Finance — Geometric Balancing

Inspired by the Breaking the Market blog, I did a six month experiment with geometric balancing.

Geometric balancing is an investment strategy that revolves around frequent re-balancing of a portfolio of (hopefully) uncorrelated assets. The theory is somewhat complicated (I summarized some its blog posts here), but in practice it seems to simplify the investment process a lot. Similar to ergodicity economics, it is a powerful tool to better understand and handle complex decisions.

I was never a very disciplined investor. I didn’t develop a good framework for it. Most of the time, I focused on the wrong questions (how to time the market, which industries or stocks to buy, etc.). Investment decisions were based on a mix of emotions, vague intuitions and selective memory. Gut type decisions (see “The Hour Between Dog and Wolf”). Depending on the mood of the day, an investment decision was driven by my best or worst investment memories.

My investment results were very mixed and often caused a fair amount of anxiety. This anxiety increased my aversion to risk and ultimately made me lose interest in investing altogether.

I was looking for a framework to help me re-enter the market and came across geometric balancing on the Breaking the Market blog. The math was not always easy to follow, but I liked the simplicity of its general framework. On top of that, I was attracted by one of the strategy’s key objectives: lowering volatility. Given my risk aversion, I was curious what geometric balanced investing would “feel” like. I also wondered if I could replicate the results achieved by the blog’s author. You can read about his one year experiment with geometric balancing in his post here.

So I decided to give geometric balancing a six month test run.

Key benefit: less stress

Two quick points before getting to the benefits.

First, I could not have done this experiment without access to the Breaking the Market blog. The blog has many posts explaining the theory and provides daily asset weight suggestions. Without these, I would not have learned about geometric balancing or even run this experiment. So I owe a debt of gratitude to Breaking the Market. Of course, any mistakes and misinterpretations are my own.

Second, on the topic of mistakes and misinterpretations, this experiment was far from perfect. I made a bunch of trading mistakes and there were several practical limitations. During the first month, I maintained a small cash balance (I couldn’t yet trade on margin), even when the suggested cash position was zero. If a suggested trade was very small, I typically would not execute it. Time zone differences made things more difficult (I think Breaking the Market is based in the UK; I’m in the Asia-Pacific region). I was not overly disciplined on making portfolio changes at exactly the same time each day. In short, there were flaws. Hopefully they didn’t affect the results too much.

The key benefit of this experiment was a material, tangible reduction in stress.

Discipline was a major factor in reducing stress. A clear framework and trading discipline made investment decisions very simple. I didn’t have to think too much or second-guess myself. I just followed the suggested allocation on a daily basis and executed the trades.

Sometimes the suggested trades were in line with my intuition. Sometimes they were not. It didn’t matter. I just did what I was told to do. This new discipline made old intuitions irrelevant.

And that was a good thing. I quickly saw how often my old intuitions were wrong. A reminder that intuitions may not work that well in complex environments.

Less volatility was another major stress reducer. The market moved violently during the experiment, providing a real test for the strategy. But there were no stubborn attachments to positions or visions about the future. Market exits and entries were swift and emotionless. At the height of market volatility (mid-March 2020), the portfolio had 11% in stocks and 60% in cash. That seemed appropriate and felt good.

In terms of investment return, the strategy outperformed. I think that may be a fluke. It’s difficult, and perhaps meaningless, to analyze investment returns over such a short time period.

While the strategy’s ability to deliver an acceptable return is important, it is probably the most uncertain variable and least predictable. If you are going to drive a particular variable, it probably makes more sense to focus on volatility than returns.

Some issues to consider

Geometric balancing requires regular re-balancing. But what is sufficiently regular? The daily adjustments, while not a ton of work, felt a bit much. Three months ago, I started a portfolio where I make only weekly adjustments. After 3 months, the weekly geometric portfolio’s returns are about the same as the daily geometric portfolio’s returns. Its volatility is slightly lower.

Portfolio adjustments are based on asset class weights that are calculated by Breaking the Market. I think its calculations are based on returns, volatility and correlations, but it is a black box. To implement this strategy I need the daily weights. If Breaking the Market stops publishing these weights, I will not be able to use this strategy.

In times of extreme volatility, it helps to have more of a finger on the pulse. It probably makes sense to set alerts for extreme market movements. Once an alarm is triggered, the default will be to check Breaking the Market weights. If no information is available there, it may make sense to move some fixed percentage of assets in or out of cash.

Going forward

I will continue to use some form of geometric balancing. I may adjust some of its elements:

  • Diversification – no changes:
    • Continue with index funds only.
    • Continue with stocks, bonds, gold and cash only.
  • Re-balancing – small changes:
    • Switch from daily to weekly re-balancing.
    • Continue with weights suggested by Breaking the Market.
    • If unavailable, switch to a conservative Fixed Combo strategy.
    • Set alerts to handle extreme volatility.

Key takeaways

  • Diversification: keep it simple.
    • Limited number of asset classes (stocks, bonds, gold).
    • Index funds (not individual stocks).
  • Re-balancing: make it easy.
    • External, objective instructions provide useful discipline.
    • Less instinctual adjustments and second-guessing.
  • Biggest benefit is lower stress.
    • Simple, easy decisions.
    • Discipline.
    • Less volatility.
  • Moderate return expectations.

Summary results

The Geometric strategy had higher investment returns than an all stock strategy (“All Stock”) and a fixed diversified portfolio (“Fixed Combo”) strategy. The strategies are explained in more detail below. The Geometric strategy was also substantially less volatile than the other two strategies:

Experiment Summary 1

An interesting side note. These results illustrate that averages can be very misleading. In this experiment, the average daily return for the All Stock portfolio was +0.01%. And yet, the All Stock portfolio was down for the period.

Process: asset selection

Step 1: initial asset selection – diversification (3 index funds + cash)

First, invest in uncorrelated assets. Or, assets that are uncorrelated as much as possible. To keep it simple, I followed the example of Breaking the Market and invested in stocks, bonds, gold and cash. This post explains the logic of picking these assets classes.

Second, invest in index funds, rather than individual stocks. For stocks, I picked “SPY”. For bonds, I picked “TLT”. For gold, I picked “GLD”. These particular index funds seem the most liquid. They can also be traded outside of regular US trading hours  (important to investors outside of the US).

Step 2: ongoing asset selection – re-balancing (daily updates)

Re-balancing is at the core of this investment strategy. Every day, the appropriate weight of each asset class (stocks, bonds, gold, cash) is assessed. As suggested allocations on the Breaking the Market blog changed, I re-balanced the investment portfolio.

I made one or more changes to the portfolio on 84 days out of the 125 trading days in this experiment (67%). In total, I made about 217 individual trades. The most traded asset was TLT (75 trades).

The Breaking the Market blog also suggests a leverage factor. I didn’t apply any leverage.

Over the course of six months, this is what the investment portfolio composition looked like.

Experiment Breakdown

Results: returns – strategy outperformed, probably “lucky”

Individual asset class performance for the relevant period was as follows:

  • Stocks (SPY): down 4%
  • Bonds (TLT): up 18%
  • Gold (GLD): up 13%

Experiment Stock Graph 1

I was most interested in how geometric balancing performed against an all stock or fixed diversified portfolio. If I wouldn’t use geometric balancing, I would put 100% of the portfolio into stocks (and keep it there). Or, I would put some amount in stocks, bond, gold and cash and leave it unchanged (in this case, 66% stocks, 16% bonds, 16% gold and 2% cash). I would not invest 100% in bonds or gold, so I was not interested in comparing geometric balancing against bonds or gold.

The all stock strategy is labeled “All Stock” and the fixed diversified strategy is labeled “Fixed Combo”. The strategies performed as follows during the six month period:

  • All Stock: down 4%
  • Fixed Combo: up 2%
  • Geometric: up 6%

Experiment Stock Graph 2


The Geometric strategy ended up outperforming the All Stock strategy (by about 10%) and the Fixed Combo strategy (by about 4%).

I was curious to what extent this out-performance depended on the day the experiment started.

Quite a bit, it turns out.

Simulating different starting dates had a big impact. Against the All Stock strategy, the maximum out-performance by the Geometric strategy was about 11%. Close to the experiment’s 10% out-performance. So I was lucky in timing the experiment. The maximum under-performance was as low as 30%. This was of course against the All Stock portfolio started on March 23, 2020, the day the stock market reached its lowest point for 2020.

The range of relative performance is illustrated by the graph below. The x-axis shows the date each portfolio was simulated to start. The y-axis shows the relative performance of the Geometric strategy (against the All Stock strategy).

Each portfolio ran until June 30, 2020. Portfolios that started later had a shorter period to run. As you move right on the graph, results probably become less meaningful.

Experiment Relative All Stock

Compared to the Fixed Combo strategy, the maximum out-performance was close to 4%. Again, about the same as the result for the experiment. The maximum under-performance was negative 2%. These are meaningful differences in returns, but a much tighter range than for the All Stock comparison.

Experiment Relative Combo

I’m not sure it makes sense to generalize any of these results. The measurement period (6 months) is short. The experiment took place during a period of very high market volatility.

Perhaps the takeaway is that if your investment objective is absolute investment returns, geometric balancing may not be your first pick.

Results: volatility – material reduction

This is where the Geometric strategy seems to be most effective.

The implied annual volatility for each of the strategies:

  • All Stock: 44%
  • Fixed Combo: 24%
  • Geometric: 11%

The first building block of reduced volatility was diversification. The Fixed Combo strategy already achieved material volatility reduction. Its portfolio was kept fixed at 66% stocks, 16% bonds, 16% gold and 2% cash. This level of diversification was enough to reduce volatility by about half (versus the stock market’s volatility).

The second building block, frequent re-balancing, further reduced volatility. The re-balancing Geometric strategy takes volatility down by another 50% or so.

The starting date didn’t seem to have much impact on volatility for the All Stock and the Geometric strategies.

For the Fixed Combo, it mattered a lot. Different starting dates had different cash allocations (which stayed the same throughout the investment period). Portfolios that started with higher cash allocations had much lower volatility. This is shown in the table below. The March 20, 2020 starting date Fixed Combo strategy had 60% in cash, and a much lower volatility.

Experiment Volatility

11 thoughts on “Finance — Geometric Balancing

  1. Hello Jeroen

    I am about 6 weeks into the exact same experiment that you have run – thank you for posting this. I would say my approach is fairly similar, and I have similar findings, so far. The biggest difference between our experiments is I am running it in 5 distinct paper trading accounts, as follows:

    1) Exact same as BreakingTheMarket website, rebalanced daily, although I do it at random times during the day. More a matter of convenience than by design.
    2) Same as BTM website allocations, but using micro futures. Bonds do not have micro futures, and it is hard to get to the exact allocation with the big contracts, so I balance this with TLT.
    3) 2X the BTM website allocations using micro futures.
    4) Same as BTM website, but using 2X ETFs
    5) Same as BTM website, but using Vanguard ETFs

    Trading in the accounts did not start on the exact same day, as Interactive Brokers had to work to get things set up to trade leveraged ETFs, which took them about 2 weeks. And I didn’t start the Vanguard account until later also. These two accounts are significantly behind on returns relative to the other accounts. As you pointed out, the start date does have an impact on these short-term experiments we are doing.

    So far, the returns are as follows after 6 weeks:

    1) SPY/TLT/GLD 2.97%
    2) Micro Futures 2.81%
    3) 2X Micro Futures 3.54%
    4) Leveraged ETFs 1.73%
    5) Vanguard ETfs 0.82%

    Of course, there is much more volatility in the 2X micro futures account, as expected. And I would likely not go that high in a real account. But it’s paper, so what the heck.

    1. Interesting stuff. In my experience, stable differences in volatility emerged pretty quickly. Differences in return were more less predictable.

      1. Good website. Where can I find the procedure for three or more assets and cash? Thank you. Greetings from Chile.

  2. Hi there,

    Nice post. I too stumbled across BTM. One of my main concerns with the method is the use of inappropriate benchmarks for comparison. As you can imagine, it’s very easy to trick oneself into thinking it works.

    I believe there are possibly three appropriate benchmarks:

    1) The Permanent Portfolio (a lot of cash though).
    2) 1/3 Split (Gold, Bonds, Stocks).
    3) Fixed weights as the average of those historically used by the Geometric Method (50 Stocks, 35 Bonds, 5 Gold, 10 Cash).

    YTD, both the Permanent and 1/3 split have returned ~10%, both beating Geometric.

    I realise that, in backtesting, BTM shows that the method’s returns exceed that of either, but I’m sceptical if the backtests are correct (e.g. include trade costs / trade lag and the rebalance frequency).

    1. Hi James,
      Thanks for the reaction.I think you are correct in being skeptical about returns. I also take your point on what benchmarks are relevant. There are much more sophisticated ways of comparing strategies.

      My ambitions with this experiment were quite limited and many of my observations are probably too specific to generalize. I picked specific benchmarks, because I wanted to find out what this strategy would do compared to what I would otherwise engage in (all stock or a reasonably diversified portfolio).

      Higher absolute returns are probably a fluke – it may or may not happen. Lower volatility is quite reliable. And that is quite valuable to me. There probably are appropriate risk-adjusted return measurements that allow you to make more meaningful comparisons.

      But that’s more sophisticated than I’m capable of and I’m not sure I need to dig that deep.

      Btw, the numbers in my post are based on an actual portfolio that was run for 6 months and the numbers are net of trading costs and include all the costs and deviations related to trading lags and errors.

      1. I’m running a script in R that rebalances monthly and accounts for trading costs.

        Using $ Spot Gold, 10 Year Treasuries and S&P, and 1% on Cash here are my numbers (YTD):

        Permanent = 11.6% Return, 10.7% annualised vol
        1/3 Split = 14.3% Return, 13.5% annualised vol
        Geometric Average Fixed Weights (50/35/10/5) = 11.6% Return, 19% annualised vol
        Thirds Plus Cash (30/30/30/10) = 13.6% Return, 12.8% annualised vol

        According to your numbers:

        Geometric = 6% Return, 11% annualised vol.

        That’s a pretty bad risk/return ratio in comparison to the simpler fixed weight methods.

        Although I totally agree that this is a VERY short period of time. I just think it’s important to compare similar asset portfolios that are simpler (and cheaper) than Geometric Rebalancing.

        On the other hand, this is *exactly* the period of time that someone would want to control the volatility in their portfolio, and Geometric fails to offer much improvement in vol over the simpler methods and disappoints with returns.

        Don’t get me wrong, I *really* like the theory of Geometric Rebalancing, but I’m deeply sceptical that trailing vol and correlation predict future returns / vol / correlations.

  3. Thanks for the feedback. Yes, a very short time period and tough to draw conclusions. At the risk of over-analyzing this, some points:

    1. For my trading account, cash gets an interest rate of 0.01%. Given how small that is, I have not corrected for this in my strategy comparisons.
    2. To compare strategies, I use SPY, TLT and GLD daily closing prices. The strategy’s daily return and volatility is simply the number of units x price for each asset plus the cash allocation.
    3. The same measuring period is used for each strategy (in this case Jan 6 – Jun 30 2020.

    Doing a quick check, the numbers shake out as follows:

    a. 33.3% SPY / 33.3% TLT / 33.3% GLD / 0% cash: period return 9%, annual volatility 16.6%
    b. 30 / 30 / 30 / 10: period return 8%, annual volatility 14.9%
    c. 50 / 35 / 10 / 5: period return 5.5%, annual volatility 17.1%
    d. geometric: period return 5.7%, annual volatility 11.1%

    For any fixed diversified portfolio to achieve a lower volatility than geometric balancing, you would probably need to have a very high cash allocation (for instance, for this particular period: 0/20/20/60 has a 6.2% period return and 10.4% annual volatility).

    Geometric balancing, depending on market conditions, may give up some return for lower volatility. How much and whether or not it is “worth it” is an open question for me.

    Whether or not trailing indicators are useful as a basis for re-balancing is a fair and important question. That’s outside of my pay grade.

    1. Thanks, that’s a good comparison, but are the weights fixed at the start or rebalanced? If the latter, how frequently and are trade costs taken into account? My numbers are rebalanced monthly and the cost of that rebalance is taken into account.

      The other major difference between our numbers is the TLT and GLD. I’m using actual gold price, but I realise that wouldn’t be as liquid / straightforward as GLD (e.g. would involve something like spreadbetting or holding physical).

      My 10 year treasury model uses a formula to calculate the price of the 10 year based on the daily yield from FRED, enabling me to go back as far as that dataset (1962), which is why I use that instead of TLT. (The 20 year can be done in the same way, but the dataset is shorter and is even more “generous” vs. TLT, which is why I use the 10 instead).

      1. Yes, for the comparative benchmarks in the previous reply, I just let the portfolio run without re-balancing to get back to the initial weighting.

        Running the same portfolios with monthly re-balancing (these are rough calculations):

        a. 33.3% SPY / 33.3% TLT / 33.3% GLD / 0% cash: period return 9%, annual volatility 16.5%
        b. 30 / 30 / 30 / 10: period return 8%, annual volatility 14.8%
        c. 50 / 35 / 10 / 5: period return 6.0%, annual volatility 18.1%
        d. 0/20/20/60: period return 6.0%, annual volatility 9.8%

        And with weekly re-balancing:

        a. 33.3% SPY / 33.3% TLT / 33.3% GLD / 0% cash: period return 10%, annual volatility 16.7%
        b. 30 / 30 / 30 / 10: period return 9.1%, annual volatility 15.0%
        c. 50 / 35 / 10 / 5: period return 6.7%, annual volatility 18.9%
        d. 0/20/20/60: period return 6.4%, annual volatility 9.4%

        Returns improve across the board. For volatility, I’m not sure you can draw too many conclusions here (other than that the stock heavy portfolio becomes more volatile still with increasing frequency of re-balancing).

  4. That’s another issue I have with BTM’s theory – shorter rebalances are not superior.

    This was discussed and shown here –

    It’s also borne out with any (accurate) backtest (e.g. Portfolio Visualiser / my local R script).

    Here are accurate results, YTD, both with and without fees applied on a 50/35/10/5 portfolio (Stocks/Bonds/Gold/Cash).

    (Again, my returns are higher because I’m using different inputs in the case of bonds and gold, but the theory holds).

    With Trade Fees:

    60 days = 12.19%
    30 days = 10.95%
    10 days = 9.8%
    7 days = 10.17%
    5 days = 9.82%

    Without Trade Fees (almost identical, but my fee estimates are low – I can specify whatever fee I think appropriate in the code):

    60 days = 12.2%
    30 days = 10.95%
    10 days = 9.81%
    7 days = 10.19%
    5 days = 9.85%

    A better pattern emerges if we run across the full dataset (1979 – 1st July 2020) because we have more datapoints that remove the noise of a “lucky” rebalance.

    With Trade Fees:

    365 days = 9.82%
    120 days = 9.67%
    60 days = 9.74%
    30 days = 9.72%
    10 days = 9.68%
    7 days = 9.74%
    5 days = 9.71%

    There is no clear optimal rebalance frequency in the long run. Many studies suggest that less rebalancing is superior. e.g. one of many links –

    Again, I don’t want to appear entirely negative or argumentative, but I don’t want people to stumble across this idea that frequent rebalancing is better.

    All that matters is the rebalancing itself, forcing the sale of “expensive” assets and the purchase of “cheap” assets.

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