**TLT and IEF**

Table 1 summarizes basic information on iShares 20+ Year Treasury Bond ETF (NYSEARCA:TLT) and iShares 7-10 Year Treasury Bond ETF (NYSEARCA:IEF), both of which were introduced on July 22, 2002 and have expense ratios of 0.15%.

**Table 1.** Characteristics of TLT and IEF.^{1}

Ticker | Effective duration | Net assets | CAGR | MDD | Mean of daily gains | SD of daily gains | Sharpe ratio |

IEF | 7.62 years | $7.3B | 5.2% | 10.4% | 0.021% | 0.43% | 0.049 |

TLT | 17.48 years | $5.3B | 6.8% | 26.6% | 0.030% | 0.87% | 0.034 |

^{1}*CAGR, compound annual growth rate; MDD, maximum drawdown; SD, standard deviation.*

As usual, if you choose the shorter duration fund here, IEF, you get better risk-adjusted returns but lower growth potential. That should come as no surprise.

**The beauty of leverage**

As I've written several times before, leverage lets you "lock in" a fund's Sharpe ratio while scaling up expected returns. Before leveraged funds existed, you could only go the other direction. You could always *scale down* expected returns at a fixed Sharpe ratio by adding a cash allocation. But that typically isn't beneficial, because lower-risk investments almost always have better risk-adjusted returns.

Anyway, with leverage, now you can scale up. Looking at Table 1, note that a perfect 2x daily version of IEF would have a higher mean than TLT (0.042% vs. 0.030%), along with slightly lower volatility (0.86% vs. 0.87%). The CAGR would be vastly better than TLT's (10.2% vs. 6.8%), and the MDD quite a bit lower (20.2% vs. 26.6%). In other words, 2x IEF would completely dominate TLT.

**UST**

Enter ProShares Ultra 7-10 Year Treasury ETF (NYSEARCA:UST). Introduced in 2010, UST aims to multiply daily gains of the ICE U.S. Treasury 7-10 Year Bond Index by a factor of 2. It has a 0.95% expense ratio and a market cap of $68.3M.

While IEF is not UST's underlying, we can get a general idea of UST's behavior by regressing its daily gains on IEF's. Tracking was not great in 2010 and 2011 (R^{2} = 0.86), but has been very good since (R^{2} = 0.98).

Figure 1 shows growth of $10k in IEF, TLT, and UST over UST's lifetime. UST has slightly outpaced TLT in terms of raw growth (68.6% vs. 62.9%).

Looking at the performance metrics in Table 2, we see that while achieving a slightly better CAGR than TLT, UST has also experienced lower volatility and a better MDD.

**Table 2.** Performance of IEF, TLT, and UST from Feb. 2, 2012, to Jan. 6, 2017.^{1}

Fund | CAGR | MDD | Mean of daily gains | SD of daily gains | Sharpe ratio |

IEF | 4.4% | 9.1% | 0.018% | 0.41% | 0.044 |

TLT | 7.3% | 20.7% | 0.032% | 0.94% | 0.034 |

UST | 7.8% | 17.6% | 0.033% | 0.80% | 0.042 |

^{1}*CAGR, compound annual growth rate; MDD, maximum drawdown; SD, standard deviation.*

**Keeping up with the expense ratio**

In Table 2, we see that the mean of UST's daily gains is actually slightly less than 2x IEF's (0.033% vs. 0.018%). The reason for that is UST's 0.95% expense ratio.

IEF has an expense ratio of 0.15%, so 0.95% represents an additional 0.8% annual drag, or about 0.0032% daily. If you take IEF's mean daily gain, multiply by 2, and subtract 0.0032%, you get 0.033%, which is exactly UST's observed mean.

The extra 0.8% expense ratio is important here, since we're dealing with bond funds with relatively low raw returns. The expense ratio is also to blame for UST's Sharpe ratio being slightly lower than IEF's.

**Conclusions**

In theory and in practice, a 2x version of the 7-10 year treasury fund IEF soundly outperforms the 20+ year fund TLT. This is not surprising, as leverage lets us take advantage of the shorter duration fund's better risk-adjusted returns, while scaling up raw returns. The 0.95% expense ratio hurts UST, but it still emerges superior to TLT.

As is often the case with strategies based on leverage, more leverage would be better. If there was a 5x version of IEF with the same 0.95% expense ratio, you could replicate UST with a 40% allocation to the 5x fund and a 60% cash holding. The net leverage would be 2, but the effective expense ratio would be only 40% of 0.95%, or 0.38%. Then, the extra drag compared to IEF's 0.15% expense ratio would only be 0.23%, much better than the 0.8% extra drag that UST carries.

On a similar note, I personally expect leveraged funds to be banned in the relatively near future. One of the most basic principles underlying all investments is that you have to take on disproportionately more risk to achieve greater returns; in other words, you have to sacrifice risk-adjusted returns to achieve greater raw returns. Leverage completely undermines that principle.

In summary, I think that UST is an extremely useful fund. It operates similarly to TLT, but with better performance metrics across the board.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure: **The author used Yahoo! Finance to obtain historical stock prices and used R to analyze the data and generate figures. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.