There has been a great deal of discussion since 2008 about the stock market exhibiting “fat tails” where the 2008 downturn was considered to be an outlier.  I thought it might be useful to investigate just how “normal” (or not) the market really is.  Normal means the distribution of returns matches the standard bell curve.

Some Statistics.  To describe a distribution, first we need to know where it is centered.  In statistics this is called the first moment (because the formula that computes it only has terms raised to the first power, i.e. nothing is raised to anything, it is just a simple arithmetic mean).  The second moment (because the formula contains squared terms) is the standard deviation or sigma (σ).  This is a measure of how spread out the data is; and it is the square root of the variance.  Those two statistics are relatively familiar, but the normality of the data is dependent on what are called the higher moments.

The third moment is skewness, a measure of whether the distribution is symmetrical or not.  If not, it has skew.  (The formula, as you have no doubt realized by now, has cubed terms.)  In a normal distribution, the mean and median (and mode for that matter) are identical.  In a skewed distribution they are not.  Positively skewed distributions have a tail going out further on the right, with the mean being higher than the median.  A negatively skewed distribution has a longer tail on the left with the mean being lower than the median.

An example of positive skew would be a graph of the distribution of wealth for a random group of people that happened to include Bill Gates; on average they are all very wealthy.  Life expectancies, on the other hand, exhibit negative skew – it is much easier to die 50 years before your life expectancy than it is 50 years after.  In investing negative skew is unfortunate because the investor receives more extreme negative results than extreme positive results.  In theory, investment returns should have a slight positive skew due to compounding, and (again in theory) would follow what is known as a log-normal distribution, which simply means the logarithms of the returns follow a normal distribution.

The fourth moment is kurtosis, and this is a measure of the “peakedness” of the distribution.  A distribution with a high middle but more weight in the tails can have the same average dispersion (standard deviation) as a distribution with the opposite.  When you hear the term “fat tails” or “black swan,” usually what the person really means is positive kurtosis.  A normal curve is said to be mesokurtic; while one with fat tails and a higher peak is leptokurtic; and one with skinny tails (or no tails) and a lower peak is platykurtic.  It is nice to know if your investments will have more extreme events than you would expect (i.e. is leptokurtic), particularly if they are negatively skewed as well.  The remainder of this post is devoted to examining empirically what the distribution of returns actually is.

Daily Data.  The length of the period we are measuring is important.  There is no question that at time frames as short as one day the market is not even close to normal.  For example, if, on October 18^th, 1987 (the day before the famous collapse) you had computed the statistics on the S&P 500 since 1950, you would have found that the odds of a decline as big as the one that actually took place the following day were astronomically (actually bigger than astronomically, but I can’t think of an appropriate adverb) against it.  It was a 26 standard deviation event.

Some context about how often daily moves in the stock market of various sizes should be expected (if they were normally distributed) is helpful here:

Standard Deviation	Expected Occurance
One	every three days or so
Two	every month or so
Three	every 1½ years or so
Four	every 63 years or so
Five	every 7 millennia or so
Six	every 2 million years or so
Seven	every 1½ billion years or so
Eight	every 236 times the age of the universe
Nine and higher	the numbers are too big to quantify

 

 

 

Keep in mind the 1987 crash was a 26 standard deviation event.  So markets on a daily basis clearly are not normally distributed and have extreme outliers, and extreme daily down moves are bigger than daily up moves (but there are slightly more up overall) as well.  So we can unequivocally state that short term market moves (daily or less) are negatively skewed and leptokurtic (and extremely so on both counts).

Monthly Data.  Monthly stock market moves are closer to normal.  The stock data used here is the total U.S. stock market (CRSP 1-10) from 1926 through 2015.  The real (inflation adjusted) and log-normal figures are similar.  Here is the distribution of nominal monthly returns over the 1,080 months in our sample:

Threshold	Predicted	Actual	Difference
>+3 σ	1	5	4
>+2 σ	25	18	-7
>+1 σ	171	103	-68
Above Avg.	540	576	36
Below Avg.	540	504	-36
<-1 σ	171	128	-43
<-2 σ	25	30	5
<-3 σ	1	10	9
Within 1σ	737	838	101
Within 2σ	1031	1021	-10
Within 3σ	1077	1054	-23

Rolling 12-month Data.  This is even more normal:

Threshold	Predicted	Actual	Difference
>+3 σ	1	4	3
>+2 σ	24	18	-6
>+1 σ	170	136	-34
Above Avg.	535	529	-6
Below Avg.	535	480	-55
<-1 σ	170	157	-13
<-2 σ	24	35	11
<-3 σ	1	4	3
Within 1σ	730	776	46
Within 2σ	1020	1016	-4
Within 3σ	1066	1061	-5

In other words, out of the 1,069 rolling 12-month periods from 1926 through 2015, if U.S. stock returns were normally distributed, a return greater than 3σ (75.6%) should have occurred once.  We have had it happen four times:

• 123.33% in the trailing twelve months through May 1933
• 154.60% in the trailing twelve months through June 1933
• 100.79% in the trailing twelve months through February 1934
• 95.05% in the trailing twelve months through March 1934

Out of the 1,069 rolling 12-month periods from 1926 through 2015, if U.S. stock returns were normally distributed, a return less than 3σ (-51.5%) should have occurred once.  We have had it happen four times:

• -52.47% in the trailing twelve months through March 1932
• -56.84% in the trailing twelve months through April 1932
• -60.35% in the trailing twelve months through May 1932
• -65.42% in the trailing twelve months through June 1932

So, what are our conclusions?  There are three:

1. Daily stock market returns have extraordinary outliers compared to a normal distribution.
2. Monthly stock market returns have a number of outliers also.
3. Rolling 12-month returns, aside from the early 1930’s, are pretty normal.

 

Vanguard has Alpha.  Morningstar has Gamma.  Envestnet has Sigma.  Apparently describing the value a high-quality advisor brings to a client’s financial planning and investment management without using a Greek letter is prohibited!  But those papers have a point, and I also believe a high-quality advisor adds significant value.  Here’s how:

1. Constructing an appropriate portfolio (I conservatively estimate the value add to be 100 bps annually from this)
   1. Proper asset allocation, factor tilts, diversification, etc.
   2. Low-cost implementation
   3. Intelligent rebalancing

2. Tax savings (I conservatively estimate the value add to be 100 bps annually from this if the client has funds in multiple tax buckets and are in a high bracket, etc. but much lower otherwise)
   1. Proper asset location strategy
   2. Proper accumulation strategy (maximizing tax-advantaged vehicles)
   3. Proper decumulation strategy (spending order)
   4. Strategic use of conversions, step-up in basis, loss-harvesting, munis, etc.
   5. Optimal transfers for children’s education, other funds to descendants and charities, etc.

3. Behavior modification (the value added is mostly unquantifiable, not as high as the methodologically-flawed Dalbar studies claim, but I would estimate 100-300 bps annually on average – but  it occurs sporadically)
   1. Maintaining an appropriate strategic allocation at market extremes
   2. Appropriate levels of saving (pre-retirement) and spending (post-retirement)

4. Other financial planning (the value added is primarily either peace of mind or only shows up in a tiny fraction of cases, for example premature death with insurance, so the average improvement to performance frequently isn’t high, but in those cases it is absolutely crucial)
   1. Risk management including appropriate insurance and asset protection
   2. Selecting optimal pension options (including Social Security)
   3. Liability management (optimal debt)
   4. Estate and end-of-life planning (not primarily tax-related)

So, for a client with pretty good behavior (though not perfect), who is in a lower tax bracket or has no investments outside of deferred accounts, the value added might be just 200 bps (100 each from 1 & 3 above) annually.  For clients with more emotional behavior, who is in a high marginal bracket, and has savings in various types of tax buckets (IRA, Roth, taxable, etc.) the value added is probably around 500 bps (100 from #1, 100 from #2, and 300 from #3).  Thus, advisory fees are typically covered 2-5x.

One of the ways a high-quality advisor adds value is by paying attention to asset location.  Low-quality advisors tend to ignore it. There are three reasons they may do so:

1. They don’t care.  The advisor may have the cynical view that clients only focus on pre-tax returns so don’t worry about it.  If the primary objective is sales rather than actually doing the best possible job, this makes sense.
2. It’s too hard.  It adds operational complexity.  Particularly for advisors with a high number of small accounts, it is easier to just “mirror” all the accounts exactly the same way.
3. They don’t know.  They either don’t know about the strategy at all, or don’t know how to implement it.

Taxes should not determine asset allocation (though it may influence it slightly at the margin), but once the proper allocation is determined, location is important.  Optimal asset location is simply locating the least tax-efficient assets inside of tax-advantaged (i.e. retirement) accounts and the most tax-efficient in taxable (i.e. non-retirement) accounts.  A combination of three factors are multiplied together determine tax efficiency:

1. Investment return. An investment with a rate of return of 0% (e.g. cash) is perfectly tax-efficient.  The higher the return the lower the efficiency.
2. Tax rate. An investment with a tax rate of 0% (e.g. munis) is perfectly tax-efficient.  The higher the rate (e.g. ordinary income vs. long-term capital gains) the lower the efficiency.
3. Turnover.  If an investment is never sold, under current tax law there is a full “step-up” in basis at death and thus is perfectly tax-efficient.  Keep in mind that yield (dividends and interest) are a form of turnover.  The higher the turnover the lower the efficiency (basically, there can be “good” turnover where losses are being harvested).  In the case of a mutual fund, use the higher of the expected fund turnover or the inverse of the investor’s expected holding period in years but not more than 100%.

In addition to the three factors above, there are two more things to keep in mind:

1. Volatility.  An investment with high volatility is more valuable in taxable account because of the possibility of being able to tax-loss harvest in an early year.  Of course, more volatile investments also tend to have higher expected returns which I noted above are better held in tax-advantaged accounts.  In general, I would say the expected return dominates the volatility, but it is something to keep in mind.
2. Foreign source income. Foreign investments (e.g. foreign stock funds) are better held in taxable accounts so as to be able to take a credit or a deduction (the credit is usually better) for foreign taxes paid.  The effect is partially offset by the fact that the yields on foreign stocks tend to be higher than those on domestic stocks which I noted above would indicate holding the higher-yielding investments in the deferred account.  In general, I would say it is just slightly better to have the foreign stocks located in the taxable account.

There are two types of tax-advantaged accounts, tax-deferred (e.g. traditional IRAs, 401(k) plans, etc.), and tax-free (e.g. Coverdell and 529 accounts if used for education, Roth IRAs, etc.).  Between those two, because (under the current tax code) the Roth does not have RMDs (Required Minimum Distributions), it is better to have higher returning assets located in the tax-free accounts.  Most people think that the reason is because it is tax-free, but this is not so.  There is no difference between a Roth and an IRA except the investor owns 100% of the Roth while (assuming a 25% tax rate) she owns only 75% of the IRA (the government is a 25% partner) but both are completely tax-free once you make that initial adjustment.

Again, the most tax-efficient assets are optimally held in the taxable account and the least tax-efficient in the tax-advantaged accounts.  But suppose relatively large amounts of inefficient holdings are end up in the taxable account anyway (either because the size of the tax-advantaged accounts is small or the holdings are large, or a combination).  For example, suppose the least tax-efficient holding in the taxable account is a total bond market bond fund (all ordinary income).  Particularly if interest rates are higher (say 6% rather than the current 2.3%), there are five things to consider doing to improve the tax efficiency:

1. Buy a municipal bond fund instead. This is particularly appropriate for high-tax-bracket investors.
2. Make non-deductible IRA contributions. While I would not make non-deductible contributions if the marginal holding is eligible for capital gain treatment and might receive a step-up on death, in a case where it is already ordinary income this probably makes sense.  The downside is the loss of liquidity if the investor is younger than 59½.
3. Use a variable annuity wrapper. This is exactly like the previous recommendation of the non-deductible IRA from a tax perspective, but has additional cost.  Despite the additional cost, if it is cheap enough (and I have in mind a plain-vanilla annuity with no riders at 25-30 basis points) and the time horizon long enough, this can make sense (not today, but in a higher interest rate environment).  I have discussed this option here.
4. Buy permanent life insurance. I am not a fan of permanent life insurance in general, but as I have noted before there are rare cases where it is recommended.  Ordinary-income holdings like bonds in the taxable account is one of the factors.
5. Pay down your mortgage instead. There are many other aspects to this decision also which I have covered here.

A full-service, fee-only, wealth management firm can only effectively handle 100 clients per financial advisor (approximately, with a sizable standard deviation and positive skewness).  A more transactional model can manage a greater number, but since many of the smaller accounts will be neglected (to some extent at least) it is unclear that the actual revenue generated will be greater than having a deeper relationship with fewer clients.  Because the number of clients that can be served is limited, it is important that the advisor ensure he or she is working with the right people.

It is far easier to get the right people from the beginning than to try to upgrade the client base later.  Firing clients who were with the advisor from the early days is at best awkward even if they are no longer a good fit.  On the other hand, it is better to “pull the Band-Aid” quickly than to let a poor fit continue.  Most advisors have at least a few clients who shouldn’t be clients.  To make sure we maintain the discipline to keep only the right relationships, we have a policy of (politely) firing one client every year.  Input on which client that should be comes from all of the associates of the firm.

A policy of proactively removing one client per year has a few positive effects:

• There is always someone who really isn’t a good fit.
• It keeps the advisor from accepting clients initially that are just going to be let go in the future.
• It reduces the stress on the firm’s associates during the year.

Let me explain that last point.  If a client is difficult or simply seems to require more work than their fees may justify, realizing that they may be the one to be let go can reduce the stress level of the associate who is dealing with them, even if they are never the client actually selected for removal.

When accepting a client initially or determining who should be asked to find another advisor, there are four things we look for (in order of importance from most to least):

1. Personality fit. If a client verbally abuses an associate or if we feel dread when seeing their name on the caller ID, that client does not qualify to work with us.  Life is too short.

2. Willingness to delegate. While our clients are intelligent (see the next point), if they do not wish to delegate portfolio management to us, obviously it won’t be a good fit.  For example, a retiree who watches financial news all day and wants to constantly discuss with us what the talking heads are saying will not be a good fit.  We are more than happy to explain what we are doing and why and obviously there has to be agreement on the appropriate risk level of the portfolio, but we are not “co-managers” of the portfolio with the client.

3. Cognitive abilities. While obviously people are paying us for our knowledge and wisdom (which are two different things), we want clients who are intelligent enough to recognize our value and who (at least at a high level) understand how we manage portfolios.  We have doctors, lawyers, CPAs, etc. and those are all very good clients for us.  We work less well with unsophisticated people.  In fact, we work well with professional people that other advisors typically struggle with; engineers, for example, are notoriously unpopular clients but we enjoy them.  Their thoroughness and analytical approach matches our approach.

4. Substantial assets. Our ideal clients have at least $1mm invested with us, but you will notice that this is the last thing on the list.  While a prospective client obviously has to have “enough” assets to be managed, once they are at that threshold, the other factors are far more important.