**For newcomers to this thread, welcome! This adventure has already taken numerous twists and turns. If you’d like to catch up with the latest developments, I’d recommend you read this post, then skip directly to post #1068 where I posted the 1955-2018 backtest.**

Inspired by market timer's famous thread on his leveraged lifecycle investment strategy during the financial crisis, I am starting a thread of my own on a risk parity strategy using 3x leveraged ETFs. This thread will be a documented record of my strategy. I intend to update the tracker below on a quarterly basis.

**Tracker [updated Feb 5, 2019]**

**What is your strategy?**

I am young (33) and willing & able to take risk. For anyone in my position, one would recommend a large allocation to equities. But might there be a better way to hold those equities? Theoretically and historically, it can be shown that by holding an uncorrelated set of assets (e.g. S&P 500 & long Treasuries) and adding leverage, one could achieve a similar volatility profile with greater returns than by holding the S&P alone.

**What is the evidence supporting your strategy?**

UPRO & TMF, the two ETFs I will use, only have a history of 10 years. EfficientInvestor has suggested a formula to simulate how these funds would have behaved in the past that takes into account the daily leverage reset, the cost of borrowing (1-month LIBOR)*, and the expense ratio:

Here is how the simulated 40% UPRO & 60% TMF (accounting for borrowing costs, expense ratios, daily leverage resets and quarterly rebalancing back to 40/60) would have performed over 1987-2018, as compared to the S&P 500:the equation I currently have in my spreadsheet for daily performance of a leveraged ETF is:

(Daily % of underlying total return index) * X - ER/250 - (X - 1) * (1 month LIBOR) * (Current date - previous date)/360

where X is the leverage (e.g. 2 or 3), the current date is the current date and the previous date is the previous trading day.

And here are the rolling returns:

And here are the drawdowns:

*The funds theoretically pay a negotiated spread above LIBOR to their total return swap counterparties, but for TMF there are times when this spread is negative. Therefore I did not model this spread in the simulated data.

**What is the theory behind this strategy?**

There are three theoretical principles behind the strategy.

First,

*diversification*. When one part of a well-diversified portfolio does poorly, the other parts do not necessarily drop in kind. Over the long run, long term Treasuries and the S&P 500 have had a correlation of approximately 0. (Shorter term Treasuries have been slightly more correlated with the stock market.)

Second,

*risk parity*. Once we have decided upon the assets to hold, the next question is in what proportion we hold them. If the two assets differ significantly in volatility, you’ll want to balance them so that the more volatile asset does not drive the volatility of the portfolio as a whole. Over the long run, the average annual volatility of long term Treasuries has been 10%; unsurprisingly, the S&P 500 has been more volatile, at 15%. Therefore, a risk parity portfolio would hold more Treasuries than stocks. Backtesting shows parity is achieved at 40/60.

Obviously, the problem with a 40/60 portfolio is that it delivers relatively conservative returns. The solution is

*leverage*. In this case, 3x leverage. So far our work has been to take risk out of the portfolio; with this last step we are putting risk back in. The upshot, though, is that our diversified, balanced portfolio delivers more return per unit of risk (i.e. has a higher Sharpe ratio) than the S&P 500 alone. So once we increase the risk of the portfolio (through leverage) to equal the risk of the S&P 500, we end up with far more return than the S&P 500. Which is exactly what the historical evidence shows.

**So you are relying on Long Term Treasuries and US Stocks not crashing together. How reliable is this assumption? Can I truly depend on a negative correlation to save me?**

Siamond gathered data on this question over the past 60 years:

Note how few data points fall into the bottom left quadrant, and how the ones that do only show one asset with a double digit decline (and the other asset with a single digit decline).

More pertinent to this strategy is the daily relationship between the assets:

(These are standard box-and-whisker charts, the box represents the middle 50% distribution, with the top and bottom of the boxes representing the 75th and 25th percentiles, respectively, and the middle line in the box representing the median)

Some observations:

1. When stocks return between -2% to +2% (normal times), LTT behave within that range as well. There is zero correlation.

2. However, when the S&P drops 2% or more in one day, there is a 75% chance that LTTs will rise. The reverse is true when the S&P rises 2% or more in a single day.

3. The negative correlation is more pronounced when stocks plunge. When the S&P drops 4% or more, LTT top 50% performance is between +1 to +3.2%. When the S&P rises 4% or more, LTT bottom 50% performance is between -0.9% and -2.4%.

All of this bodes well for the strategy.

**How confident are you that your simulated backtest actually tracks the real UPRO and TMF?**

UPRO tracks extremely well. TMF has some issues, but siamond's analysis indicates that since 2013 it has also "fallen in line" with the formula. I have uploaded the data here, if you would like to play with it yourself.

**I don't trust a single backtest with only one sequence of returns. Can you run a simulation instead of all possible combinations of observed returns?**

Forum member pezblanco did just that. He simulated several thousand runs of 20-year periods using 1985-2018 data. Here are the distribution of returns (20-year CAGRs on the X-axis, incidence of returns on the Y-axis), with the green bars being this 3x daily leveraged balanced portfolio, and the blue bars being the S&P 500.

**Still not good enough for me. What about the 70s when interest rates were rising?**

Here is the same simulation run from 1968-2018:

**Don't you know that leveraged ETFs are only intended to be held for one day?**

Whenever leveraged ETFs are mentioned on this forum, people inevitably post on the dangers of "volatility decay", and how holding these funds for a longer period will guarantee that you won't get 3x performance out of them. "Decay" sounds like there is something nefarious going on with the fund, but it's nothing more than simple arithmetic of compounding returns.

Let's say over five days the daily returns of the index are +1%, -2%, +3%, -4%, +5%, and you start with $100.

At the end of the five days your $100.00 becomes $102.76.

Now let's use a 3X leveraged ETF. Ignoring ER and other costs, the daily returns are +3%, -6%, +9%, -12%, +15%.

At the end of the five days your $100.00 becomes $106.80.

$6.80 is not 3X $2.76. That's the "decay", and it's nothing more than simple math. This dynamic can also work in your favor: if you check the performance of UPRO against the S&P 500 since inception, you will see that UPRO has delivered

**5x**the returns of the index. If an index tends to go up over time (i.e. exhibits positive momentum), a 3x leveraged ETF will tend to perform better than 3x the index over the long term.

**What are the risks of your strategy?**

The main risk is that the S&P 500 and long Treasuries crash together in the same short period of time. In the past 30 years this has not happened, and I can't think of a real-world scenario in which this would happen. I acknowledge this risk and move forward having accepted it.

More potential risks have been brought up in the hundreds of posts in this thread; I assess them here.

**What if the funds shut down?**

If either long Treasuries or the S&P 500 were to drop -33.4% in a single day, the corresponding 3x fund would be wiped out. But realize that would be the fund working as intended. The strategy I am proposing here rests on the idea that if one asset were to drop so precipitously, the other asset would rise sharply to save the portfolio.

I suppose there is another concern that the companies managing the funds could shut down for some reason unrelated to the underlying assets. I am unconcerned about this; here are the reasons why.

**Doesn't this strategy rely on a stock bull market?**

No. Let's consider the period Aug 2000 - Apr 2010, the "lost decade" for US stocks when the S&P 500 crashed twice and delivered 0% total return. My strategy would have delivered 5% CAGR during this period.This is the beauty of risk parity, when one asset goes down, the other does not.

**Doesn't this strategy rely on a bond bull market?**

No. Let’s not forget that this strategy levers up both stocks and bonds. During rising interest rates (when bonds fall), it turns out that stocks tend to go up.

In the second simulation above which includes the 1970s, the right tail of returns still stretches into the 20 - 30% CAGR range.

**Why not just 100% UPRO?**

Because the drawdowns will be super deep during market crashes, and it may take decades to recover. Here is the backtest between 40/60 3xS&P/3xLTT (Portfolio 1) and 100% 3xS&P (Portfolio 2).

**Why not add gold / commodities / NASDAQ QQQ / small cap / international stocks?**

When considering which assets to hold in 3x leveraged form, you should ask yourself two questions:

1. How volatile is the asset? Is there a high risk of it going to zero in 3x form?

2. Does adding it improve the portfolio’s overall diversification?

Commodities, small caps, emerging markets, tech stocks, are all super volatile (>20% annual volatility, vs. 15% for the S&P 500 and 10% for Long Term Treasuries), and so there is a high risk that volatility decay will cause them to collapse in a -90% drawdown over a short period of time.

Developed market stocks is the only equity asset I would consider holding in addition to the S&P 500, as it is only slightly more volatile than the S&P. However, siamond has found serious issues with the way the DZK ETF is implemented that prevent us from recommending it:

And gold. I just don’t believe we will ever see the kind of inflation again where holding a small portion of gold will actually make a difference to your portfolio. Stocks do reasonably well during moderate inflation.

**Why don't you use futures? Wouldn't that be cheaper?**

It is hard to control your exact leverage exposure with futures due to the large contract sizes and daily cash settlement. For example, one S&P 500 emini contract has a notional value of $140k. I’m willing to pay the extra costs of the ETFs to avoid the time required to monitor and maintain a futures position.

**How much money are you committing to this? How does this account relate to your overall AA?**

I'm investing $100k and letting it ride. As of today (Feb 2019) this represents 15% of my investable assets. I will exclude this account from my overall AA going forward. This is the only way for this to work and grow into the millions; otherwise I would be constantly rebalancing away from this strategy and it would never be able to compound successfully. The rest of my assets will be invested "normally".

**What is your goal with this strategy?**

$10M. If past is prologue, I should be able to hit this number in 25-30 years. If interest rates (and therefore borrowing costs) stay low, the CAGR should be in the mid-20s, allowing me to reach $10M within 20 years.

**If this such a sure thing, why hasn’t anyone else done it?**

They

*have*. Bridgewater’s famous All Weather Fund is built upon these same principles. More here and here.

**All this cavalier talk about leverage makes me think we are at a market high. What if the market crashes from here?**

Once again, this strategy is market agnostic. No matter what the market does from here, the strategy is intended to perform similarly to the S&P 500 on the downside. Samsdad ran through how "Bob, the world's worst market timer" would have done with this strategy over the past 30 years:

viewtopic.php?p=4413245#p4413245

**Ok, you’ve convinced me. Let me copy what you're doing.**

This should go without saying, but I will say it. This is a

**risky**investment. My backtesting shows strong performance vs. holding the S&P 500 by itself, but there is no guarantee this will continue. I am risking money that is a limited amount of my net worth, and if I lost it all, would not materially change the course of my retirement savings.

**Proceed at your own risk.**