The Five Laws of Gold

The Richest Man In Babylon was originally a collection of parables penned by George Clason in 1926 that focused on the judicious handling of money. Ninety years later these stories are still very applicable to our modern financial lives, with many of the lessons having been repeated numerous times in various forums. For all the time spent analyzing portfolio strategies and understanding asset class behavior there are some foundational concepts that must be in place to ensure personal financial success. Sound advice seldom, if ever, changes.

First Law

Gold cometh gladly and in increasing quantity to any man who will put by not less than one-tenth of his earnings to create an estate for his future and that of his family. [p.93]

While it sounds like a statement of the obvious, in order to be wealthy one must actually possess money. Simply having the indicators of wealth (car, house, etc.) is an illusion, and should be viewed with caution in our modern credit based economy. The ruinous outcomes that result from pursuing an image of opulence is all too often on display in the ranks of professional athletes (Mike Tyson, Allen Iverson, et al) that end up broke shortly after retirement. In some circumstances these individuals were taken advantage of, but more often than not they spent lavishly on symbols of wealth, while their real wealth was drained.

The continuous accumulation of material objects beyond one’s means can be incredibly deleterious. There’s nothing wrong with having nice things, but acquisition should be kept in check with an eye on long-term financial security. Attainment of objects requires that the owner has spent and is no longer in possession of those funds. Purchasing material objects thus represents an opportunity cost in terms of future investment returns. Savings is the necessary fuel of investment, without which future returns (in the absolute dollar sense) will likely suffer.

It never hurts to improve savings. A little more Sam Walton, a little less Russian oligarch.


Second Law

Gold laboreth diligently and contentedly for the wise owner who finds for it profitable employment, multiplying even as the flocks of the field. [p.94]

Compound interest, what Benjamin Franklin called the eighth wonder of the world, is perhaps one of the greatest innovations of all time, financial or otherwise, period. The idea that money can be lent out or used to fund other economic activities and concurrently increase in value for its owner is a potentially lucrative prospect.

Extra emphasis should be placed on the “wise” descriptor. It suggests that money be invested prudently, and it’s owner be willing to take on a measured level of risk corresponding with the expected return. Not all investment opportunities are created equal–some are undoubtedly more reasonable than others. The prospect of high rates of return typically bear a large amount of risk.


Third Law

Gold clingeth to the protection of the cautious owner who invests it under the advice of men wise in its handling [p.95]

One of the more direct interpretations of this passage suggests finding trustworthy advisor to handle financial affairs (I would add that they should be a fiduciary). The alternative would be self management, which isn’t for everyone. It requires time, effort and some humility. In The Four Pillars of Investing William Bernstein outlines the four key areas that individuals should master if they plan to effectively manage their own money: theory, history, psychology and business.

One of the major reasons I started this site was to hold myself accountable through an informal manner of self-education. It has allowed me to clarify my opinions (backed by factual evidence), and improve my own understanding. I’ve generally found that I learn best when I’m engaged, and provided with a controlled amount of freedom to make mistakes–that’s where real education occurs. Knowledge, like interest, has to be earned and compounds over time.

When seeking the guidance and opinion of others I’ve found especially useful to find those that disagree with my own perspective, and understand their reasoning and thought process. It’s an excellent way to defeat confirmation bias and challenge my own thoughts.


Fourth Law

Gold slippeth away from the man who invests it in businesses or purposes with which he is not familiar or which are not approved by those skilled in its keep. [p.95]

Whether you end up working with an advisor or travel the do-it-yourself route, prime importance should be given to understanding what you own and the risks involved. Everything has a cost and a potential downside.

Charlie Munger has often quoted a famous line from Confucius: “Real knowledge is to know the extent of one’s ignorance.” Beyond knowing what you own, exercising some humility and admitting what you don’t know is far more advantageous to an investor. Mr. Market is smarter than all of us, and fluctuates up and down, sometimes violently and without notice. To expect otherwise is to disregard economic history and human behavior.


Fifth Law

Gold flees the man who would force it to impossible earnings or who followeth the alluring advice of tricksters and schemers or who trusts it to his own inexperience and romantic desires in investment. [p. 96]

Having an idea as to what constitutes a reasonable rate of return is an essential foundation for investment planning. Without this understanding it’s easy to be tempted into schemes that promise high rates of return. Keep in mind that it’s incredibly difficult to beat the market, some do, but the legitimate ones are few and far between. Furthermore, it’s difficult to discern if their outcome is a consequence of luck or skill. Don’t be fooled.

John Law. Charles Ponzi. Ivan Boesky. Ken Lay. Bernie Madoff. Financial history is replete with characters promising great deals that ultimately end in disaster for shareholders and investors. If something sounds too good to be true, it is.

1. Clason, George S. The Richest Man In Babylon. Signet. 1988.

NOTES – The Richest Man In Babylon.pdf

What I’m Reading
The Playbook Interview: Warren Buffett (Daniel Lippman and Jake Sherman)
The Titanic Risks of the Retirement System (Mohamed El-Erian)
A senseless subsidy (The Economist)
A Dozen Ways Michael Bloomberg Thinks Like Charlie Munger (Tren Griffin)
This Basically Anonymous Fund Manager Oversees $800 Billion (Bloomberg)
How Lending Club’s Biggest Fanboy Uncovered Shady Loans (Bloomberg)
podcast: Masters in Business With Michael Mauboussin (Barry Ritholtz)
ETFs May Actually Make Weak Players Weaker (EconomPic)

Quantitative Value

The idea of buying stocks that are cheap and holding on as they appreciate in value over time is well aligned with the simple heuristic “buy low and sell high.” This central concept has created, for myself, a natural and intuitive pull towards value investing. The problem is that not all “cheap” stocks eventually go on to appreciate in value. Some are cheap for a reason–they have poor prospects and will likely end up in Wall Street’s corporate boneyard.

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Getting Real With Inflation

Inflation is one of the oldest and most well known adversaries faced by investors. Simply put it measures the change in price of goods and services that we purchase or consume including food, fuel, utilities, housing, clothing, entertainment, etc. That being said, investors must achieve a rate of return in excess of the rate of inflation in order to improve their purchasing power.

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Cost of Capital

Good businesses, by definition, earn more than they spend. Those that can’t or don’t simply cease to exist. A quick glance at any corporate balance sheet reveals a wide ranging list of liabilities including: wages and salaries, accounts payable, employee benefits, etc. But there is an additional liability not disclosed on GAAP compliant balance sheets: the cost of capital.

Cost of capital is essentially what a company must pay it’s investors for financing its business activities. It is roughly equivalent to the return an investor should expect to receive for investing in a company.

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Deconstructing Peter Lynch

Actively managed mutual funds have earned their place among the most unloved of paper assets, and rightly so. The high fees combined with persistent under-performance are a serious drag on growing one’s capital. Peter Lynch, famed manager of Fidelity’s Magellan Fund briefly touched on the failure of active managers in his book Beating the Street and even went so far as to suggest allocations to index funds as part of one’s portfolio. This was somewhat prescient as the book was written in the early 1990s, well before the passive investment fad was in high gear. But remember, Lynch himself was an active fund manager. Based on return alone he’s considered among the greatest ever. From May of 1977 through May of 1990 Lynch captained Magellan to an annualized return of 29.06% compared to just 15.52% for the S&P 500.

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The Folly of Stock Market Forecasting

This post simultaneously appeared at

The idea that one can predict stock market movements is somewhat insane.

The major problem with stock market forecasting is the lack of evidence that it is possible. I am unaware of any market commentator that has been successful–on a consistent basis–at predicting the future direction of the market. Certainly, every once in a while a pundit or luminary may get something right, but it doesn’t occur often enough by the same party to demonstrate any significant level of skill. Throw enough darts at the dartboard, and your bound to hit a bulls-eye sooner or later. (For a humorous look at the track record of various pundits I suggest a piece by Michael Johnston for fundreference.com1)

There are certain instances where an estimate of future performance is not just a nice thing to have, but is a necessary input to making business decisions. Corporate CFOs and other finance professionals routinely perform these types of assessments, particularly when deciding which projects should receive capital and which ones should be set aside or abandoned. Unfortunately for them, their estimates don’t appear to be much better. Campbell Harvey, John Graham and Itzhak Ben-David conducted a ten year study from June 2001 to March 2011 that examined the ability of corporate CFOs to estimate the range of potential outcomes of the S&P 500. Their work was summarized in a paper titled, “Managerial Miscalibration,” which appeared in the 2013 issue of The Quarterly Journal of Economics. A quote from the abstract:

According to the confidence bounds that they provided, the CFOs are severely miscalibrated: the realized one-year S&P 500 returns fall within their 80% confidence intervals only 36.3% of the time. Even during the least volatile quarters in our sample, only 59% of realized returns fall within the 80% confidence intervals provided.2

Perhaps we shouldn’t be surprised that it is really difficult to forecast the movement of the stock market. Even educated, well informed professionals fail to realize the range of possible outcomes. Their expectations, as expressed through confidence intervals, were too narrow to capture what actually occurred.

With this evidence in mind, there has been a variety of seemingly compelling evidence that long-term expected returns are highly predictable. On the surface this appears to be forecasting dressed up with some mathematical formulations, and it’s got some big names attached to it: Jack Bogle, William Bernstein and Research Affiliates to name a few.3,4,5 These are credible sources. So why have these thought leaders started to engage in what seems to be stock market forecasting?

The History of Returns
Before diving into the formulations it’s important to understand the meaning of the phrase “long-term” as it is fairly generic in describing the time frame of interest. Five years? Ten years? Fifty years? Research Affiliates places a ten year time horizon on their estimates, citing a preference for strategic asset allocation as opposed to shorter-term tactical inferences.5 Historic returns may also help shed some light on the subject. The historic volatility of returns is plotted below as a function of length of investment.

US Stocks Volatility
Source: Shiller7

Forecasting returns over short periods of time, say 1 or 2 years, would appear to be highly speculative, having more in common with gambling than making a serious estimate. Returns have been substantially more stable over longer periods of time (the implication being that they are possibly more predictable), with a standard deviation of less than 5% once the length of investment reached 20 years. Time, as it turns out, has been a fantastic means of reducing volatility. A ten year time horizon ends up somewhere in the middle–substantially less speculative, but not exactly a slam dunk either.

Start Simple
The most straightforward development of the expected return formulation for stocks starts with the Gordon equation (sometimes referred to as the dividend discount model or Gordon growth model). The formula is attributed to economist Myron Gordon, and serves as a method to value the price of a stock based on current dividend, D, dividend growth rate, g, and a discount rate/expected rate of return, k.6 The equation is similar to that used in a discounted cash flow analysis:

Gordon Equation

Solving for expected return, k, results in the following

k = D/P + g = Dividend Yield + Dividend Growth Rate

The calculation for expected return requires data on dividend yield and dividend growth rate, both of which can be derived from Robert Shiller’s Irrational Exuberance data.7 The real dividend growth rate, calculated over the entire 1871-2015 period, comes out to a 1.5% real rate of growth. (I should mention that all returns from this point forward will be real returns. This means using real dividend growth in the above calculation.) Dividend yield was taken as the end-of-year yield on US large company stocks from Ibbotson’s SBBI classic yearbook. The forecast and actual 10 year forward returns were computed every year starting in 1926 and running through 2005 for a total of 80 observations.

Gordon Equation 10 Year Accuracy

Here is a table of forecasting statistics associated with the chart above:

10 Year Forecasting Statistics
Gordon Forecast Actual Returns
Average 5.59% 6.82%
Standard Deviation 1.68% 5.57%
Minimum 2.65% -3.81%
Maximum 11.22% 17.90%
Range 8.56% 21.71%


Use of this simple model has painted a rather rosy picture. There was no ten year period with a real annualized forecast of less than 2.65%. However, when compared to actual realized returns, the forecast suffered from the same problem as the CFOs–returns were expected to fall within a much tighter range than was realized. From this rather simple analysis it would appear that dividends, and the growth of dividends, fail to capture the full nature of 10 year forward stock returns.

The finding that forecasted returns using the Gordon equation are less volatile than realized returns is not a new idea. Stephen Foerster and Stephen Sapp of The University of Western Ontario came to a similar conclusion when they investigated the use of the dividend discount model to estimate the intrinsic value of the S&P 500.

Although many subsequent studies continue to find evidence in support of the predictive ability of dividends for equity returns, studies using longer time series of data bring the generalizability of these results into question – the predictive ability of the dividend ratio appears to be specific to a few time periods (e.g., Goyal and Welch (2003)). As a result, there is uncertainty regarding the importance one should give to dividends in the valuation of equities over time.8

An Improvement?
To improve the outlook Bogle, Bernstein and Research Affiliates all append an additional term to the Gordon equation. This term is meant to account for the change in price that, in theory, accompanies a change in dividend yield. As Bernstein explains in his book:

What if the dividend yield changes over time? For example, between 1926 and 1999, the dividend on the S&P 500 decreased from 5 percent to 1.1 percent. This annualizes out to a price increase from this fall in dividend of 2.1 percent per year. By contrast a rise in dividend implies a fall in price.4

As suggested by Bernstein in his book Rational Expectations, Shiller’s CAPE ratio has become the foremost tool for use in predicting the expected price change of US stocks.9 From 1881 through 2015, Shiller’s Cyclically Averaged Price-Earnings (CAPE) Ratio has averaged approximately 16.6. Using this information combined with the end-of-year CAPE one can formulate a “CAPE Mean Reversion” term that is annualized over ten years to estimate the annualized change in price:

CAPE Mean Reversion

Combining the Gordon equation with the mean reversion of the CAPE ratio produces a new expected returns equation:

k = Dividend Yield + Real Dividend Growth Rate + CAPE Mean Reversion

After running this updated model, a simple visual inspection shows that forecast returns now track actual returns a little better.

Gordon Equation + CAPE 10 Year Accuracy

The statistics below confirm that the model now captures the broader range of possibilities:

10 Year Forecasting Statistics
Gordon+CAPE Forecast Actual Returns
Average 6.23% 6.82%
Standard Deviation 5.44% 5.57%
Minimum -6.68% -3.81%
Maximum 17.17% 17.90%
Range 23.85% 21.71%


At first blush the above numbers look spectacular, especially compared to the original model without the mean reverting CAPE. A regression analysis also shows a reasonable trend:

Gordon Equation + CAPE Regression

The Perfect Solution?
Don’t get too excited. Although the model has, collectively, captured the range of historic 10 year returns, it is still very much a blunt instrument. In any given 10 year period the error of this “improved model” has been huge. Since 1985 it has under-predicted actual 10 year annualized returns by an average of almost 6%. On two occasions the annualized error exceeded the actual return by more than 10% (1931 and 1989).

Gordon Equation + CAPE 10 Year Error

In a similar manner, Shiller’s own forecasting effort with the CAPE ratio wasn’t exactly accurate. When he first proposed using the CAPE ratio back in 1997 his comments read as follows:

Noting that the price-smoothed earnings ratio for January 1997 is a record 28, the regression illustrated in Exhibit 6 is predicting a decline of 0.5 in the log real stock price. In percentage terms, it is predicting that the real value of the market will be 40% lower in ten years than it is today. The corresponding forecast for the cumulative continuously compounded real stock return is -15% over ten years.10

From Shiller’s own data the real stock price in January 1997 was 1156.35, and by January 2007 it was 1689.35—46% higher than it was in 1997. While not incredibly accurate for the 10 year period, the forecast did warn that the market was overvalued, with the ensuing crash beginning in 2000 and extending into early 2003.

Being Reasonable
The major difference between expected returns and the market prediction du jour is that the former deals with the mechanics of asset valuation. It assumes a reversion to the mean without knowledge of when that reversion will occur. As the regression above shows, the forecast does have a relationship to the forward ten year returns, it just isn’t very accurate. On a practical level the formulations presented above require a strong dose of humility. Consider Rob Arnott’s comments from his Research Affiliates whitepaper:

It is very difficult, if not impossible, to create a model that results in perfect absolute forecasts, but if the model is internally consistent, the results will allow for relative comparison between asset classes, even if the estimated absolute returns prove to be inaccurate.5

My intention here was not to poke holes in mathematical models or attempt to come up with a better one. It was to highlight the realities of real world forecasting, which I believe has applications well beyond the world of finance. As the results above suggest, we live in a highly unpredictable world in which there is a very broad range of possible outcomes. This shouldn’t come as a surprise. Models aren’t bad. Historic probabilities aren’t bad. But they need to be used in a responsible manner. Their shortcomings should be understood and potential errors assessed. Reliance on models without acknowledging where they can and will go wrong is a recipe for disaster.

For those looking for more in-depth views of forecasting models, I recommend you check out Wes’s old post on the subject.

1. Johnston, Michael. A Visual History of Market Crash Predictions. July 16, 2015.
2. Ben-David, Itzhak, John R. Graham and Campbell R. Harvey. Managerial Miscalibration. The Quarterly Journal of Economics. September 2013.
3. Rekenthaler, John. JACK BOGLE: Get ready for a decade of 6% annual returns in the stock market. Business Insider. November 13, 2015.
4. Bernstein, William. The Investor’s Manifesto. John Wiley & Sons, Inc. Hoboken, NJ. 2010. pp. 25-35.
5. Capital Market Expectations. Research Affiliates white paper.
6. Gordon, Myron J. The Investment, Financing, and Valuation of the Corporation. Martino Publishing. Mansfield Centre, CT. 2013. pp. 63-66.
8. Foerster, Stephen R. and Stephen G. Sapp. Dividends and Stock Valuation: A Study From the Nineteenth to the Twenty-First Century. University of Western Ontario. March 13, 2006.
9. Bernstein, William. Rational Expectations. 2014. pp. 36-39.
10. Shiller, Robert J. and John Y. Campbell. Valuation Ratios and the Long-Run Stock Market Outlook. The Journal of Portfolio Management. Winter 1998. pp. 11-26.

Berkshire Hathaway As An Asset Class?

Admit it, if you’re using some sort of asset allocation strategy this question has crossed your mind. I’m not talking about indirectly owning Berkshire through a fund*, but a direct concentrated holding of the stock itself. Aside from having one of the greatest investors of all time run your money there are some additional fringe benefits. At the very least it gets you a ticket to the shareholder meeting held in Omaha every spring. Dilly bars anyone? Many have written about various pros and cons of Buffett’s businesses. The shareholder letters are publicly available to anyone who wants to read. But how has Berkshire performed as an asset in the context of an overall portfolio?

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