are 9%, 14.2% and 15%. As standard deviation increases, leverage return decreases, and higher leverage ratios are effected more.
Assume the same scenario as the last paragraph, but average annual returns are 0-6% and standard deviation is 20%. Index, 2X and 3X returns are 3%, 2% and -2.9%. Volatility has overwhelmed the leverage effect.
Assume the same scenario as in the last two paragraphs, but average annual returns are 12-18% and standard deviation is 20%. Index, 2X and 3X returns are 15%, 27.1% and 35%. The increased return outweighs the volatility drag.
The author outlines a strategy where the VIX is used to predict volatility. The VIX average from January 1990 to December 2009 was 20.2%. He mentions that the annualized daily volatility is a bit less than that, and that this overestimate decreased from 5% to 2% in 2003. In this strategy, the investor switches from index funds to constant leveraged funds when the VIX is less than 20, and vice versa when it is greater than 20. He compares this switching strategy to a buy and hold strategy of constant leveraged funds. He shows that from 1990 to 2009, results are similar, but the Sharpe ratio is higher for the switching strategy. From 1990 to 1999, the buy and hold strategy outperforms. But from 2000 to 2009, the buy and hold strategy results in losses, whereas the switching strategy results in gains. As mentioned previously, the high returns of 1990-1999 probably overcame the volatility drag.
In a previous post, several links were given to papers describing a rebalancing strategy when using leveraged ETFs. Leveraged ETFs sell when prices decline and buy when prices increase. The rebalancing strategy buys when prices decline and sell when prices increase. This counteracts the rebalancing losses inherent in a constant leverage strategy. One possible downside to this strategy is that money has to be set aside to buy shares when prices decline.
The link in this post describes a different strategy. When volatility is low, use leveraged ETFs. When volatility is high, use unleveraged index funds.
A case could be made for combining both strategies. Assume returns are in the 6-12% range. The following comes from the Monte Carlo simulation. With a standard deviation of 10%, returns of the index, 2X constant leveraged strategy and 3X constant leveraged strategy are 9%, 17.7% and 25.8% respectively. So rebalancing might make sense for a 3X fund at this SD, although a case could be made for buy and hold. With a standard deviation of 15%, returns are 9%, 16.2% and 21.2%. A better case could be made for rebalancing, especially the 3X fund. With a standard deviation of 20%, returns are 9%, 14.2% and 15%. One should rebalance or possibly switch to unleveraged funds. With a standard deviation of 25%, returns are 9%, 11.6% and 7.4%. The case for switching to unleveraged funds, as opposed to rebalancing, becomes better. Remember that these returns don’t take into account costs
Comments, including criticisms, are most welcome. I have edited the part prior to the link being given, to make the rebalancing cost aspect of constant leverage clearer.