Nonlinear Relationships and our Glass (not Black) Box
In the Southern Indian Sree Krishna Swamy Temple of Ambalapuzha there is a tradition of serving Paal Paysam, or rice pudding, to visiting pilgrims. Legend has it the tradition arose after a chess game between the reigning king, and the Indian deity, Krishna who was disguised as an old travelling sage.
To make the match more interesting, and confident in his playing abilities, the king asked the sage to choose a prize if he won. Claiming to be a man of few material needs, the sage asked for a few grains of rice, with the amount determined using the chessboard. One grain of rice was to be placed in the first square, two grains in the second square, four in the third square, and so on with each successive square doubling the amount of its predecessor. The king considered the requested reward insignificant given the vast riches in his empire and the game began.
Exhibit 1. Rice on Chessboard
Needless to say, the king lost and began placing grains of rice on the board to pay the prize. He quickly realized the true cost of the sage’s request. Before long, the royal stockpiles of rice were exhausted and the king determined he would never be able to repay the debt. The sage then appeared in his true form as Krishna and told the king that he did not have to repay the rice immediately but could do so over time. The king began serving rice pudding in the temple freely to the pilgrims every day until the debt was paid off.
There is no need to rush to the temple in Ambalapuzha get your free rice pudding any time soon. They will be fulfilling the king’s obligation until the end of time. The geometric progression, or exponential growth, of the amount of rice needed to fulfill the king’s obligation appeared insignificant beginning with one grain of rice, but after doubling each successive square 63 more times, the obligation grew to 9,223,372,036,854,775,808 grains of rice on the 64th square alone (263 or more than 9 quintillion). The total amount of rice on the board would be 18,446,744,073,709,551,615 grains, or over 1.4 trillion metric tons. To put that into perspective, it equates to about 2,800 times 2020’s global milled rice production.
The story highlights the difficulty humans have in understanding nonlinear relationships. Our last quarterly note highlighted our model’s greater prediction accuracy compared to Wall St. analysts(see Exhibit 4). In this note, we will show why we believe accounting for nonlinear relationships within our predictions gives us a sustainable competitive advantage in accurately forecasting dividend growth.
Wall St. analysts usually take a linear approach in forecasting dividends, utilizing the current payout ratio and multiplying it by their forecasted EPS. In their models, dividend growth is a function of EPS growth, at a one to one ratio (assuming a stable payout ratio which many of them do). As the Harvard Business Review states in an article entitled “Linear Thinking in a Nonlinear World”, the human brain likes simple straight lines. However, we know dividends are influenced by much more than just two factors. The general macro environment, management’s view on future business prospects, their sustainable free cash flow generation, and where the corporation is in its lifecycle are just a few of the factors affecting prospective dividend growth not accounted for in many models.
The many variables that go into the decision on dividends make forecasting dividend growth accurately quite complex. We have over 1,000 features as inputs into our dividend prediction model. These are specific data points that we believe have some impact on dividends. Of these, 200-300 have a significant effect on our predictions and 20-30 really matter. Even processing the 20-30 highly relevant data points to produce a good prediction without the use of a machine learning model would be extremely difficult, much like trying to get your head around how big 264 really is.
The Weber-Fechner Law states that human perception is a logarithmic function of the amount of stimulus. We are very fast and accurate assessing few data points but slower and less accurate in assessing large amounts of information. In the exhibit below, both bottom squares have ten more dots than the upper ones, but it is much easier to see between the boxes on the left compared to the right.
Exhibit 2. Weber-Fechner Law
Source: Bristol Gate Capital Partners, Wikipedia.
In his book, Scale, Geoffrey West defines a complex system as one composed of a myriad of individual constituents that once aggregated take on collective characteristics that are usually not manifesting in, nor could easily be predicted from, the properties of the individual components themselves. The relationships between the variables in our model and their impact on our predictions is greater as a whole and different than the simple linear sum of the component parts.
Our model not only provides us the ability to process many variables but perspective into how each impacts our dividend predictions. It is not the perceived black box that many often believe it is, but a glass box that allows us to look in and gain unique insights.
In the graphs that follow, the y-axis represents the contribution to our dividend growth prediction and the x-axis is the value of the feature we are looking at.
Exhibit 3. Feature Impact on Dividend Prediction
Note: Analysis relates to Bristol Gate’s US Equity Strategy.
Source: Bristol Gate Capital Partners.
Some features, like dividend yield, represent fairly linear relationships (a straight line). It is not surprising the higher the dividend yield, the more negative the impact on our dividend growth prediction. But other features, we will call them X, Y and Z in this example to protect some of our proprietary insights, do not follow the same pattern and have distinctive influences on our predictions.
For feature X, negative values have a much larger effect (indicated by the slope of the line) than positive values. For feature Y, beyond a certain sweet spot the impact on dividend growth is negative and converges toward a certain number the larger it gets. Feature Z shows minimal consequences on our dividend prediction at low rates, but large, negative step changes as it grows.
Identifying and incorporating nonlinear relationships like these into our predictions is why our model is consistently more accurate at forecasting dividends than the consensus of Wall St. analysts.
Exhibit 4. Average Dividend Growth Prediction Error – Bristol Gate vs Consensus and Naïve Forecasts
Note: Analysis relates to Bristol Gate’s US Equity Strategy.
Source: Bristol Gate Capital Partners, FactSet.
While some firms have incorporated advanced analytical techniques as an integral part of their investment processes, we believe we are a long way from the broader market adopting such tools. Until they do, we think we can sustainably identify tomorrow’s dividend growers before most others. In the meantime, we continue to develop our analytical capabilities and advance our process forward. Our efforts in data science and machine learning are not restricted to dividend growth or one model, but pervasive throughout our process, including areas such as risk analysis, portfolio construction, and in operating our firm to improve efficiency. Continuous improvement and data science are fundamental components of our culture.
US Equity Strategy
The trailing 12 month median dividend growth of our portfolio companies was 13.5% at quarter end. This compared to the market’s 5.0% median dividend growth. Although our portfolio’s trailing dividend growth is lower than our historical norm, we believe this is a strong result given the impact COVID had on the overall global economy over the last year.
During the quarter, the US Equity Strategy returned 9.9%, approximately 140 basis points ahead of the S&P 500 Total Return Index. Relative to the benchmark, Moody’s, Intuit and Roper Technologies were our largest relative contributors. Our technology and related areas were the biggest drag with Activision, Texas Instruments, and Broadcom being our biggest individual relative detractors.
On an absolute basis, Intuit, Moody’s and Zoetis were our largest contributors. We had no individual negative returns during the quarter, however Texas Instruments, Mastercard and Starbucks were our lowest returning stocks.
Exhibit 5. US Equity Strategy Returns & Risk
All stocks were brought back to equal weights in early April. No other changes to the portfolio were made during the quarter.
Year to date market returns have been dominated by a “dash for trash”, with lower profitability companies providing the highest returns thus far. Q2 saw a slight reversal of this trend with the higher profitability quality, growth and momentum factors all gaining back some ground. As we have discussed in previous notes, these are factors that have commonly been well represented in our portfolio of high dividend growers. Despite this factor headwind, our year to date results are in line with the Index’s.
Exhibit 6. S&P 500 Sector & Factor Performance YTD and Q2/21 vs. Q1/21
Source: Source: S&P Dow Jones Indices LLC. Data as of June 30, 2021.
Factors and sectors that have worked best through the first half of the year have some of the highest correlations to economic growth. We cannot help but ask ourselves what happens to their relative performance as the supernormal economic growth coming out of a recessionary bottom reverts to the mean?
Exhibit 7. Three Year Factor & Sector Correlation to GDP
Source: S&P Dow Jones Indices.
We are well positioned for the next phase of the economic recovery yet still maintain defensive characteristics within our portfolio for any potential disruptions along the way. The types of companies that we try to invest in – sustainable high dividend growers being driven by strong fundamentals – have less correlation to the economic cycle because they are often driven by secular themes that are somewhat independent of the broader economy. Take the mega trend related to digitization and datafication (exposure through AVGO, TXN, MSFT, INTU, ROP, MCO, V, MA, etc.). It did not stop during the COVID recession, the trend intensified.
In the upper graph of the exhibit below we have charted the dividend yield of our US Equity Strategy minus the dividend yield of the S&P 500 Total Return Index. The tight spread between the two is near historical levels. In the second graph we have charted the historical price of our US Equity Strategy relative to the price of the S&P 500 Total Return Index. You can see that prior periods of relatively tight dividend yield spreads to the market have generally resulted in reasonably strong subsequent relative performance for our strategy.
Exhibit 8. US Equity Strategy Dividend Yield Spread & Relative Price vs. S&P 500 TR Index
Note: Class A of our pooled fund is used as a proxy for our US Equity Strategy returns.
Source: Bristol Gate Capital Partners, Bloomberg.
Although past performance is no guarantee of future results, with a tight dividend yield spread to the market and quality trading at discounts not seen since the dot com bust, we like our positioning into the second half of the year and believe our portfolio is attractively valued considering the opportunities our companies have ahead of them. We estimate our portfolio is trading at a substantial discount to the market on a FCF yield basis despite lower capital intensity, higher margins, better returns, more sustainable growth in our view.
Exhibit 9. Quality at a Discount
Canadian Equity Strategy
The trailing 12 month median dividend growth of the portfolio companies in the Canadian Equity Strategy was 9.6% at quarter end. This compared to the S&P TSX Composite 2.9% median dividend growth.
During the quarter, the Canadian Equity Strategy returned 5.2% compared to 8.5% for the S&P TSX Composite Total Return Index. Relative to the benchmark, Stella Jones, Enghouse and Open Text Corp were our largest relative detractors. Thomson Reuters Corp, Zoetis and Tormont Industries were our largest contributors. All our detractors for the quarter are holdings that outperformed the broader market in the first half of 2020 as their business models were conducive to a pandemic reality. Since the vaccine news and the onset of economic re-openings they have underperformed but we remain optimistic on the long-term prospects of these companies, regardless of how COVID-19 evolves.
On an absolute basis, Stella Jones, Canadian National Railway and Jamieson Wellness were our largest detractors. Zoetis, Brookfield and InterRent were our largest returning holdings.
All stocks were brought back to equal weights in early April. No other changes to the portfolio were made during the quarter.
Exhibit 10. Canadian Equity Strategy Returns & Risk
Year to date the Canadian Strategy has returned 11.7% compared to the Index’s 17.3%. Many of the trends we observed in the US were consistent in Canada. For example, companies in the TSX Composite with an ROE greater than 20% on average returned almost 500 basis points less than those with a negative ROE (source: Bristol Gate Capital Partners, Bloomberg). Our portfolio has consistently maintained a much higher ROE than the broader market and although that quality has not been fully recognized by the market thus far this year, we are confident the long term fundamentals and operational consistency of our holdings will not only ensure they generate higher income growth for our investors but also provide competitive capital returns over time. Similar to our US strategy, the Canadian portfolio is trading at an attractive discount to the market on a FCF yield basis despite higher profitability and more sustainable growth in our view.
The Canadian economy remains behind the US in terms of reopening but dividend trends appear to have already turned the corner. According to BMO Capital Markets, TSX corporate actions have stabilized over the last several months, with the number of companies showing year over year dividend cuts declining, while the number of companies showing year over year dividend growth improving from recent troughs levels. We believe the pending recovery will provide us with opportunities to augment the dividend growth we achieved over the last 12 months.
Exhibit 11. LTM Count of S&P TSX Companies Cutting vs. Growing Dividends
Source: BMO Capital Markets Investment Strategy Group, Compustat, FactSet, IBES.
Over the past year we have taken the opportunity to reflect on our business and investment processes and consider what will make us better going forward. As a result, we have upgraded our trading systems so that we can operate effectively as our business and account types grows.
We have addressed the issues of being a signatory to the UN PRI agreement. After considerable effort we are very comfortable that our approach to ESG investment has been well designed.
Finally, our data science team has tackled a long standing question concerning the Bristol Gate approach to using equal weights in our portfolios. The results will soon be published in a Research Paper which we will forward as soon as it is available. In a nutshell, the modified approach should significantly reduce transactions and result in better tax efficiency for our investors.
As at June 30, 2021 our AUM/AUA is $2.5 billion CAD and a growing pipeline of further opportunities.
To all our investor clients, thank you for your continued trust and confidence. We look forward to seeing you in real life sometime soon.
The Bristol Gate Team
 There are various versions of the chessboard and rice story. See Wikipedia, https://en.wikipedia.org/wiki/Ambalappuzha_Sree_Krishna_Swamy_Temple, https://en.wikipedia.org/wiki/Wheat_and_chessboard_problem.
 Economic Research Service of the U.S. Department of Agriculture https://www.ers.usda.gov/topics/crops/rice/market-outlook/
Gross returns in this report refer to the Bristol Gate US Equity Strategy Composite and Canadian Equity Strategy Composite. No allowance has been made for custodial costs, taxes, operating costs, management and performance fees, which will reduce performance. Past performance is not indicative of future results. Allowance for withholding tax in the US strategy composite is partially reflected in the composite returns for periods commencing January 2017 and after. The Net returns for the Bristol Gate US Equity Strategy Composite and Canadian Equity Strategy Composite are reflective of the maximum management fee charged by Bristol Gate of 1% and 0.70%, respectively.
The Bristol Gate US Equity Strategy Composite was formerly known as the Bristol Gate US Dividend Growth Composite until April 1, 2015. The Composite inception date was May 15, 2009. The Composite consists of equities of publicly traded, dividend paying US companies and is valued in US Dollars.
The Bristol Gate Canadian Equity Strategy Composite was formerly known as the Bristol Gate Canadian Dividend Growth Composite until April 1, 2015. The Composite inception date was July 1, 2013. The Composite consists of equities of publicly traded, dividend paying Canadian and US companies and is valued in Canadian Dollars.
The S&P 500® Total Return Index measures the performance of the broad US equity market, including dividend re-investment, in US dollars. This index is provided for information only and comparisons to the index has limitations. The benchmark is an appropriate standard against which the performance of the strategy can be measured over longer time periods as it represents the primary investment universe from which Bristol Gate selects securities. However, Bristol Gate’s portfolio construction process differs materially from that of the benchmark and the securities selected for inclusion in the strategy are not influenced by the composition of the benchmark. For example, the strategy is a concentrated portfolio of approximately equally weighted dividend-paying equity securities, rebalanced quarterly whereas the benchmark is a broad stock index (including both dividend and non-dividend paying equities) that is market capitalization weighted. As such, strategy performance deviations relative to the benchmark may be significant, particularly over shorter time periods. The strategy has concentrated investments in a limited number of companies; as a result, a change in one security’s value may have a more significant effect on the strategy’s value.
SPDR S&P 500 ETF Trust (SPY US) sourced from Bloomberg has been used as a proxy for the S&P 500® for the purpose of providing non-return based portfolio statistics and sector weightings in Exhibit 5.
The S&P/TSX Total Return Index measures the performance of the broad Canadian equity market, including dividend re-investment, in Canadian dollars. This index has been provided for information only and comparisons to the index has limitations. The benchmark is an appropriate standard against which the performance of the strategy can be measured over longer time periods as it represents the primary investment universe from which Bristol Gate selects securities. However, Bristol Gate’s portfolio construction process differs materially from that of the benchmark and the securities selected for inclusion in the strategy are not influenced by the composition of the benchmark. For example, the strategy is a concentrated portfolio of approximately equally weighted dividend-paying equity securities, rebalanced quarterly whereas the benchmark is a broad stock index (including both dividend and non-dividend paying equities) that is market capitalization weighted. As such, strategy performance deviations relative to the benchmark may be significant, particularly over shorter time periods. The strategy has concentrated investments in a limited number of companies; as a result, a change in one security’s value may have a more significant effect on the strategy’s value.
iShares Core S&P/TSX Capped Composite Index ETF (XIC CN) sourced from Bloomberg has been used as a proxy for the S&P/TSX Total Return Index for the purpose of providing non-return based portfolio statistics and sector weightings in Exhibit 10.
There is the opportunity to use leverage up to 30% of the net asset value. Leverage is not used as an investment tool to enhance returns, but for cash management needs of certain composite portfolios.
This Report is for information purposes and should not be construed under any circumstances as a public offering of securities in any jurisdiction in which an offer or solicitation is not authorized. Prospective investors in Bristol Gate’s pooled funds or ETF funds should rely solely on the fund’s offering documents, which outline the risk factors associated with a decision to invest. No representations or warranties of any kind are intended or should be inferred with respect to the economic return or the tax implications of any investment in a Bristol Gate fund.
Bristol Gate claims compliance with the Global Investment Performance Standards [GIPS®]. To receive a list of composite descriptions and/or a presentation that complies with the GIPS® standards, please contact us at email@example.com. Bristol Gate Capital Partners Inc. has been independently verified for the periods commencing May 2009 until December 2015 by Ashland Partners International PLLC and from January 1, 2016 – December 31, 2020 by ACA Group, Performance Services Division.
A Note About Forward-Looking Statements
This report may contain forward-looking statements including, but not limited to, statements about the Bristol Gate strategies, risks, expected performance and condition. Forward-looking statements include statements that are predictive in nature, that depend upon or refer to future events and conditions or include words such as “may”, “could”, “would”, “should”, “expect”, “anticipate”, “intend”, “plan”, “believe”, “estimate” and similar forward-looking expressions or negative versions thereof.
These forward-looking statements are subject to various risks, uncertainties and assumptions about the investment strategies, capital markets and economic factors, which could cause actual financial performance and expectations to differ materially from the anticipated performance or other expectations expressed. Economic factors include, but are not limited to, general economic, political and market factors in North America and internationally, interest and foreign exchange rates, global equity and capital markets, business competition, technological change, changes in government regulations, unexpected judicial or regulatory proceedings, and catastrophic events.
Readers are cautioned not to place undue reliance on forward-looking statements and consider the above-mentioned factors and other factors carefully before making any investment decisions. All opinions contained in forward-looking statements are subject to change without notice and are provided in good faith. Forward-looking statements are not guarantees of future performance, and actual results could differ materially from those expressed or implied in any forward-looking statements. Bristol Gate Capital Partners Inc. has no specific intention of updating any forward-looking statements whether as a result of new information, future events or otherwise, except as required by securities legislation.