**Background**

Direxion Daily 20+ Year Treasury Bull 3x Shares (NYSEARCA:TMF) aims to multiply daily gains of the ICE U.S. Treasury 20+ Year Bond Index by a factor of 3. It was introduced in April 2009 and has a net expense ratio of 0.95%. According to Google Finance, its market cap as of Jan. 16, 2017, is $84.75M.

**Performance to date**

Figure 1 shows growth of $10k in TMF since inception, alongside iShares 20+ Year Treasury Bond ETF (NYSEARCA:TLT), which is essentially an unleveraged version of TMF.

Overall, it's been a wild ride for TMF. It experienced a near-50% drawdown right at the beginning of its lifetime and jolted up and down several times over the next 7.5 years. It achieved considerable separation from TLT in 2015-2016, but gave up virtually all of it when bonds fell following the US election.

Performance metrics for the two funds are shown in Table 1.

Table 1. Performance of TLT and TMF since TMF's inception.Fund | CAGR | Maximum drawdown | Mean of daily gains | SD of daily gains | Sharpe |
---|---|---|---|---|---|

TLT | 5.4% | 20.7% | 0.025% | 0.95% | 0.027 |

TMF | 6.1% | 53.3% | 0.065% | 2.88% | 0.023 |

I think the overall conclusion here is that TMF's slightly better raw returns are not justified by its vastly greater volatility and drawdown potential.

Moreover, the fact that TLT achieved an excellent CAGR during this time period, and TMF only slightly beat it, tells me that TMF may underperform TLT in a more common scenarios where TLT gains 3-4% annually (its current weighted average coupon is 3.23%).

**Daily gains, TMF vs. TLT**

In Figure 2, we see that daily gains map almost perfectly from TLT to TMF, with data points falling very close to the Y = 3X line. This is exactly what you would expect from a 3x leveraged ETF behaving like it should.

**Monthly gains and volatility decay**

Monthly gains also map predictably from TLT to TMF, but the relationship is significantly non-linear (Figure 3; Data is for Jan. 2010 through Dec. 2016).

If we compare the red curve to the blue line, we see that TMF does slightly worse than 3x TLT's monthly gain except at the left and right ends of the graph -- to be exact, whenever the TLT monthly gain is between -6.2% and 5.4%. This is a direct consequence of volatility decay or beta slippage, which I've described in other articles (e.g. Clearing Up Some Beta Slippage Myths).

Now, I'm guessing a lot of readers are thinking that the red curve is practically no different than the blue line; I'm probably overanalyzing and missing the big picture. Actually, the non-linearity here *is the big picture.*

If TMF followed the blue line, and achieved exactly 3 times TLT's monthly gain, then in months when TLT was unchanged, TMF would also be unchanged. The y-intercept for Y = 3X is of course 0.

Instead, TMF follows the red curve, which has a y-intercept of -0.45%. That means that in months when TLT is unchanged, TMF averages a 0.45% loss. That's not negligible; a 0.45% monthly decline corresponds to an annualized loss of 5.3%.

So what's the break-even point for TMF? If TMF followed the blue Y = 3X line, then its x-intercept would be 0, and TMF would average positive growth whenever TLT had positive growth. But the x-intercept for the red curve is 0.15%. That means that on average TMF only grows when TLT gains 0.15% or better in a given month. Again, not negligible -- 0.15% monthly growth is 1.8% annualized.

Of course, if we're investing in TMF, we don't just want positive growth, we want to outperform TLT. If we were on the blue line, we'd be in good shape, since Y = 3X is greater than X (the black line) whenever X is greater than 0, which we expect it to be since TLT is made up of yield-generating bonds. But on the red curve, if you could zoom in far enough, you'd see that TMF outperforming TLT requires TLT growth of 0.22% or better (2.7% annualized).

TLT's current weighted average coupon, 3.23%, is indeed higher than the 2.7% needed for TMF to outperform. Following the red curve, we expect TMF to gain 0.35% monthly (4.3% annualized) when TLT grows in the amount of its current 3.23% coupon.

Is the extra 1% worth sustaining drawdowns 2-3 times as severe? Probably not.

**Long-term underperformance despite higher expected monthly returns**

While TMF's expected monthly return is slightly higher than TLT's -- by my estimates, 0.35% vs. 0.26% -- a basic resampling experiment suggests it is likely to underperform TLT over a longer period.

Briefly, in each of 100,000 trials, I sample with replacement 5 years of daily gains for TLT, using data on TLT since its inception. I calculate TMF gains simply as 3x TLT gains minus the daily equivalent of the 0.95% expense ratio, then calculate performance metrics for the 5-year period.

Table 2. Results of resampling experiment.CAGR range for TLT | Trials in which TMF outperforms TLT | Median CAGR for TLT | Median CAGR for TMF |
---|---|---|---|

2.0%-2.5% | 0/2526 (0.0%) | 2.25% | -0.00% |

2.5%-3.0% | 1/2598 (0.0%) | 2.75% | 1.41% |

3.0%-3.5% | 715/2705 (26.4%) | 3.26% | 2.98% |

3.5%-4.0% | 2602/2756 (94.4%) | 3.75% | 4.43% |

4.0%-4.5% | 2852/2852 (100.0%) | 4.25% | 5.96% |

We see here that TMF almost always underperforms TLT in 5-year periods where TLT averages less than 3% annual growth, and usually outperforms TLT in 5-year periods where TLT averages greater than 3.5% annual growth. In the 3.0-3.5% range, though, where we expect TLT to be given its average coupon, TMF only outperforms TLT 26.4% of the time.

Interestingly, results would be vastly different if TMF did not carry its 0.95% expense ratio. Repeating the same experiment with TMF having the same expense ratio as TLT, in that middle strata where TLT has CAGR of 3.0% to 3.5%, the median CAGR for TMF is 3.97%, and it outperforms TLT in 94.3% of simulations.

**Conclusions**

I believe that TMF makes for a poor long-term investment due to three factors:

- Its high leverage results in 3x the volatility of TLT, and drawdowns 2-3 times as bad.
- Volatility decay translates to substantial losses when TLT is approximately flat, e.g. over 5% annually.
- With the 0.95% expense ratio, TMF will tend to underperform TLT in 5-year periods of typical TLT growth.

On a final point of wishful thinking, I would love to see Direxion or a different company offer a version of TMF that worked on monthly rather than daily gains, as a small number of leveraged ETFs do (e.g. DXSLX). Such a fund would be far less prone to volatility decay, and would be much more appealing overall.

**Disclaimer:** 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.

**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.