John Bogle has cautioned, “Too many investors-individuals and institutions alike-are constantly making investment decisions based on the lessons of the recent, or even the extended, past.”

Here is a chart of the major asset classes sorted by the differences between the penultimate downturn and the last one:

Asset Class	8/2000 – 9/2002	10/2007 – 2/2009	Difference
DJ US REIT	21%	-66%	87%
Alerian MLP	59%	-28%	87%
R2000V	8%	-51%	59%
GSCI	6%	-49%	55%
R3000V	-18%	-54%	36%
R1000V	-19%	-54%	35%
MSCI EAFE Small	-25%	-57%	32%
Barcap Long	30%	4%	26%
R2000	-25%	-51%	25%
Barcap 5-10yr	30%	6%	24%
MSCI EM	-34%	-57%	23%
CSFB HY	-2%	-24%	22%
Barcap AGG	25%	7%	18%
Barcap 1-5yr	22%	8%	14%
MSCI EAFE	-42%	-55%	13%
ML Conv.	-27%	-39%	13%
3Yr TSY	23%	11%	11%
R3000	-40%	-50%	10%
DJ Broad Stock Mkt.	-40%	-50%	10%
R1000	-41%	-50%	9%
S&P 500	-41%	-50%	9%
3Mo TSY	8%	2%	5%
6Mo CD	11%	6%	4%
3Mo CD	9%	5%	4%
BLS CPI	5%	2%	3%
R2000G	-51%	-50%	0%
R3000G	-58%	-47%	-11%
R1000G	-58%	-46%	-12%

As you can see, owning REITS, commodities, small value stocks, and MLPs all were great in the dot com aftermath and fixed income did really well also.  While the S&P 500 was going down 41%, equal weighting of the four assets mentioned earlier would have been up 24%, and an equal weighting of the four fixed income indexes highlighted would have been up 27%.  Thus a 75/25 portfolio (pretty aggressive) of 50% S&P 500, 6.25% each in the 4 fixed income assets, and 6.25% in the 4 other assets mentioned would have been down 8.1% in the earlier downturn.  But in the more recent financial crisis it would have been down 35.7%.

Suppose a client is going to contribute $X per month.  A trade could be done every month, incurring a transaction fee, or every other month, or every third month, etc.  When is the optimal time?

It depends on the spread of expected return of the asset class to be invested in over the expected return on cash (that isn’t really right, because they actually ought to be risk adjusted returns, but I am going to ignore that for simplicity), the amount of cash, the expected next inflow and amount, and the transaction cost.

For example, assume a client is going to add $1,000 to their account each month, the cost of the trade is $10, the expected return on cash is zero and on the prospective investment 8%.

The first month there is $1,000 in cash and investing it will cost $10.  That is a 100 bps cost but the expected return (monthly) is just 64 bps [1.08^(1/12)-1] so that is a bad deal.  The next month there is $2,000 and investing it costs only 50 bps, but the return for a month is still 64 bps so now it should be invested.

Here is the formula:

((1+I)/(1+C))^(T/12)-(T/D)-1

Where:

• D is the dollar amount of the proposed trade
• T is the transaction cost of the trade in dollars
• C is the expected annual return on cash
• I is the expected annual return on the proposed investment
• T is the time in months until there will be additions to the account or a rebalancing, etc. (I am assuming these changes will be of significant size.  Obviously, if the upcoming deposit is $1 it wouldn’t be worth waiting for.)

If the solution to the formula below is positive, do the trade, if negative, don’t.

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