Geometric Balancing, With Leverage

Leverage is a double-edged sword, but one I’ve grown to appreciate over the last few years. If you’re not careful, it will destroy you. However I’m not sure it’s possible to create world class, spectacular, returns without it. Used wisely, leverage actually increases the risk adjusted returns of a portfolio.

Leveraged Geometric Balancing uses a similar portfolio presented in the unlevered version of the strategy, it’s just scaled differently.¹ For example, if the unlevered version calls for 50% SPY, 30% TLT, 20% GLD, and the levered portfolio calls for 2X leverage, the levered portfolio would be 100% SPY, 60% TLT, 40% GLD and -100% Cash.

As discussed in the welcome post the strategy:

• Invests long only.  No shorting. 
• Invests in 4 items:  the S&P500, the 30 year US Treasury Bond, Gold, and Cash.
• Rebalances frequently. 
• Applies up to 3X leverage via the Kelly criterion.²
• Uses a “factor of safety” in portfolio construction.
• Does NOT use momentum in any way.

The unlevered strategy aims to limit drawdowns to 15%. With leverage, the strategy pushes for returns. Therefore the drawdown target is relaxed to 40%.³ Yes, this is high, but we’re looking for performance in this strategy. What can Geometric Balancing really achieve?⁴

The Performance

Turns out Geometric Balancing outperforms most other return focused strategies (save RenTec of course) with a theoretical 21.3% geometric return over 41 years. The worst year was 2015 at -11.52%. The best years were in 1985 and 1995 at a whopping 95%. Only 6 years result in losses. Even though the strategy targets a max drawdown of 40%, the results only pulled back 30%. Thank the Kelly criteria’s magical powers for that.

Unlike the unlevered version, this strategy usually beats the S&P 500 in both the up years and the down years, outperforming the market 2/3rds of the time (27 of the 41 years).⁵

The following chart shows 3X Leveraged Geometric Balancing vs the S&P 500. You can see the portfolio absolutely trounces the S&P, while never suffering painful, large drawdowns of similar magnitude. Annual returns averaged 10% higher than the S&P 500, with only slightly more volatility. But importantly, most of this volatility is upwards, as the maximum drawdown is nearly half the market over the same timeframe.

Selective Leverage

Unlike many leveraged portfolios, this one adjusts leverage based on the current market conditions. I call it an “Up to 3X leveraged” strategy because it’s allowed to go to 3 times leverage, but the rules above will often not let the strategy go that far.

• On average, the portfolio runs 2X leverage.
• Its only pushes to 3X leverage 31% of the time, with most of those dates falling this century.
• The portfolio will go 100% cash, the last time being early 2001
• The portfolio has gone 300% stocks once, for 2 days in August 1995.
• The strategy’s highest bond amount was 230% on November 29th, 1987.
• I’ve capped gold at 96%.
• The historical average is about 120% stocks, 65% bonds, 15% gold, and -100% cash. Although as you can tell actually residing at this average is rare.

Drawdowns

Next is a chart of the drawdown of the portfolio. The worst drawdown happened on July 3rd, 2002, barely passing September 21st, 2001. Other strong drawdowns occurred in 1978, 2009, and 2016.

Draw downs are definitely deeper, and more frequent with leverage. They also don’t always line up with stock market drawdowns. You’re going to feel these. Of course you’re going to feel a 20+% annual return as well, but in a good way.

Sharpe Ratio

Theoretically, when you leverage a portfolio, its Sharpe ratio should stay the same. But Geometric Balancing does not apply leverage uniformly. Similar to card counting in blackjack, it tries to apply leverage – increasing the bet amount – only when the odds are strongly in our favor.

It appears that the strategy works, as the Sharpe ratio of the leveraged portfolio is 1.01, vs .88 without any leverage.⁶ By using the Kelly criterion to size our “wagers”, does Leveraged Geometric Balancing successfully time the market?

A Different Way to Approach Market Timing

Most market timing strategies attempt to predict the direction of the market. Will it go up or down in the short term? Geometric Balancing does not have any idea if the portfolio will go up or down tomorrow. I assure you it doesn’t. Instead it determines the portfolio size by evaluating the consequences of repeating the next day.

Some say volatility is a measure of risk. I believe it is an indicator of the dangers of repetition.

Since the market is one gigantic repetition game, is this the the ultimate key: scaling your portfolio through the the Kelly criterion?²

1-The unlevered portfolio actually does use “leverage”, it just uses negative leverage. Most of the time when you see cash in the portfolio, its levering down either due to risk concerns (minimize drawdown) or to actually increase the total return of the portfolio, aka the Kelly criterion.

2-This post shows how to mix cash and a single asset. Tha same math works with cash and a portfolio. I should also note, I never target the Kelly Maximum point, but always stop short (to the left), which will be the topic of a later post.

3-You certainly can add leverage to a 15% draw down strategy. But due to to the risk limits it’s often going to be quite restricted. Since this post is aimed at showing the strategy’s top end capabilities, that restriction is counter productive for this post.

4-I will say I’ve never traded Geometric Balancing with 3X leverage. I’ve used some leverage, but a much tamer version. Partially because I’m only trading weekly right now, and waiting a week to pull down high levels of leverages is frightening.

5-I kept the analysis through the end of 2018 so that this post is comparable to the unlevered version. For reference, in 2019 through the end of November, the strategy would have returned 58%, with a standard deviation of 18% and a Sharpe Ratio of 2.67 on paper.

6-Sharpe ratio calculations are much trickier than they seem. It could be argued that my Sharpe ratios are too high, and that my standard deviations are too low. My values are calculated from daily data and then scaled through the almost universally accepted

Annual σ = Daily σ x √ 250

Problem is this formula is an approximation and is only accurate when the underlying asset has no expected return. It’s result are often low. I used it here since almost everyone else uses the formula too, allowing for comparisons to others work. At a daily level, where no scaling of the data is required, the Sharpe ratios are 0.052 unlevered and 0.056 levered, still showing nearly a 10% improvement due to leverage. For reference, the S&P 500 has a daily Sharpe of 0.029.