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Diversification and Correlation

Administrative note: There will be no new post tomorrow–taking the day off for Thanksgiving. And on that note, thanks to each of you for the roles you play here (whether buying one of my books, sharing the blog with others, or participating in the discussion). Being able to do this full-time is literally a dream come true for me. So, thanks. 😀

There appears to be a prevailing sentiment that diversification failed in 2008 because U.S. stocks, international stocks, and REITs all went down at the same time.

The thing is, that’s what usually happens when one of them goes down. They are, after all, positively correlated.

In fact, even bonds–the asset class most frequently used as a diversifier for an otherwise stock portfolio–have a historically positive correlation with the U.S. stock market. If stocks go down in a given year, more likely that not, bonds went down also.

Does this mean bonds are ineffective as a diversifier? Of course not. They’re a helpful diversifier because their correlation to U.S. stocks, while positive, is quite low.

Math Refresher: Correlation Coefficient

In case it’s been a while since you studied correlations, here’s a refresher:

  • If two variables have a correlation coefficient of 1, they move in perfect lockstep. One goes up, so does the other.
  • If two variables have a correlation coefficient of 0, they’re completely independent. The movement of one has no value for predicting the movement of the other.
  • If two variables have a correlation coefficient of -1, they’re perfectly negatively correlated. When one goes up, the other goes down.

Negative Correlations: Dream On.

The dream asset class is one that would have a long-term expected return similar to stocks as well as a negative correlation to stocks (such that when one has a bad year, the other usually has a good year).

However, it’s rare that you’ll find asset classes with negative correlation to the stock market (aside from asset classes with negative expected returns). In fact, even looking for a zero correlation is quite difficult. In most cases, a low positive correlation is all we can hope for.

Seeking Low Correlations

You benefit any time you add an asset class to your portfolio that has:

  • A correlation (to the rest of your portfolio) of less than 1, and
  • A similar expected return to the rest of your portfolio.

That’s why international stocks make a worthwhile diversifier to U.S. stocks even though their correlation is quite high. When one has a bad year, there’s at least a chance that the other had a good year. Or, more likely, when one has a truly terrible year, the other may only have a “sorta bad” year.

And with bonds, even if they lose money in 2/3 years in which stocks lose money, they still provide a diversification benefit because:

  • In the other 1/3 bad years, they must have gone up, and
  • Even in the 2/3  bad years in which bonds also went down, they likely went down less than stocks.

In other words, all we’re looking for when we diversify is asset classes that will behave differently from stocks (without sacrificing too much expected return), not asset classes that always go up when stocks go down.

So did diversification fail us?

Just because U.S. stocks, international stocks, and REITs all went down in 2008 doesn’t mean “diversification failed us.” They did, in fact, all perform differently from each other–exactly what we’d hope they would do. And bonds had a great year, with many bond funds putting up double-digit returns.

It seems to me that diversification didn’t fail at all. It worked perfectly according to plan–practically a banner year for the “here’s why you should diversify” message. So what failed? The general public’s expectations and understanding of diversification.

International Allocation: Maximum and Minimum

What percentage of the stock portion of your portfolio should be invested internationally? Vanguard’s website (in a section only accessible if you’re logged in) contains this statement:

“Investing up to 20% of your stock portfolio in international stocks can help you diversify. Between 20% and 40%, your diversification improves, but at a lower rate. And because of the risks of international investing, an upper limit of 40% is wise.”

20-40%. That’s more or less in keeping with conventional wisdom.

But conventional wisdom seems to gloss over something here: Having 80% of your portfolio (more than 80% if we assume that the entire bond portion is invested in U.S. bonds) invested in one country is not diversified–especially for anybody whose income is largely dependent upon the U.S. economy.

Past and Future

I assume Vanguard’s statement is based on an analysis of historical returns. I can only guess which exact period(s) they’re looking at, but surely it’s limited to the 20th century plus the first decade of this century–a period during which the United States went from being a young upstart nation to being the world’s largest economic superpower.

It’s hardly a surprise that based on an analysis of that period, a U.S.-heavy portfolio looks pretty darned good. What I’m not so sure we can expect is for the next 10, 20, 30, or 60 years to look the same.

Starting Point: Market-Weighted Portfolio

To me, it seems that the starting point for discussion should be a market-weighted portfolio. At the moment, such a portfolio would be invested approximately 40% in the U.S. and 60% internationally.

From there, you can make adjustments to cater to your specific needs. For example, if you’re in (or close to) retirement, it could makes sense to decrease your international allocation for two reasons:

  • First, you’re going to be spending down your investments soon, which means that it would be good to minimize currency risk (the risk caused by fluctuations in exchange rates that comes with owning non-U.S. investments).
  • Second, you have fewer years remaining in the workforce, meaning that you’re less dependent upon the U.S. economy that somebody who is, say, 25 or 30.

Alternatively, if you’re in your 20s or early 30s, it could make sense to increase your international allocation relative to a market-weighted portfolio for precisely the opposite reasons.

Avoiding the “Growth Trap”

What I’d caution against, however, is falling into the growth trap–overweighting emerging markets (China or India, for instance) simply because you know they’re going to grow at a faster rate than the U.S. over the next couple decades.

When it’s obvious that a country’s economy will be growing quickly, that growth should already be reflected in the price of their stocks. To earn above-market returns, you need to invest not in countries (or companies) that grow quickly, but in countries (or companies) that grow more quickly than expected.

If you’re going to invest more of your portfolio in non-U.S. investments than conventional wisdom would suggest, do it with the goal of diversification, not with the goal of earning superstar returns.

Testing EMH: The Joint Hypothesis Problem

Hypotheses cannot be proven. They can only be disproved. As Taleb reminds us, even with hundreds of thousands of white swan sightings and no black swan sightings, it was never possible to prove the statement “all swans are white.” Yet one single sighting of a black swan could (and did) immediately disprove the statement.

In finance, people often seek to disprove the efficient market hypothesis (and thereby give hope to active fund managers, active fund investors, stock pickers, market timers, and stock newsletter publishers that their efforts aren’t doomed to failure). The trick is that EMH is an incomplete hypothesis, and it cannot be disproved.

Testing EMH

We can say “markets are efficient” and “an efficient market would look like X.” But if we test, and find that markets don’t look like X, we don’t know whether:

  • Markets are not efficient, or
  • Our description of what an efficient market looks like is inaccurate/incomplete.

This is what’s known as the joint hypothesis problem. When we attempt to test EMH, we’re automatically testing two hypotheses:

  1. “Market’s are efficient” <— the efficient markets hypothesis, and
  2. “Efficient markets look like X.” <—the secondary hypothesis.

If the joint hypotheses are proven false, it’s impossible to know which one was proven false.

For example, we might describe an efficient market as one in which asset classes have expected returns proportional to their risk (as measured by volatility of returns). And if we found two asset classes with equal volatility where one reliably outperformed the other, we might be tempted to say that markets are not efficient.

But that’s not necessarily the case. Perhaps the market is smarter than our description of it, and there are other factors at work. For example, there may be forms of risk other than volatility (illiquidity for instance) that would cause an efficient market to allow one asset class to have higher expected returns than the other.

The Takeaway for Investors

So what’s the point of all this? The point is that you should be extremely leery anytime you see somebody claiming that:

  1. “Markets are not efficient, and I have proof!” or
  2. “I can help you increase your return without increasing risk.” (which, by the way, is just the I’m-about-to-sell-you-something version of claim #1).

Of course, for precisely the same reason EMH can’t be proven false, it can’t be proven true either. EMH’s value lies, in my opinion, not in our ability to prove or disprove it but rather in its usefulness as a lens through which we can examine market phenomena and perhaps come to a better understanding of why the market does what it does.

Efficient Market Hypothesis: Strong, Semi-Strong, and Weak

If I were to choose one thing from the academic world of finance that I think more individual investors need to know about, it would be the efficient market hypothesis.

The name “efficient market hypothesis” sounds terribly arcane. But its significance is huge for investors, and (at a basic level) it’s not very hard to understand.

So what is the efficient market hypothesis (EMH)?

As professor Eugene Fama (the man most often credited as the father of EMH) explains*, in an efficient market, “the current price [of an investment] should reflect all available information…so prices should change only based on unexpected new information.”

It’s important to note that, as Fama himself has said, the efficient market hypothesis is a model, not a rule. It describes how markets tend to work. It does not dictate how they must work.

EMH is typically broken down into three forms (weak, semi-strong, and strong) each with their own implications and varying levels of data to back them up.

Weak Efficient Market Hypothesis

The weak form of EMH says that you cannot predict future stock prices on the basis of past stock prices. Weak-form EMH is a shot aimed directly at technical analysis. If past stock prices don’t help to predict future prices, there’s no point in looking at them — no point in trying to discern patterns in stock charts.

From what I’ve seen, most academic studies seem to show that weak-form EMH holds up pretty well. (Take, for example, the recent study which tested over 5,000 technical analysis rules and showed them to be unsuccessful at generating abnormally high returns.)

Semi-Strong Efficient Market Hypothesis

The semi-strong form of EMH says that you cannot use any published information to predict future prices. Semi-strong EMH is a shot aimed at fundamental analysis. If all published information is already reflected in a stock’s price, then there’s nothing to be gained from looking at financial statements or from paying somebody (i.e., a fund manager) to do that for you.

Semi-strong EMH has also held up reasonably well. For example, the number of active fund managers who outperform the market has historically been no more than can be easily attributed to pure randomness.

Semi-strong EMH does not appear to be ironclad, however, as there have been a small handful of investors (e.g., Peter Lynch, Warren Buffet) whose outperformance is of a sufficient degree that it’s extremely difficult to explain as just luck.

The trick, of course, is that it’s nearly impossible to identify such an investor in time to profit from it. You must either:

  • Invest with a fund manager after only a few years of outperformance (at which point his/her performance could easily be due to luck), or
  • Wait until the manager has provided enough data so that you can be sure that his performance is due to skill (at which point his fund will be sufficiently large that he’ll have trouble outperforming in the future).

Strong Efficient Market Hypothesis

The strong form of EMH says that everything that is knowable — even unpublished information — has already been reflected in present prices. The implication here would be that even if you have some inside information and could legally trade based upon it, you would gain nothing by doing so.

The way I see it, strong-form EMH isn’t terribly relevant to most individual investors, as it’s not too often that we have information not available to the institutional investors.

Why You Should Care About EMH

Given the degree to which they’ve held up, the implications of weak and semi-strong EMH cannot be overstated. In short, the takeaway is that there’s very little evidence indicating that individual investors can do anything better than simply buy & hold a low-cost, diversified portfolio.

*Update: The video from which this quote came has since been taken offline.

Tax Diversification: Roth IRA vs. Traditional IRA

If you’re eligible to contribute to either one, the “Roth IRA vs. traditional IRA” decision is primarily determined by one question:

Do you expect to be in a higher tax bracket when you withdraw the money than you’re in now?

  • If the answer is yes, then a Roth IRA is better (because the benefit gained from a Roth–tax-free distributions in retirement–will be more valuable than the benefit gained from a traditional IRA–a current deduction).
  • If the answer is no, then a traditional IRA is better (for the opposite reason).

The catch, of course, it’s that it’s quite difficult to predict your future tax rate. I’d argue that it’s downright impossible if you’re more than a couple decades away from retirement.

Case in point: For those of you who were working in 1979, did you guess your 2009 tax bracket correctly?

Oops, I guessed wrong!

If you do all of your investing via tax-deferred accounts–such as a 401(k) account or a traditional IRA–and you end up in a higher tax bracket in retirement than you’re in now, then you guessed wrong. You would have been better off putting a portion of your money into a Roth.

And it’s worth noting that the more you have invested in tax-deferred accounts, the higher your taxable income–and tax rate–will be in retirement. In other words, the more you put into a traditional IRA or 401(k), the more attractive a Roth IRA becomes.

Conversely, the more you put into a Roth IRA or Roth 401(k), the more attractive traditional IRA and 401(k) accounts become.

Tax Diversification: A little bit of both.

The idea of tax diversification is simple: Do a little bit of both. Put some money in tax-free accounts and some money in tax-deferred accounts. This minimizes the risk of incorrectly guessing your future tax rate.

One practical way to tax diversify is to prioritize your investments as follows:

  1. Contribute enough to your 401(k) to get the full employer match,
  2. Max out your Roth IRA,
  3. Go back to your 401(k) and max it out,
  4. Invest via taxable accounts.

Also, by tax diversifying, you give yourself the ability to strategically plan your IRA and 401(k) distributions in retirement. For example, each year, you could take sufficient distributions from tax-deferred accounts to put yourself at the very top of your current tax bracket, at which point you could switch over to distributions from your Roth in order to avoid a higher tax rate.

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Review: The Investor’s Manifesto

Investor'sManifestoIt’s always fun to hear that one of your favorite authors has released a new book. Given that William Bernstein’s The Four Pillars of Investing is quite literally my favorite book on investing, you can imagine how eager I was to read his newest release: The Investor’s Manifesto: Preparing for Prosperity, Armageddon, and Everything in Between.

End result: I might have a new favorite. If nothing else, I have a new favorite to recommend for people just beginning to invest.

The Book’s Message

The Investor’s Manifesto is essentially a more accessible version of Four Pillars. The book’s core messages are that:

  • Risk and expected return are related. There’s no escaping it.
  • The best potential future returns are available when things are scariest (i.e., when risk is at its highest).
  • Picking stocks is a bad idea for individual investors. No, you’re not an exception.
  • Picking actively managed funds is perhaps worse than picking stocks.
  • With a handful of exceptions, the financial services industry exists to steal your money.

Behavioral Investing Mistakes

Lots of books and articles claim that our brains are hardwired to fail us when it comes to investing. I agree with that general premise, but I’ve always been somewhat hesitant to accept at face value any claims about the workings of a brain–perhaps the single least-understood organ in the human body–written by a financial author/journalist.

However, when the person making the claims is an M.D. (a neurologist in fact), such claims have an entirely different level of credibility. In The Investor’s Manifesto, Bernstein lays out several aspects of human psychology that detract from our ability to invest successfully. For example:

We use stories to understand things once they become too complex. And in the process, we oversimplify things to the point where our understanding is as wrong as it is right.

We want to be entertained. We love picking stocks, especially the high-flying growth stocks of popular companies.

We make too many analogies. We transfer characteristics across categories, even when it’s inappropriate to do so. For example, we assume that a good company must make a great stock, or that a quickly growing economy must mean high market returns. (Jeremy Siegel calls this the “growth trap.”)

We all think we’re better than average. We pick stocks (and expect to succeed!) even though the people we’re trading with are, in all probability, full-time investment professionals with far larger resources of data and computing power.

Highly Recommended

At just under 200 pages, The Investor’s Manifesto is a quick read. Its advice is sound. And it’s entertaining to boot. I can’t recommend this one highly enough.

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