Stock splits are an interesting topic.  There appears to be a widespread belief that a stock is somehow worth more after it splits and a somewhat related myth that lower-priced stocks have less risk and more return.

The best way for an individual to think about stock ownership is as if they were buying the entire company.  If you were going to buy the entire thing what would it be worth?

Suppose ACME is worth $1,000 and there are 100 shares outstanding.  Each share is obviously worth $10.  If the stock is split 2/1 there are now 200 shares each worth $5 because the company is still worth $1,000.  The investor’s position is unchanged. If the stock split 10/1 instead of 2/1 there would be 1,000 shares each worth $1 and many investors might have the mistaken idea that it is a great investment now because it appears so cheap (“It used to be $10!”), but the company has exactly the same value, in total, as it did before.

Another (frequently used) analogy would be cutting a cake.  Cutting a cake into more slices does not mean you have more cake.

Now, there are three things about splits that are positive though:

1. If the stock has a very high price per share, then splitting it will increase demand because more people have the wherewithal to buy it.  This is rarely true (even Berkshire Hathaway has “B” shares that are affordable).

2. Management doesn’t split the stock if they think it might go down.  They will be pretty certain that the business is going to do well (this applies to dividend increases also) before they make that announcement.  Thus the market, appropriately, takes the announcement as a very good sign for the company’s future.

3. There may be people who mistakenly (as explained above) believe it is a better deal post-split because the price is lower and they may purchase the stock driving up the price slightly.  To the extent they do this, the more knowledgeable market participants will be selling at the “too high” price (or possibly even shorting the stock).  In an illiquid stock though, the ignorant masses (so to speak) could move the price.

Now despite those reasons that a split is positive, there still isn’t an investment opportunity because the price will move on the announcement not on the split (actually it will begin moving on the anticipation of an announcement).  Stock prices (actually all securities prices) incorporate known information which certainly includes things that have been announced.  So the announcement from management is a good signal, but it is the announcement, not the actual split that moves the price (to the extent it wasn’t already anticipated).

Let me explain that anticipated part as well.  Using our earlier example ACME is “worth” $1,000 with no split announcement.  If there is a split announcement, analysts, investors, etc. will raise their expectations for the future of the company and value it say at $1,100 (essentially non-public information – management’s strong belief in the future – has become public).  Suppose there is a 90% chance that an announcement will be made. (Obviously opinions will vary as to probability, current value, value after the announcement, etc., but assume these are the consensus estimates.)  In that case the stock will already be trading at $1,090 ahead of the announcement reflecting the 90% chance that it is worth $1,100 and the 10% chance it is worth $1,000.  (Obviously in real life there are more than two possible futures and each one of those futures has an attached probability, but the concept is identical.)  You can only profit as an investor by having a better estimate than the average of all market participants.  This is extraordinarily hard to do.

In my last post (here) I discussed risk vs. uncertainty.  In this post I will discuss three types of risk.

1. Goal Risk – you run out of money in retirement.
2. Absolute Risk – your portfolio fluctuates with the market.
3. Tracking Risk – your portfolio underperforms your neighbor’s portfolio.

To minimize Goal Risk, you have to take more of Absolute Risk or Tracking Risk (unless you have more money than you have goals; a 90-year old with $10 million, no legacy desires, and a spending need of just $100,000 a year has no goal risk – the funds would last 100 years at no interest).

One of the issues with reducing Goal Risk by increasing Absolute Risk or Tracking Risk is the salience of Absolute Risk and Tracking Risk is higher. In other words, because they are high frequency and short term, they feel more threatening. Goal Risk, being longer term, seems like it isn’t as big a worry.

An example may help. Let’s assume there are just four investments available, all of which have their good and bad times on different occasions (in technical terms none of them are perfectly correlated with any of the others):

1. U.S. Large Stocks
2. Int’l Large Stocks – same expected returns and volatility as U.S. Large
3. U.S. Small Stocks – higher expected returns and volatility than the Large stocks
4. Bonds – lower expected returns and volatility than all of the others

Suppose your friends, neighbors, etc. all invest 60% in U.S. Large and 40% in Bonds.  Further assume that you are not likely to reach your financial goals with that 60/40 mix (perhaps because of high goals or low previous savings) so you invest in 80% U.S. Large and 20% Bonds.  That move increases Absolute Risk but is expected to help with Goal Risk (if it always helped it wouldn’t be called risk).

Suppose you went a step further and the 80% stocks was invested 60% U.S. Large and 20% Int’l Large.  Now you have also introduced Tracking Risk since returns will be out of sync (sometimes positively and sometimes negatively) with your neighbors, but because the returns happen at different times, you have actually reduced Absolute Risk somewhat.

Suppose you went yet another step and the 80% stocks was allocated 40% U.S. Large, 20% U.S. Small, and 20% Int’l Large.  Since U.S. Small has higher risk and higher expected returns and will experience those at different times, it helps with Goal Risk but hurts both Absolute Risk and Tracking Risk.

So, what’s important to you as an investor?  There is no one right answer for everyone, but in our experience clients are psychologically more able to take Goal Risk over Absolute Risk (because it is less salient) and Absolute Risk over Tracking Risk (because when you experience poor returns everyone else will too).

As we see it, our responsibility is to focus more on the long run (the goal) and encourage taking prudent levels of Absolute Risk and Tracking Risk. That inevitably means sometimes the portfolio will be volatile (Absolute Risk) and sometimes it will be out of sync (Tracking Risk). This short-term discomfort is expected to pay off in the long run in a pleasant retirement (or whatever the specific goals are).

I have posted on risk previously (here), but while markets are (relatively) calm, I thought I would talk about risk vs. uncertainty.

One of the primary findings from behavioral finance is significant overconfidence in our predictions.  Though some of these might be more than you would want to tackle, I highly recommend the following as antidotes to hubris:

• Risk, Uncertainty And Profit (1921) by Frank Knight
• Pearl Harbor: Warning and Decision (1962) by Roberta Wohlstetter (just the forward by Thomas Schelling, 2005 Nobel Memorial Prize in Economic Sciences winner)
• The Psychology of Intelligence Analysis (1999) by Richard Heuer
• The Black Swan: The Impact of the Highly Improbable (2007) and Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets (2008) by Nassim Nicholas Taleb
• The Signal and the Noise: Why So Many Predictions Fail – But Some Don’t (2012) by Nate Silver
• Rumsfeld’s Rules: Leadership Lessons in Business, Politics, War, and Life (2013) by Donald Rumsfeld (just chapters 5&6, “Planning for Uncertainty” and “The Unknown Unknowns”)

Frank Knight made a crucial distinction between risk (you know the probability distribution, but don’t know the specific outcome) and uncertainty (you don’t even know the probability distribution).  For example you know the probability of rolling a one on a traditional six-sided die is 1/6 – so a roll is risky.  But what is the probability of rolling a one on a die specified only as polyhedral?  That roll is uncertain.

Donald Rumsfeld pointed out another level of problem with his “unknown unknowns” where you don’t even know that you are uncertain.  I.e. you assume something referred to as a “die” has six sides, but in fact it may not.

Despite all this, we can’t simply throw up our hands, we have to make a call for our clients despite the murkiness of the future.

I leave you with some of my favorite quotes on planning and prognosticating:

• “[P]lans are useless, but planning is indispensable.” – Dwight D. Eisenhower
• “Everyone has a plan ’till they get punched in the mouth.” – Mike Tyson
• “It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.” or “It ain’t ignorance causes so much trouble; it’s folks knowing so much that ain’t so.” and other variants – variously attributed to Josh Billings, Abraham Lincoln, Will Rogers, and Mark Twain (Josh Billings has the best claim)
• “No plan survives first contact with the enemy.” – Helmuth von Moltke the Elder
• “Prediction is very difficult, especially about the future.” – variously attributed to Niels Bohr, Samuel Goldwyn, Nostradamus, Yogi Berra, Mark Twain, and Will Rogers (but probably an old Danish saying)
• “The inevitable never happens.  It is the unexpected always.” – John Maynard Keynes
• “The unexpected is the prince of the battlefield.” – Carl von Clausewitz
• “There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don’t know. But there are also unknown unknowns. There are things we don’t know we don’t know.” – Donald Rumsfeld
• “Those who know, don’t talk.  Those who talk, don’t know.” – Lao Tzu
• “To be absolutely certain about something, one must know everything or nothing about it.” – Olin Miller
• “When the number of factors coming into play in a phenomenological complex is too large, scientific method in most cases fails. One need only think of the weather, in which case the prediction even for a few days ahead is impossible.”  ― Albert Einstein
• “When you know a thing, to hold that you know it; and when you do not know a thing, to allow that you do not know it; this is knowledge.” – Confucius

We practice what is now being called “evidence-based investing” (description here for example) – so-called because sound academic research supports it.  This month I thought I would review the key findings of some of the seminal papers in the field. I present these in chronological order with a one-sentence summary in bold at the end of each synopsis:

Can Stock Market Forecasters Forecast? (1932) by Alfred Cowles III. He concluded:

Sixteen financial services, in making some 7500 recommendations of individual common stocks for investment during the period from January 1, 1928, to July 1, 1932, compiled an average record that was worse than that of the average common stock by 1.43 per cent annually. Statistical tests of the best individual records failed to demonstrate that they exhibited skill, and indicated that they more probably were results of chance.

Twenty fire insurance companies in making a similar selection of securities during the years 1928 to 1931, inclusive, achieved an average record 1.20 per cent annually worse than that of the general run of stocks. The best of these records, since it is not very much more impressive than the record of the most successful of the sixteen financial services, fails to exhibit definitely the existence of any skill in investment.

William Peter Hamilton, editor of the Wall Street Journal, publishing forecasts of the stock market based on the Dow Theory over a period of 26 years, from 1904 to 1929, inclusive, achieved a result better than what would ordinarily be regarded as a normal investment return, but poorer than the result of a continuous outright investment in representative common stocks for this period. On 90 occasions he announced changes in the outlook for the market. Forty-five of these predictions were successful and 45 unsuccessful.

Twenty-four financial publications engaged in forecasting the stock market during the 42 years from January 1, 1928, to June 1,1932, failed as a group by 4 per cent per annum to achieve a result as good as the average of all purely random performances. A review of the various statistical tests, applied to the records for this period, of these 24 forecasters, indicates that the most successful records are little, if any, better than what might be expected to result from pure chance. There is some evidence, on the other hand, to indicate that the least successful records are worse than what could reasonably be attributed to chance.

In other words, no, forecasters can’t forecast. (Mr. Cowles had a follow-up paper in 1944 as well which concluded much the same thing. See also The Fortune Sellers and The Signal and the Noise.)

Portfolio Selection (1952) by Nobel laureate Harry Markowitz. This landmark paper introduced what became known as Modern Portfolio Theory (MPT). With estimates of the expected returns and variances of investment opportunities, along with expected correlations between them, an optimal portfolio may be constructed that maximizes the expected returns for the risk taken or (identically) minimizes the risk for the expected return. Constructing an optimal portfolio is a mathematical, not creative, exercise.

Challenge to Judgement (1974) by Nobel laureate Paul Samuelson. He concluded, “What is interesting is the empirical fact that it is virtually impossible for academic researchers with access to the published records to identify any member of the subset with flair [the ability to outperform].” Active management doesn’t seem to win.

The Loser’s Game (1975) by Charles Ellis. He concluded, “[E]fforts to beat the market are no longer the most important part of the solution; they are the most important part of the problem.” The way to win (outperform) is not to lose (by incurring high costs).

Common Risk Factors in the Returns on Stocks and Bonds (1993) by Nobel laureate Eugene Fama and Ken French. This paper introduced what became known as the “three-factor model” for stocks (plus two, credit and term, for bonds). There is a return from owning stocks over bonds, plus a premium for smaller companies (earlier identified by Banz in 1980), plus a premium for less expensive (aka value) stocks (earlier identified by Basu in 1977). Despite these earlier papers from Banz and Basu, the 1993 Fama and French paper is much more widely cited. Value (cheaper) and smaller stocks tend to outperform.

The Arithmetic of Active Management (1991) by Nobel laureate William Sharpe. Passive investors own the market portfolio and thus earn the market return. Active investors, in aggregate, must own the market portfolio as well and thus will also earn (gross) the market return, but due to much higher costs will inevitably underperform (as a group) net. Active management can’t win.

Determinants of Portfolio Performance (1995) by Brinson, Hood, and Beebower. In a study of 91 large U.S. pension plans they determined that the strategic allocation to stocks, bonds, and cash was by far the crucial decision. Indeed, the decisions of which individual securities to buy or the decision to deviate tactically from the strategic allocation (presumably with the view that investments were cheap or expensive) removed value! In other words, if these pension plans had just selected an asset allocation, bought index funds to implement it, and rebalanced back to the target periodically, they would have had better performance. Pick an allocation, implement it cheaply, rebalance periodically and otherwise resist the temptation to “do something.”

On Persistence in Mutual Fund Performance (1997) by Mark Carhart. This paper added momentum (previously identified by Jegadeesh and Titmanto in 1993) to the small-cap and value factors previously identified by Fama and French (above) as leading to improved returns. Despite the earlier paper from Jegadeesh and Titmanto, the 1997 Carhart paper is much more widely cited. Investments that have done well (poorly) in the past year tend to continue to do well (poorly).

Despite all of these papers being at least two decades old, most of the industry persists in being “faith-based” instead of “evidence-based” – probably because the management fees are higher for hope! So let me summarize the whole thing:

1. The most important thing is to get the allocation to stocks, bonds, and cash right and diversify appropriately.
2. Trying to beat the market through timing or security selection generally doesn’t work and costs matter a great deal.
3. Notwithstanding the previous point, systematically tilting a portfolio toward smaller companies (small-cap), cheaper companies (value), and investments that have done well recently (momentum) does appear to work (on average over time, of course).

In previous posts I have explored After-Tax Returns to Different Types of Accounts and Tax-Efficient Spending from a Portfolio.  In this post, I will expand a little further on how the type of account which holds an investment can affect the distribution of returns.

Advisors don’t generally consider the after-tax allocations of their clients’ portfolios for two reasons: first, because the complexity is very high and second, because clients don’t think in those terms.  Nevertheless, in theory, we really should use after-tax allocations.  Here is the simple version:

Assume an account value of $100, a tax rate of 25%, a return of 10%, and a standard deviation of 20%.  (The actual numbers selected aren’t important to my point.)

If the account is a Roth and the basis is anything lower than $100, the liquidation value is $100, the return is 10%, and the standard deviation is 20%.  (You are undoubtedly thinking, “duh” but stay with me.)

If the account is an IRA, and the basis is zero then the liquidation value is $75, and the return is 10%, and the standard deviation is 20%, both calculated on that $75 value, not on the $100 ostensible balance.

In other words $100 in stocks in an IRA and $100 in bonds in a Roth is really $75 in stocks and $100 in bonds.  (As you can also see if you considered a Roth conversion between the two buckets where the taxes are paid out of the IRA instead of an outside source.)  So it would be more logical for us to do asset allocations based on net after-tax values but as noted above clients don’t think in those terms.

Now that is ugly enough, but it gets much, much worse if there is basis.  If there is no basis, the result would be at the far right of this graph (i.e. with no basis the ratio would be infinity and the ostensible and actual numbers would match.  Also note that the math is identical for a taxable account as well (though the rate would be cap gains rates).

So for an account or position where there are enormous losses (the left side of the graph above), oddly the true returns and standard deviations are much diminished (the higher moments of the distribution – skewness and kurtosis – are unchanged), but as the position or account increases in value the numbers asymptotically approach the stated values. Remember, these returns are from the liquidation value, not the number on the statement that has embedded taxes.  To tweak the example above, for all investments assume a 10% return, a 20% standard deviation, a 25% ordinary income bracket, and a 15% capital gains rate:

• Assume a Roth with a basis of $100 and a value of $1,000.  It should be considered as an investment of $1,000 with a return of 10% and a standard deviation of 20%.
• Assume an IRA with a basis of $500 and a value of $1,000.  It should be considered as in investment of $875 with a return of 8.57% and a standard deviation of 17.14%.
• Assume a taxable account with a basis of $2,000 and a value of $1,000.  It should be considered as an investment of $1,150 with a return of 7.39% and a standard deviation of 14.78%.

These three “identical” investments in the three different accounts for one client would commonly be considered an investment of $3,000 with a return of 10% and a standard deviation of 20% but it is really an investment of $3,025 with a return of 8.59% and standard deviation of 17.19% (the weighted averages of the after-tax values).

Assume an astute financial advisor then harvests the loss in the client’s taxable account.  She saves $150 on her taxes (assuming there are other long-term gains to take it against) and then has a taxable account with a value of $1,000 and a return of 8.5% and a standard deviation of 17%.  Now the entire portfolio has a value of $2,875 with a return of 9.04% and a standard deviation of 18.09%.  Harvesting losses increases risk and return while lowering the initial value of the portfolio (because the tax savings has been realized).