2277 Stocks and Still Not Diversified.

The single greatest misperception we encounter with clients, and many Advisors as well, is the idea that material diversification can be achieved with a large number of individual stocks or stock mutual funds. This just isn't true; further, it is less true now than ever because of high average stock correlations within and across markets.

In order to achieve true diversification, and the critical advantage this provides - lower volatility - it is essential to diversify across asset classes. That is, your portfolio should at the very least hold some stocks and some bonds, and a material portion of your bond holdings should be high quality government bonds because these are the only assets whose diversification benefits increase when all other markets are in crisis.

To illustrate the misperception about stock diversification and emphasize the importance of asset class diversification, we created two portfolios out of 5 major markets and tested their performance back to 1995:

1. The All-Stock Portfolio consisted of equal weightings in U.S. (SPY), EAFE (EFA) and emerging market (EEM) stock indices, rebalanced quarterly.
2. The Asset Class Portfolio consisted of equal weightings in U.S. stocks (SPY), U.S. long Treasury bonds (TLT), and gold (GLD).

Note that the All-Stock Portfolio consists of 2277 of the largest stocks from around the world, so it is about as diversified as it is possible to be in stocks alone. It is certainly much more diversified than any individual's stock portfolio, or any individual or basket of stock mutual funds.

The chart below shows three important pieces of information:

1. The actual daily realized volatility of each market. For example, the volatility of EEM over the period was 28.3% annualized.
2. The average of the individual volatilities for the three markets in each portfolio. For example, the 'Average of Stocks' bar shows the average of the volatility for each of EEM, EFA and SPY: (28.3% + 22.1% + 20.9%)/3 = 23.8%. This approximates what the volatility would be if there were no diversification benefit of holding all three markets in a portfolio.
3. The actual average observed volatility of each portfolio. This number captures the volatility after realizing the benefits of diversification. For example, the actual average observed volatility of the All-Stock Portfolio was 21.8%.

Markets that are held in the All-Stock Portfolio are underlined in red, while assets that are held in the Asset Class Portfolio are underlined in green. ETF symbols which track the markets are used in the chart rather than the full name of each market to save space (see symbol guide above).

Source: Butler|Philbrick|Gordillo & Associates. Data from Yahoo.

The average volatility of the individual stock market indices is 23.8%, but when we assemble them in a portfolio the portfolio volatility decreases slightly to 21.8%. The difference, 2%, represents the free lunch that results from the fact that the three stock indices do not move in perfect sync; that is, they are not perfectly correlated, so combining them produces a small diversification benefit. The percentage improvement to portfolio volatility - the diversification advantage - from combining international stock markets is about 8.4% [(21.8% - 23.8%)/23.8%], which is nice, but hardly comforting.

In contrast, while the average volatility of the individual asset class indices is lower at 16.5%, when we assemble them in a portfolio the portfolio volatility drops very substantially, to 9.1%. We can therefore infer that combining different asset classes in a portfolio produces a diversification advantage of almost 45%.

In other words, asset class diversification provides over 500% more diversification than diversifying across stock markets alone (45% vs. 8.4%).

Lest you assume that the Asset-Class Portfolio must have earned lower returns because of its much lower volatility, take a look at the following chart which adds annualized returns and maximum portfolio peak-to-trough drawdowns to our dataset. The Asset-Class Portfolio delivered over 50% better returns and less than half the drawdown of the All-Stock Portfolio over the time period considered.

Source: Butler|Philbrick|Gordillo & Associates. Data from Yahoo.

Links to other websites or references to products, services or publications other than those of Macquarie Private Wealth Inc. (MPW) on this website do not imply the endorsement or approval of such websites’ products, services or publications by MPW. MPW makes no representations or warranties with respect to, and is not responsible or liable for, these websites’ products, services or publications. Macquarie Private Wealth Inc. is a member of Canadian Investor Protection Fund and IIROC.

The Evolution of Strong Groups

Recently Falkenblog pointed to a study he came across in Jonathan Haidt’s book, The Righteous Mind, on the dynamics of group selection in evolution. This study relates quite strongly to the mechanics that we have discovered work best for selecting investment portfolios over time.

Systematic investing is really starting to feel its oats; many investors and Advisors, both retail and institutional, are beginning to realize that a thoughtful, mechanical approach to investing is required to short-circuit the dozens of biases buried deep in our wetware, and which sabotage our best efforts at rational decision making in markets. However, the vast majority of systematic investors apply rules and screens to find the top individual assets or securities according to a specific criteria, which they assemble in portfolios, usually in equal weight. It turns out this may not be the optimal approach.

Haidt describes a study whereby a group of geneticists worked with hens to improve egg yields. In a twist on traditional breeding techniques, where individual organisms with strong target traits are bred together to create a 'super-breed', the geneticists focused on how egg production improved or worsened depending on how the hens were grouped. Working with cages containing twelve hens each, they identified the cages with the highest aggregate egg yields, and inter-bred the groups of hens in the highest yielding cages.

The results?

It turns out that breeding the individual hens with the highest egg yields created hyper-aggressive hens which, when placed in a population of other high-yielding but hyper-aggressive hens, peck each other to death, which in turn causes total egg yields to drop.

However, groups of hens with high aggregate yields contain the right mix of high yielding hens and passive hens, such that when high-yielding groups were inter-bred, the resulting new groups contained even more concentrated versions of both traits, with incredible practical results. Notably, within 6 generations of group breeding, eggs produced per dozen hens rose from 91 to 237, for a 260% improvement.

Our approach selects baskets of assets which work well together to deliver strong stable returns. Importantly, this does not mean that portfolios contain the strongest individual assets; if strong assets possess qualities (correlation or volatility traits) that do not complement the other members of the group, they are not selected. This is critically important and is the conceptual root of our strategy's outsized return/risk ratio.

To see how this applies to your portfolio see here:

Darwin Investment Strategy

Retirement's Volatility Bogeyman

Links to other websites or references to products, services or publications other than those of Macquarie Private Wealth Inc. (MPW) on this website do not imply the endorsement or approval of such websites’ products, services or publications by MPW. MPW makes no representations or warranties with respect to, and is not responsible or liable for, these websites’ products, services or publications. Macquarie Private Wealth Inc. is a member of Canadian Investor Protection Fund and IIROC.

Objective Function, What's Your Function?

Conjunction Junction


In between cartoons on Saturday mornings in the 1980s the networks would run educational vignettes about grammar and math topics set to catchy music. One such video has stuck with me for 30 years: Conjunction Junction. The jingle for the vignette went, "Conjunction Junction, What's Your Function?" To this day, I remember the function of a conjunction because of this video. (For those who don't remember, a conjunction is a word that joins other words in a sentence, like 'and', 'or' or 'but'.)

Objective Function

In the domain of quantitative finance, we spend a great deal of time thinking about something called an 'Objective Function', which always reminds me of the above vignette. The objective function is the goal that we try to optimize with our investment strategy.

For example, most mutual fund managers are compensated on their ability to maximize an objective function called the 'Information Ratio'. The Information Ratio quantifies the extra return that a manager has achieved over a certain benchmark, like the S&P TSX Composite index of Canadian stocks, without straying too far from the benchmark. By implication, mutual fund managers are compensated for delivering slightly better returns than their benchmark, not for delivering superb absolute returns. That's why a Canadian equity mutual fund manager can receive full compensation in a year when his fund loses 40%.

Unfortunately, this doesn't serve most investors very well. Most investors are concerned about achieving the highest return possible at a given level of risk. Taking this a step further, most individual investors want the highest, most consistent returns for a certain level of risk.

Now let's disentangle the three concepts: returns, risk, and consistency.

Consistent Growth with Minimal Volatility

Everyone is familiar with returns; this just refers to the growth in your portfolio. Returns can come from capital gains, dividends or interest, with preferential tax treatment for capital gains and dividends. 

Risk is a little more fuzzy. Most institutional investors think of risk as portfolio volatility. Volatility captures both upside and downside gyrations though, and most people like the upside gyrations, so maybe we should just concern ourselves with downside volatility.

However, we know that in markets downside volatility tends to cluster around bear markets, and bear markets often take a few years to recover from, so a more prudent measure of risk might focus on maximum potential loss, and the duration of that loss. This is especially relevant for retirees, who from a pure mathematical standpoint cannot afford to endure large sustained losses while continuing to also withdraw income.

This brings us to the idea of return consistency. For most people, it isn't enough to earn an 8% average return over 5 years if the returns arrive inconsistently, for example as 0%, 0%, 0%, 0%, 40% sequentially. Most people would prefer a return sequence closer to 8%, 8%, 8%, 8%, 8%, and in fact this more consistent return stream also helps to maximize the retirement equation.

Bringing it all together, investors want strong returns, with tax treatment favouring capital gains over dividends, and dividends over interest. Furthermore, they want the lowest risk of large sustained losses, which means maximizing the consistency of returns over time. So how can we capture this in an objective function?

Our preferred objective function is the DVR, which measures the amount of return per unit of risk (sometimes called the Sharpe ratio), and multiplies this ratio by a measure of the linearity of the return stream, called the R-Squared. An investment strategy which maximizes the DVR delivers strong returns with minimal volatility where returns occur in a predictable sequence over time.

Oh, The Humanity

Purely from a mathematical standpoint, the DVR is the most rational objective function for non-pensioned investors to pursue in order to optimize their retirement sustainability and withdrawal rates. However, while many investors claim that all they want from their Advisor is strong, consistent returns with minimal risk, their behaviour is often inconsistent with this goal.

In our experience, many individual investors obsess over business news or the business section of newspaper, where they are inundated with performance metrics and exuberant market forecasts for their local stock market. Investors can't help but anchor their expectations to the optimistic return prospects trumpeted by analysts through thick and thin, which contaminates their emotional objective function. 

Rather than focusing on the most consistent long-term returns at the lowest possible risk, investors focus on capturing as much of the upside returns as possible from their local stock market index. Only when the index is dropping precipitously do investors begin to ignore the index and focus on those strong, persistent returns that will get them to retirement. 

This presents an interesting challenge for managers: most investors have one objective function in rising markets and another objective function in falling markets. Unfortunately, this is impossible to facilitate. 

So I would urge you to do some soul-searching about what your objective function really is. Are you really trying to optimize your retirement nest egg, sustainability and retirement income? Or are you determined to watch the business news and follow the investment media?

This is not a trivial matter. If you come to the conclusion that you are wedded to market outcomes, and like to feel the excitement of rising stocks, then we would urge you to look elsewhere for an Advisor. There are plenty to choose from, because most Advisors adhere to this objective function as well, either by choice or default because they have no alternative.

If, after careful contemplation, you discover that you would rather maximize your chance of retirement success rather than chase short-term market returns, or engage in the excitement of daily stock market drama, then our Core Diversified Program may be right for you.

-1.6% Average Returns to U.S. Stocks Through 2020: O'Shaughnessy

Jim O'Shaughnessy is one of the good guys. In 1996 he authored one of the all-time great investment references, What Works on Wall Street, where he analyzed an enormous variety of equity related financial metrics to determine which factors work to predict strong future individual stock performance. After analyzing dozens of equity metrics, from common ones like P/E, ROE, P/B and Earnings Growth to more esoteric ones like NAV/EBITDA.


Jim revisited some of the lessons in his original book during a recent presentation at the Fortigent Winter Forum in Savannah, Georgia.


Some take-ways:

1. To make inferences, investors should look at performance across longer time-frames. He recommends 20-years.
2. History doesn't repeat, but it rhymes: "It rhymes because human beings are the agent of changing prices on the stock market.”
3. The market is mean-reverting; stocks will both over-perform and under-perform their relevant benchmarks, but return to a long-term mean.
4. Composite indicators of several valuation metrics work better than any single one because the efficacy of single metrics go in and out of favour over time.
5. Value composites work in the long-term, but momentum works best in the short term.
6. Momentum works best when adjusted for volatility (you don't say ;).
7. Over the 20-year period from the March 2000 peak, U.S. large-cap stocks will mimic their performance after the 1929 peak, and deliver approximately 0.3% per year.

Let's take a moment to examine this last point. O'Shaugnessy expected returns to the S&P 500 to average 0.29% per year over the 20 years following the March 2000 peak. In fact, since that peak the S&P has delivered total returns including dividends of 1.57% per year. But there are still 8 years left before his forecast horizon expires in 2020.

Out of curiosity, we calculated the implied average stock returns from today through March 2020 that would be required to manifest O'Shaugnessy's well researched forecast.

(1 + 0.0157)^12 x R = (1 + 0.0029)^20

R = (1.0029^20)/(1.0157^12) - 1

R = -0.016, or -1.6%

By implication, O'Shaughnessy expects returns over the next 8 years to average negative 1.6% per year. Not a very compelling case for stocks. Of course, this jives with our own quantitative forecast, which you can find here.

How do you invest when everything's expensive? Adapt!

h/t Katie Southwick at AdvisorPerspectives.com

Thank you for smoking.

The movie 'Thank You for Smoking' is about a spin-doctor who works for big tobacco. His job is to discredit the evidence presented by anti-smoking groups like medical associations and health-advocate groups through obfuscation, and by quoting research findings from the tobacco industry's own research organization. The tobacco industry funded research organization intentionally hires misguided researchers who publish spurious studies with bold headings but insignificant findings.

The investment industry smacks of a similar plot. Investment firms hire research analysts to make forecasts about the economy and future market prices, but there's a catch. Banks and investment firms make substantial income by helping public companies raise cash in markets by selling stock to the public. But companies may delay expansion plans, which requires new capital from markets, if they perceive that the economy or markets may weaken. And investors won't buy new stock or bonds from these companies if they feel they may be able to get the same stock or bonds at lower prices in the future.

So what are these strategists to do? In our experience, strategists say what they need to say to keep their jobs. That is, they do what they can to find data to support optimistic forecasts, to keep the deals flowing. Incidentally, optimistic forecasts are much more palatable to TV stations and newspapers, so optimistic analysts appear on TV more often, which is a self-reinforcing problem.

This phenomenon reared its ugly head recently during a presentation from a large Canadian pension consulting firm. The firm cited spurious sources to assert that stock returns over the next 10 years were likely to be higher than average. We stayed behind afterward to discuss their analysis, and presented them with a more comprehensive version of the analysis we are about to present to you below. They were persuaded by our analysis, but the presenter then inquired:

But what do you tell clients?

If you're a chicken, would you trust Colonel Sanders to give you an honest forecast about your future?

Don't Be a Chicken

If you listen to most investment professionals quoted in the newspaper or on TV, then you're effectively making the same mistake. That's because most investment professionals quote 'rule of thumb' ratios related to economic activity, market valuation, etc. in order to make optimistic forecasts about the future without any evidence that these ratios are meaningful.

In most cases, the statistical significance of widely cited economic and market valuation ratios is effectively zero. The most common ratio cited by strategists is related to the market's Price to Earnings ratio, which is the ratio between the current value of an index (for example, as I write the S&P 500 index is trading at 1365) divided by the aggregate earnings generated by all of the companies in the index (trailing earnings for companies in the S&P 500 over the past 12 months are about $91.50). If we use earnings over the last 12 months to generate our PE ratio, it is called the Trailing Twelve Month, or TTM PE; it is currently 14.92 (1365 / 91.50).

Analysts sometimes also cite the Forward PE, which is based on analysts' own estimates for company earnings over the next 12 months. This is doubly suspect, because they are basing a forecast on another forecast. Yikes!

Using data from Robert Shiller's database, which has market data back to 1870, as well as information from the Federal Reserve, and Standards and Poors, we studied the efficacy of various market valuation techniques to forecast future market returns over meaningful time periods of 5 to 30 years. We used statistical regression techniques to discover the statistical significance of each valuation metric in order to separate meaningful metrics from spurious ones.


For those who are interested in a full explanation of the mechanics of this study, please see our full report here.


Matrix 1. below quantifies the ability of each of the valuation metrics we studied to forecast future returns over each horizon.

Matrix 1. Explanatory power of valuation metrics over various horizons (R-Squared value).

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)


The third row from the bottom of Matrix 1. illustrates the explanatory power of the TTM PE ratio to forecast future returns at each horizon (1 is good, 0 is bad). Despite being the most commonly cited valuation metric, you can see that this ratio exhibits the lowest explanatory power of any ratio over all forecast horizons.

In contrast, the ratio with the greatest explanatory impact is the price residual data at the 15-year horizon, with a factor of 0.74 (bottom row). For more on this metric, please see this post from Doug Short.

Just the Facts

Matrix 2. provides the current forecasts for market returns over the same horizons using the same market valuation metrics.

Matrix 2. Forecasts for metrics over various horizons (annualized total return after inflation).

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

Focusing on the PE1 or TTM ratio again, you can see that this ratio provides for the highest forecast rate of return of all the ratios in the matrix. For example, this ratio forecasts returns of 11.21% over the next 10 years, and almost 11% over the next 5 years. Pretty exciting!

Unfortunately, the most optimistic forecasts in the matrix have the lowest forecasting accuracy. Which begs the question:

Do strategists start with the answer they want, and then torture the data until they get it?

Obviously, we subscribe to the opposite approach: 

Start with an open mind and let the data tell the story.

To achieve the best accuracy we integrated several of the most powerful explanatory ratios using multiple regression. The second row from the bottom provides the results from this analysis, and the bottom row shows the explanatory power. You can see that our model has the most explanatory power at the 15-year and 20-year horizons (R-squared ratios of 0.82 and 0.83), and the model forecasts returns of -0.12% and 1.35% over these horizons, respectively.

What do we tell clients?


How about the truth?! If history is any guide (and what else do we have to go on, really?), then stocks are unlikely to deliver meaningful returns over the next 20 years after inflation. Of course that doesn't mean that stocks won't offer any opportunities over that period, only that stocks are likely to offer much better value at least once over the next two decades.

In the meantime, stocks and other asset classes will go through long periods of bull and bear markets, which means lots of opportunities for gains over coming years for those with the tools to harvest fleeting opportunities. The Global Dynamic Asset Allocation approach that we employ is a good option for any market, but especially useful during periods where stocks on their own are likely to experience headwinds.

Retirement's Volatility Bogeyman

Investment marketing is like watching a talented magician ply his trade. While the marketing geniuses keep everyone focused on the hottest new funds and stocks in an effort to chase strong returns, people forget about the single most important thing that matters to your retirement portfolio: volatility.

So let's be crystal clear: retirement sustainability is extremely sensitive to portfolio volatility. Further,  volatility is the only portfolio outcome that we can actively control. Therefore, volatility is the critical variable in the retirement equation, not returns.

To repeat: Volatility is the critical variable in the retirement equation, not returns.

Forget Returns; It's About SWR and RSQ

If you're within 5 years of retirement, or are already in retirement, it's time to learn some new vocabulary:

Safe Withdrawal Rate (SWR): the percent of your retirement portfolio that you can safely withdraw each year for income, assuming the income is adjusted upward each year to account for inflation.

Retirement Sustainability Quotient (RSQ): the probability that your retirement portfolio will sustain you through death given certain assumptions about lifespan, inflation, returns, volatility and income withdrawal rate. You should target an RSQ of 85%, which means you are 85% confident that your plan will sustain you through retirement.

Forget about investment returns! From now on, the only question a retirement focused investor should ask their Investment Advisor when discussing their options is: How does this effect my RSQ and SWR?

Portfolio Volatility Determines RSQ and SWR

The chart below shows how higher portfolio volatility results in lower SWRs, holding everything else constant:

1. All portfolios deliver 7% average returns
2. Future inflation will be 2.5%
3. Median remaining lifespan is 20 years (about right for a 65 year old woman).
4. We want to target an 85% Retirement Sustainability Quotient (RSQ). 

Note how SWR declines as portfolio volatility rises.

The green bar marks the volatility of a 50/50 stock/U.S. Treasury balanced portfolio over the long-term, while the red bar marks the long-term volatility of a diversified stock index. Note the SWR of the stock/bond portfolio is 6% versus 3.4% for the stock portfolio, highlighting the steep tax volatility levies on retirement income.

Steady Eddy and Risky Ricky

This is actually quite intuitive when you think about it. Imagine a scenario where two retired persons, Steady Eddy and Risky Ricky by name, draw the same average annual income of $100,000 from their respective retirement portfolios. Both draw an income that is a percentage of the assets in their retirement portfolio at the end of the prior year.

Steady Eddy's portfolio is invested in a balanced strategy with a volatility of 9.5%, while Risky Ricky is entirely in stocks with a volatility of 16.5%. Both portfolios earn the same return (as they have done for the past 15, 20 and 25 years, though we will address this in greater detail below).

Due to the lower volatility of Steady Eddy's portfolio, his income is less volatile: 95% of the time his income is between $82,000 and $117,000. In contrast, Risky Ricky's portfolio swings wildly from year to year, and therefore so does his income: 95% of the time his income is between $67,000 and $133,000. Of course, both of their incomes average out to the same $100,000 per year over time.

All other things equal, which person would you expect to be more conservative in the amount of income they spend each year? Obviously, if your income were subject to a large amount of variability each year then you would tend to be more conservative in your spending; perhaps you would squirrel away some income each year in case next year's income comes in on the low end of the range.

This relates directly to the impact of volatility on SWRs in the chart above. Volatility introduces uncertainty which is amplified by the fact that money is being extracted from the portfolio each and every year regardless of portfolio growth or losses.

How Much Gain Will Neutralize the Pain?

Of course, this effect can be moderated by increasing average portfolio returns, which would then increase average available income. The question becomes, how much extra return is required to justify higher levels of portfolio volatility?

The chart below defines this relationship quantitatively by illustrating the average return that a portfolio must deliver to neutralize an increase in portfolio volatility. In this case we hold the following assumptions constant:

1. Withdrawal rate is 5% of portfolio value, adjusted each year for inflation
2. Inflation is 2.5%
3. Retirement Sustainability Quotient target is 85%
4. Median remaining lifespan is 20 years

Again, the green bar represents the balanced stock/Treasury bond portfolio discussed above, and the red bar represents an all-stock portfolio. From the chart, you can see that the balanced portfolio needs to deliver 6.8% returns to achieve an 85% RSQ with a 5% withdrawal rate. The higher volatility stock portfolio, on the other hand, requires a 9.2% returns to achieve the same outcomes.

In theory, higher returns in your retirement portfolio should equate to higher sustainable retirement income. In reality, higher returns at the expense of higher volatility actually reduces your retirement sustainability.

Focus on What You Can Control

There are many ways of improving the ratio of returns to volatility in a portfolio, mainly through thoughtful diversification across asset classes (our particular specialty). However, many investors are (perhaps rationally) concerned about diversifying into bonds now that the long-term yield is 3% or less, so let's see what can be done with a pure stock portfolio to take advantage of the growth potential of stocks while keeping volatility at an appropriate level to maximize RSQ and SWR.

What if, instead of letting the volatility of the stock portfolio run wild, we set a target volatility for our portfolio and adjust our exposure to stocks up and down to keep the portfolio volatility within our comfort zone.

For example, let's set a target of 10% annualized volatility, so if stock volatility is 20%, our allocation to stocks =  target vol/observed vol = 10% / 20% = 50%, with the balance in cash. If stock volatility drops to 15%, our allocation would be 10% / 15% = 66.6% invested, with the balance in cash.

For the purposes of this example, we will assume that cash earns no interest, because it currently doesn't, and we want to focus on the effect of managing volatility alone.

More specifically, let's assume we measure the trailing 20-day volatility of the SPY ETF (which tracks the performance of the U.S. S&P500 stock market index) at the end of each month, and adjust our portfolio at the end of any month where observed volatility is 10% above or below the volatility we measured at the end of the prior month.

For example, if we measured volatility last month at 15% annualized, and the volatility this month was greater than 16.5% or less than 13.5% (10% either way from the prior month), then we adjust our exposure to the SPY ETF according to the most recently observed volatility using the technique described in the last paragraph. If this month's volatility does not exceed the threshold to rebalance, then we do not trade this month.

By using this simple technique to control volatility since the SPY ETF started trading in 1993, we achieve 6.65% annualized returns with a realized average portfolio volatility of 10.73%. This compares with returns on the buy and hold SPY ETF of 7.99% with a volatility of 20%. Note that our average exposure to the market over that period was just 69%, with the balance earning no returns. All returns include dividends.

The chart below shows the Sustainable Withdrawal Rate for the two portfolios: the volatility target SPY and the buy and hold SPY. 

Source: Butler|Philbrick|Gordillo & Associates, 2012, Algorithms by QWeMA Group.

You can see that by specifically targeting portfolio volatility our sustainable withdrawal rate rises to 4.7% per year, adjusted for inflation (at 2.5%) versus the Buy and Hold portfolio which will support a withdrawal rate of 3.65% per year. This despite the fact that the Buy and Hold portfolio outperforms the volatility-targeted portfolio by 1.35% per year.

We can't control the returns that markets will deliver in the future, but we can easily control portfolio volatility by observing and adapting. Withdrawal rates from retirement portfolios are highly sensitive to this volatility, and we have demonstrated that by controlling volatility we can increase our safe withdrawal rates, and therefore boost retirement income, by almost 30% before tax.

Just imagine what's possible with a diversified portfolio of asset classes when you volatility-size them. But... that's for another article.

Another Expert Bites the Dust

We have discussed ad-nausea the challenges of investment professionals adding value consistently over time via prediction (see here). This post highlights another example of the fallacy of experts.

Pimco boasts $1.357 Trillion in assets under administration and over 2000 employees in 11 countries. Bill Gross, lead manager of Pimco's Total Return Fund behemoth, is constantly featured in the media, and the PIMCO team is without a doubt the global leader in bond investing.

Yet the PIMCO Total Return Fund dramatically under preformed a myriad of low cost passive bond ETFs in 2011.

Source: ETFReplay.com

In mid-2011 Bill Gross made a bold call; he asserted that Treasury prices had peaked, and sold off the majority of his Treasury holdings, only to see Treasuries have one of their best years ever.

If anyone was going to "see" the massive rally in U.S. Treasury bonds and position themselves for it, wouldn't it have been them? Yet their prognostications of a year ago were of the exact opposite direction.

This reminds us of Danish physicist Neils Bohr famous quote: "Prediction is very difficult, especially about the future."

Estimating Future Returns

"Mankind are so much the same, in all times and places, that history informs us of nothing new or strange in this particular. Its chief use is only to discover the constant and universal principles of human nature." - David Hume

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Long-time readers will know that we do not make predictions in the normal sense. That is, we endorse the decisive evidence that markets and economies are complex, dynamic systems which are not reducible to normal cause-effect analysis. However, we are willing to acknowledge the likelihood that the future is likely to rhyme with the past. Thus, we apply simple statistical models to discover mean estimates of what the future may hold over meaningful investment horizons (10+ years), while acknowledging the wide range of possibilities that exist around these averages.

There are several reasons why it may be useful to have a more robust estimate of future expected returns on stocks:

• People who are approaching retirement need to estimate probable returns in order to budget how much they need to save.
• A retiree's level of sustainable income is largely dictated by expected returns over the early years of retirement.
• Investors of all types must make an informed decision about how best to allocate their capital among various investment opportunities.

Many studies have attempted to quantify the relationship between Shiller PE and future stock returns. Shiller PE smoothes away the spikes and troughs in corporate earnings which occur as a result of the business cycle by averaging inflation-adjusted earnings over rolling historical 10-year windows.

This study contributes substantially to research on smoothed earnings and Shiller PE by adding three new valuation indicators: the Q-Ratio, total market capitalization to GNP, and deviations from the long-term price trends. The Q-Ratio measures how expensive stocks are relative to the replacement value of corporate assets. Market capitalization to GNP accounts for the aggregate value of U.S. publicly traded business as a porportion of the size of the economy. In 2001, Warren Buffett wrote an article in Fortunewhere he states, "The ratio has certain limitations in telling you what you need to know. Still, it is probably the best single measure of where valuations stand at any given moment." Lastly, deviations from the long-term trend of the S&P inflation adjusted price series indicate how 'stretched' values are above or below their long-term averages.

These three measures take on further gravity when we consider that they are derived from four distinct facets of financial markets: Shiller PE focuses on the earnings statement; Q-ratio focuses on the balance sheet; market cap to GNP focuses on corporate value as a proportion of the size of the economy; and deviation from price trend focuses on a technical price series. Taken together, they capture a wide swath of information about markets.

We analyzed the power of each of these 'valuation' measures to explain inflation-adjusted stock returns including reinvested dividends over subsequent multi-year periods. Our analysis provides compelling evidence that future returns will be lower when starting valuations are high, and that returns will be higher in periods where starting valuations are low.

This last point may seem obvious, but I want to emphasize a critical point about traditional wealth management of which most investors are not aware:

Traditional investment planning does not account for whether markets are cheap or expensive. An investor who visited a traditional Investment Advisor at the peak of the technology bubble in early 2000 would, in practice, be advised to allocate the same proportion of his wealth to stocks as an investor who visited an Advisor near the bottom of the markets in early 2009. This despite the fact that the first investor would have had a valuation-based expected return on his stock portfolio from January 2000 of negative 2% per year, while the second investor would expect inflation-adjusted compound annual returns of 6.5%. For an investor with $1,000,000 to invest, this would represent a difference of more than $1.26 million in cumulative wealth over a decade.

Said differently, traditional wealth advice is rooted in the assumption that the best estimate of future returns is the average long-term return to stocks. No matter where markets are on the continuum from very cheap to very expensive, traditional Advisors will make recommendations on the assumption that investors should expect 6.5% inflation adjusted returns on stocks over all investment horizons.

John Hussman at Hussman funds is careful to qualify the value of this analysis: "Rich valuation is strongly associated with weak subsequent returns, but only reliably so over periods of 7-10 years. In contrast, the present syndrome of overvalued, overbought, overbullish, rising-yield conditions is typically associated with abrupt and often steep losses, but is more commonly resolved over a period of months rather than years." (Hussman, Feb 14, 2011). Thus, we are not making a forecast of market returns over the next several months; in fact, markets could go substantially higher from here. However, over the next 10 to 15 years, markets are very likely to revert to average valuations, which are much lower than current levels. This study will demonstrate that investors should expect 6.5% returns to stocks only during those very rare occasions when the stock market passes through 'fair value' on its way to becoming very cheap, or very expensive. At all other periods, there is a better estimate of future returns than the long-term average, and this study will quantify that estimate.

Investors should be aware that, relative to meaningful historical precedents, markets are currently expensive and overbought by all three measures, indicating a strong likelihood of low inflation-adjusted returns going forward over periods as long as 20 years.

This prediction is also supported by evidence from an analysis of corporate profit margins. In his recent book, Vitaly Katsenelson provided in Chart 1 of long-term profit margins to U.S. companies. Companies have clearly been benefitting from a period of extraordinary profitability.

Source: Vitaly Katsenelson (2011)

The profit margin picture is critically important. Jeremy Grantham recently stated, "Profit margins are probably the most mean-reverting series in finance, and if profit margins do not mean-revert, then something has gone badly wrong with capitalism. If high profits do not attract competition, there is something wrong with the system and it is not functioning properly." On this basis, we can expect profit margins to begin to revert to more normalized ratios over coming months. If so, stocks may face a future where multiples to corporate earnings are contracting at the same time that the growth in earnings is also contracting. This double feedback mechanism may partially explain why our statistical model predicts such low real returns in coming years. Caveat Emptor.

Modeling Across Many Horizons

Many studies have been published on the Shiller PE, and how well (or not) it estimates future returns. Almost all of these studies apply a rolling 10-year window to earnings as advocated by Dr. Shiller. But is there something magical about a 10-year earnings smoothing factor? Further, is there anything magical about a 10-year forecast horizon?

Kitces (2008, PDF format) demonstrated that "the safe withdrawal rate for a 30-year retirement period has shown a 0.91 correlation to the annualized real return of the portfolio over the first 15 years of the time period". So there is clearly merit in studying a 15-year forecast horizon as well. Further, the tables below will demonstrate that statistical models have the greatest explanatory power at the 15-year horizon.

This study will attempt to address the question of 'perfect forecast horizon', perfect valuation factor, and 'perfect earnings smoothing factor', by analyzing the explanatory power of earnings, the Q-Ratio, and regressed historical stock returns, over return horizons from 1 to 30 years. We will also put all of the factors together to construct an optimized model.

Table 1. below provides a snapshot of some of the results from our analysis. The table shows estimated future returns based on several factor models over some important investment horizons. The "Best Fit Multiple Regression" is by far the most accurate model, but other results are provided for context.

Table 1. Factor Based Return Forecasts Over Important Investment Horizons

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

You can see from the table that every single valuation factor model generates results which suggest a very low future return environment for stocks. Further, the 'Best Fit Multiple Regression', which has historically provided a surprising degree of forecast accuracy, confirms this outlook with a high degree of confidence (see explanation below). Those who are not interested in our process can skip to the bottom sections, 'Putting the Predictions to the Test', and 'Conclusion'.

Process

The following matrices show the R-Squared ratio, regression slope, regression intercept, and current predicted forecast returns for each valuation factor. The matrices are heat-mapped so that larger values are reddish, and small or negative values are blue-ish. Click on each image for a large version.

Matrix 1. Explanatory power of valuation/future returns relationships

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

Many analysts quote 'Trailing 12-Months' or TTM PE ratios for the market as a tool to assess whether markets are cheap or expensive. If you hear an analyst quoting the market's PE ratio, odds are they are referring to this TTM number. Our analysis slightly modifies this measure by averaging the PE over the prior 12 months rather than using trailing cumulative earnings through the current month, but this change does not substantially alter the results. As it turns out, TTM average earnings have very mild explanatory value over periods greater than 8 years. However, the explanatory power of TTM earnings is substantially less reliable than all other factors studied in this analysis, so investors may wish to pay little heed to this indicator of whether stocks are cheap or expensive.

Forecasting Expected Returns

The next matrices provide the slope and intercept coefficients for each regression. We have provided these in order to illustrate how we calculated the values for the final matrix below of predicted future returns to stocks.

Matrix 2. Slope of regression line for each valuation factor/time horizon pair.

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

Matrix 3. Intercept of regression line for each valuation factor/time horizon pair.

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

Our final matrix below shows predicted future real returns over each time horizon, as calculated from the slopes and intercepts above, by using the most recent values for each of the 13 earnings series, the Q-Ratio, and the return series as inputs. For statistical reasons which are beyond the scope of this study, we have substituted the ordinal rank for the nominal value for each factor in running our analysis. Therefore, when we solve for future returns based on current monthly data, we apply the monthly rank in the equations.

For example, the 15-year return prediction based on the current Q-Ratio can be calculated by multiplying the current ordinal rank of the Q-Ratio (1031) by the slope from Matrix 2. at the intersection of 'Q-Ratio' and '15-Year Rtns' (-0.00007), and then adding the intercept at the same intersection (0.09706) from Matrix 3. The result is 0.0234, or 2.34%, as you can see in Matrix 4. below at the same intersection (Q-Ratio : 15-Year Rtns).

Matrix 4. Modeled forecast future returns using current valuations.

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

Finally, at the bottom of the above matrix we show the forecast returns over each future horizon based on our best-fit multiple regression from the factors above. We began testing the multiple regression against the Q-ratio, the 15-year Shiller PE, the price regression, and the market cap to GNP as a 4 factor model. However, we discovered that the 15-year PE provided more noise than signal to the regression (that is, these factors were not statistically significant and reduced the F-score), so we narrowed the regression to include just the Q ratio, market cap/GNP, and the real price series over each forecast horizon.

We provided the R-squared for each multiple regression at the bottom of each forecast horizon column in Matrix 4.; you can see that at the 15-year forecast horizon, our regression explains 82% of total returns to stocks. Further, the regression is very highly statistically significant, with a p value of effectively zero.

Chart 2. below demonstrates how closely the model tracks actual future 15-year returns. The red line tracks the model's forecast annualized real total returns over subsequent 15-year periods using the Q ratio and deviation from price regression as inputs at each period. The blue line shows the actual annualized real total returns over the same 15-year horizon.

Chart 2. 15-Year Forecast Returns vs. 15-Year Actual Future Returns

Click for a larger image

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

You can see that 15-year "Regression Forecast" returns are -0.12% per year and 10-year returns are forecast to be 1.47% per year using market valuations as of March 1st, 2012.

Putting the Predictions to the Test

A model is not very interesting or useful unless it actually does a good job of predicting the future. To that end, we tested the model's predictive capacity at some key turning points in markets over the past century or more to see how well it predicted future inflation-adjusted returns.

Table 2. Comparing Long-term average forecasts with model forecasts

Source: Shiller (2011), DShort.com (2011), Chris Turner (2011), World Exchange Forum (2011), Federal Reserve (2011), Butler|Philbrick & Associates (2011)

You can see we tested against periods during the Great Depression, the 1970s inflationary bear market, the 1982 bottom, and the middle of the 1990s technology bubble in 1995. The table also shows expected 15-year returns given market valuations at the 2009 bottom, and current levels. These are shaded green because we do not have 15-year future returns from these periods yet. Note real total return forecasts of 6.7% annualized from the bottom of the market in February 2009. This suggests that prices just approached fair value at the market's bottom, but they were nowhere near the level of cheapness that markets achieved at bottoms in 1932 or 1982. As of the end of May 2011, expected future returns over the next 15 years are almost exactly 0 percent.

We compared the forecasts from our model with what would be expected from using just the long-term average real returns of 6.5% as a constant forecast, and demonstrated that estimates form long-term average returns yield over 450% more error than estimations from our model over these 15-year forecast horizons (1.24% annualized return error from our model vs 5.55% using the long-term average). Clearly the model offers substantially more insight into future return expectations than simple long-term averages, especially near valuation extremes.

Conclusions

The 'Regression Forecast' return predictions along the bottom of Matrix 4. are robust predictions for future stock returns, as they account for over 100 different cuts of the data, using 3 distinct valuation techniques, and utilize the most explanatory statistical relationships. The models explain up to 82% of future returns based on R-Squared, and are statistically significant at p~0. It is worth noting, however, that even this model has very little explanatory power over horizons less than 6 or 7 years, so almost anything is possible in the short-term.

Returns in the reddish row labeled "PE1" in Matrix 4 were forecast using just the most recent 12 months of earnings data, and correlate strongly with common "Trailing 12-Month" PE ratios cited in the media. Note that our Matrix 1. proves that this trailing 12 month measure is not worth very much as a measure for forecasting future returns over any horizon. However, the more constructive results from this metric probably helps to explain the general consensus among sell-side market strategists that markets will do just fine over coming years. Just remember that these analysts have no proven ability whatsoever in predicting market returns (see here, here, and here). Further, it can be argued that their firms have a substantial incentive to keep their clients invested in stocks.

Investors would do much better to heed the results of robust statistical analyses of actual market history, and play to the relative odds. This analysis suggests that markets are currently expensive, and asserts a very high probability of low returns to stocks (and possibly other asset classes) in the future. Remember, any returns earned above the average are necessarily earned at someone else's expense, so it will likely be necessary to do something radically different than everyone else to capture excess returns going forward.