Humans are captivated by stories, but largely oblivious to data. In addition, we really want certainty and conclusions when generally all that is available is uncertainty and probabilities.

For example, people frequently want a prediction of what the market will do this year, and I think there are two reasonable answers based on history:

1. Most likely between a 29% loss and a 53% gain, but there is about a 1-in-20 chance it could be outside that range. (The average 12-month return from 1926-2018 for U.S. stocks was 12.05% with a standard deviation of 20.90%. 95% would be within 1.96 standard deviations so 12.05% +/- 40.96% is a range of -28.91% to +53.02%.)

2. Most likely between a 20% loss and a 45% gain, but there is about a 1-in-20 chance it could be outside that range. (If you assume that the world is safer or different now so post-WWII numbers are a better estimate of the future, the average 12-month return from 1946-2018 for U.S. stocks was 12.21% with a standard deviation of 16.52%. 95% would be within 1.96 standard deviations so 12.21% +/- 32.37% is a range of -20.16% to +44.58%.

You could also argue that equity returns will be lower by some amount – maybe 1% lower because of lower inflation and another 2-3% lower from a lower ERP (Equity Risk Premium) going forward so the whole distribution is shifted down by that amount. If so you can adjust the ranges down by 3-4%. I also do think that starting post-WWII is too aggressive, but I can understand the logic of someone using it and I wouldn’t say they are wrong. I would point out though, if that is the correct distribution then 2008 was a huge outlier. If we use from 1926 it was fairly normal. (The worst 12-months in that debacle was March 2008 to February 2009, which had a 42.48% loss – a rare but reasonable 2.53 standard deviation event (1 in 175) if we use from 1926 to the month prior to that period, but an improbable 3.26 standard deviations (1 in 1795) if we start in 1946.) So, my best answer would be: “Most likely between a 33% loss and a 50% gain, but there is about a 1-in-20 chance it could be outside that range.”

Also, if you want to know the 100-year-flood number that would be 2.58 standard deviations. 12.05% minus a 3.5% adjustment for lower returns in the future is 8.55% minus 2.58*20.90% = -45.36%. (Of course, there is also a 1-in-100 chance of a positive 62.47%) Keep in mind, the worst-case scenario that has ever happened (in any area, not just market returns) was not the worst-case just prior to it happening. Think about that for a while.

I am anticipating some questions, here are the answers:

1. You undoubtedly think those answers are wrong – you just really don’t think the range is that high. I feel the same way, but I know I’m wrong…

2. Clients must be profoundly unhappy with an answer like that. I know, but it is what it is. If I could improve on those figures I would be running a hedge fund engaged in market timing.

3. I used the CRSP 1-10 figures, not the S&P 500 because the question is “what do you think the market will do?” not “what do you think the S&P 500 will do?” Most people think it is the same thing, and substantially they really are, the correlation is above 99%, the difference in geometric returns has been 25 basis points (advantage S&P500) and average annualized difference in standard deviation was 34 basis points (advantage CRSP 1-10). So, I wouldn’t really quibble if someone used the S&P500 to do these calculations, but I didn’t.

4. I rounded off to a reasonable number of decimal places as I typed this up, but all the calculations used all the decimal points I had available – just in case you are following my math and find something slightly off.

6. The correct returns to use for this exercise are arithmetic, not geometric. If you want to convert, the rough estimate (but it’s pretty good) is given by squaring the standard deviation (to get the variance), then subtracting half of that from the return. For example, I said, “The average 12-month return from 1926-2018 for U.S. stocks was 12.05% with a standard deviation of 20.90%.” 0.2090^2= 0.0437 That divided by 2 equals 0.0218. 12.05% minus 2.18% is 9.87% geometric return, which is the figure you are more accustomed to seeing. For more on this topic you can see my calculator here.

7. I used 12-month periods, the maximum drawdown to expect is higher because it can go on for longer than 12-months. For example, from October 2007 through February 2009 was a 50.19% decline, but 2008 was just 36.71%, and as mentioned above, March 2008 to February 2009 had a 42.48% loss.

8. I used a normal distribution rather than a log-normal one because for a one-year period they are trivially different. There was already more than enough math here to make most people’s heads hurt without introducing that complication.

My latest quarterly ramblings to my Financial Professionals list are out: Financial Professionals Fall 2019

If you have a good portfolio – i.e. did the “right” things and diversified internationally, tilted to value, etc. it hasn’t worked well recently.  This is where the mettle of quality advisors is tested. Can we keep clients on-board and on-track, continuing to do the right things even when it hasn’t worked for a while?

Of course, there is a difference between perseverance and stubbornness, but I think this is perseverance. Diversification and value have too much evidence – evidence that is pervasive (in lots of markets and asset classes), persistent (in lots of time periods), robust (to various specifications), and economically meaningful (makes you money, not just a statistically significant t-stat).

This is similar to the late 90’s in a way, but there the pain was brief and acute (huge underperformance for about four years), here it is more of a chronic and dull pain – it just goes on, and on …

I thought it would be helpful to everyone if I walked through how to think about it. This will be a little long, but hopefully useful.

First, assume we have two asset classes, Stocks and Bonds. Assume there is no serial correlation in the returns (i.e. no momentum or reversals). Bonds have a lower expected return than Stocks, but less risk too. The mix in that case will entirely depend on risk tolerance – the psychological risk tolerance, the time horizon doesn’t matter. Remember in our set-up I specified no serial correlation. In reality there is negative serial correlation in the short run (i.e. reversals in daily returns), positive serial correlation in the medium run (i.e. momentum over a year or two) and negative serial correlation again in the longer run (i.e. reversals in the five to ten year period). The first and last of those are not tradable (transaction costs kill daily unless you are a market maker, and after a run up stocks may have lower long-run expected returns but it will still almost always be higher than bonds). So, suppose we settle on 60% Stocks and 40% Bonds.

For the 60% stocks suppose we have two options:

• US Stocks
• Int’l Stocks – same expected return as US Stocks, same risk as US Stocks, but not perfectly correlated.

If we are merely trying to maximize risk-adjusted return, it is clear we should split Stocks 50/50 between US and Int’l. But there are two reasons not to:

1. Most people benchmark (at least partially) off of their family/friends/neighbor’s returns. And those folks are overweight US. So going 50/50 won’t maximize happiness since a shortfall compared to others will be more painful than a surplus compared to others would be pleasurable. This is the psychological reason (Kahneman and Tversky’s Prospect Theory combined with Framing).

2. This is subtly different from the previous point. We are competing against others for retirement resources so having a portfolio different from everyone else increases the risk of being able to obtain those resources. In other words, suppose my neighbor Bob will invests in US only and at retirement will be buying assisted living services. I invest 50/50 US and Int’l and will end up with either more or less than Bob at retirement. If I “win” I can buy more assisted living than him, but if I lose I get less. But here’s the subtlety, since the “Bobs” in the US outnumber me when US wins it will push up the prices of assisted living (more competition and more willingness to pay on the demand side) so it is entirely rational to partially hedge (since “not losing” is more important than “winning”). This is the objective reason.

So, given that, in my hypothetical example it might make sense to be 40% Bonds, 40% US Stocks, and 20% Int’l Stocks. (This isn’t an asset allocation recommendation, just an exposition of the thinking.)

Now, let’s take it one step further.  Suppose we have two choices for our US Stocks:

1. US Core

2. US Value – higher expected return than US Core, same risk as US Core, and perfectly correlated (in reality the risk is actually lower, and the correlation isn’t perfect, but I’m making a point)

In that case, from a purely mathematical perspective you should invest all of it in US Value. Time horizon is irrelevant – do you want higher expected returns or lower ones? Everything else (in my set up) is the same! There are three reasons not to be so extreme however:

1. Periods of underperformance are likely more painful than periods of outperformance are pleasurable. So, it would make sense from a psychological perspective to not go 100% US Value.

2. In reality, since US Value is also lower risk, we should do even more US Value (potentially even if we had to short US Core to do so).

3. In reality, since the correlation isn’t perfect having some US Core makes sense from a diversification perspective.

Those last two issues are offsetting and in practice not as big a deal. (Russell 3000 Value is 95% correlated to Russell 3000 – that’s not perfect correlation but it’s pretty close.)

Make sense? Time horizon is irrelevant except for from a psychological perspective where people are benchmarking off of undiversified (US) or untilted (no factor exposure) portfolios. Which they are. But I can’t easily provide a mathematical answer to a psychological question. It is a function of how well we can manage client expectations (and maybe how sophisticated the clients are). So that’s why I said, “This is where the mettle of quality advisors is tested. Can we keep clients on-board and on-track, continuing to do the right things even when it hasn’t worked for a while?”

Good portfolios lose regularly!

“The best way to measure your investing success is not by whether you’re beating the market but by whether you’ve put in place a financial plan and a behavioral discipline that are likely to get you where you want to go.”

“In the end, how your investments behave is much less important than how you behave.”

Both of those quotes are from The Intelligent Investor by Benjamin Graham (1965 edition).

Recently Anitha and I were talking about whether someone we knew was “good with money” and we disagreed. We were momentarily confused until we realized our definitions of that phrase were different.

When I said “good with money,” I meant behaviorally. For example, we know a couple who are a perfect example of the point I’m trying to make. For several years when they were young, the wife stayed home with their first child while the husband worked a blue-collar job that was seasonal. Since he was going to be laid off for four months every year, they saved half his pay during the months when he was working steadily. (If you are doing the math and thinking that doesn’t work out – to levelize spending they should save a third of the income – you are correct, but that is what they did.) Then, during the four months of no income (aside from odd jobs), they still never touched the savings. In other words, they had enough left over from the “spending” half to make it through the four months of little or no income without touching the half they had put away for that purpose!

Conversely, when Anitha used the phrase, “good with money,” she meant technically. In other words, does someone have the knowledge to invest the funds wisely in a well-diversified, low-cost portfolio, take advantage of tax-advantaged retirement vehicles such as IRAs and 401(k) plans, etc. And the folks in the example above left their savings in a bank savings account for decades – imagine if it had been invested! They were not “good with money” in a technical sense.

But of course those folks are doing just fine in retirement because of their frugal lifestyle.

Conversely, if someone possessed all the technical knowledge to optimize their financial planning, but they stayed perpetually in debt and never saved, their retirement would probably be a disaster.

So, there are two versions of “good with money”:

1. Behavioral – which is mostly the ability to delay gratification (i.e. have income exceed outgo by a reasonable amount).
2. Technical – efficient portfolio construction, optimal tax strategies, etc.

In other words, simply increasing savings is clearly a more effective road to financial success than conducting an in-depth analysis of the investment choices offered in a 401(k) plan while not contributing.  Far too many people focus on improving their finances by the second definition without realizing the first is usually much more important to their financial future.

It sounds trite, but not spending is a prerequisite to wise investing.

My latest quarterly ramblings to my Financial Professionals list are out: Financial Professionals Summer 2019