Index funds and exchange-traded funds (ETFs) have been gaining popularity as investors recognize the advantages of the passive approach. During the past few years, some ETFs have moved to blend the benefits of passive indexing with a strategy that offers some potential to exceed the market’s performance. Smart beta funds use such factors as value, momentum, size, and dividends to construct portfolios. A newer, less well-known strategy involves using leverage to alter the performance characteristics of ETFs. These leveraged exchange-traded funds (LETFs) use leverage to offer returns that are some multiple of the underlying index’s performance. The multipliers can be positive for bull funds or negative for bear funds. In Leveraged Exchange-Traded Funds: A Comprehensive Guide to Structure, Pricing, and Performance, Narat Charupat and Peter Miu, professors of finance at McMaster University, help readers gain insight into these relatively new investment vehicles.
At first glance, it seems trivial to cover the topic of LETFs. Seemingly, investors who want to double an index’s performance should simply use a 2× fund. For those who would like to bet on the direction opposite the market’s, a –1× or –2× fund would be appropriate. Little elaboration would appear necessary; intuitively, using a 2× fund would provide twice the return of the market with a corresponding increase in risk. The reality, however, is not that straightforward. For example, investors might expect the tax consequences of LETFs to resemble those of traditional ETFs, but that is not the case. Charupat and Miu delve into this issue and others, drawing on their research into LETFs.
Although the book is compact at 164 pages of text plus notes and a bibliography, it is packed with insight into LETFs. The authors begin with the basics, defining LETFs as well as the regulations and taxation issues associated with them. They move on to more complicated issues, such as return dynamics, compounding effects, pricing efficiency, and tracking errors. Their exploration of these topics leads to findings that may enable investors to use superior trading strategies.
The key to formulating an optimal trading strategy is understanding the return dynamics and compounding effects. Although it would seem that a 2× fund should have a return twice that of a 1× fund, the mathematics are not that simple. The LETF issuer’s goal is to generate returns that are some specified multiple of the daily returns on the benchmark before expenses. As a result of portfolio rebalancing, however, the targeted multiple might not be achieved over longer holding periods. For example, consider a 2× fund. If the index rises on Day 1, the fund will need to increase the amount of leverage it uses to maintain its 2× leverage ratio, which will lead to a greater than 2× return over the index during the two-day holding period if the index rises on Day 2. Alternatively, if the index falls on Day 2, the fund will realize a return that is less than twice the index because of the added leverage.
Volatility can also play a significant part in determining investors’ realized returns. High volatility in the underlying index’s returns reduces the compound returns. This effect is particularly pronounced in sideways markets, where the underlying index moves up and down with no trend. Volatility drag also arises from the use of leverage, and this drag differs for a fund’s long and short positions. To provide a better understanding of return distribution with respect to volatility, Charupat and Miu conduct a number of simulations. Their findings indicate that higher volatility increases skewness and raises the mean return for bull funds but lowers the mean return for bear funds.
Pricing efficiency involves the fund’s price relative to its net asset value (NAV). Prices that deviate significantly from NAV provide arbitrage opportunities. Charupat and Miu find that bull funds tend to trade at a discount and that the size of the discount is proportional to the degree of leverage used. In contrast, six of the nine bear funds they examine traded at premiums. Despite certain discrepancies, the authors find that the pricing of LETFs is efficient on the whole.
Charupat and Miu move on to address tracking error—that is, the extent to which LETFs’ returns deviate from the benchmark. Unlike price efficiency, which normally remains within the arbitrage boundaries, deviations from the leveraged returns of the benchmark can grow over time because of portfolio rebalancing. Using regression analysis, the authors find that tracking error grows as the holding period increases.
The initial chapters’ empirical analysis provides the background for determining appropriate trading strategies. One such strategy involves selecting a fund with the optimal leverage ratio, given the investor’s market outlook. For an investor who is bullish, a higher leverage ratio would at first glance lead to higher returns, but the resulting investment returns will also be subject to a larger volatility drag. Because the reduction in returns resulting from the volatility drag exceeds the increase in returns resulting from a higher leverage ratio, an optimal leverage ratio can be found by balancing these trade-offs. The authors’ research also indicates that seemingly equivalent strategies, such as taking a long position in a bull fund and shorting a bear fund, are not truly equivalent because of differences in volatility drag between long and short funds. Accordingly, two different investors pursuing the same objective can obtain different results as a result of using non-equivalent trading strategies.
The book concludes with a look at options on LETFs. Options provide an additional way to invest in LETFs but at an increased risk, because they provide a second layer of leverage on top of the leveraged returns on the underlying LETFs. The authors use the Black–Scholes model to derive a pricing model for options on LETFs. Their findings indicate that the price effect of changes in the moneyness ratios differs across LETFs with different leverage ratios. The differences in return volatilities for LETFs using different amounts of leverage produce differences in price sensitivities. Funds that use a greater amount of leverage will see their prices drop less as the moneyness ratio increases because greater return volatility increases the chances that the option will still finish in the money. Again, the pricing of options on LETFs hinges on the peculiarities of volatility discussed in an earlier chapter.
Leveraged Exchange-Traded Funds provides investors with the tools they need to navigate the complexities of LETFs. The book provides both an overview of trading strategies for investors and a summary of some of Charupat and Miu’s research findings on this topic. It is an excellent resource for those who are new to the field as well as those who have already begun using these investment vehicles and want to explore them further.
—R.L.M.