# How should you think about passive investing?

September 26, 2011

It is exciting to speculate on the markets. Betting on the future level of UK interest rates, the price of nickel, or the exchange value of the Vietnamese dong versus the Thai baht requires skill, insight, and luck. Consistently making money in the markets requires incredible discipline, intelligence, and time. That is why most of us will never make a living just by investing.

But we still invest all the time, even if it is just a decision whether to leave money in a savings account or stock up on canned food. Most people also have 401k (or 403b) accounts and IRA accounts. Despite the enormous sums of money people put away for retirement, they spend very little time thinking about the best way to do it.

Luckily for you, I used to help some of the world’s biggest and most sophisticated investors with this problem. What follows are some of the lessons I learned. No proprietary materials, data, or analyses were involved in creating the charts and tables that follow.

There are plenty of books and articles that tell you how to save your money. Most of them are deeply flawed. Jeremy Siegel’s *Stocks for the Long Run*, for example, always seems to have a new edition appear just before shares take a dive. Moreover, as we saw in an article I posted earlier, his analysis fails to take into account the experiences of countries outside the United States.

Burton Malkiel’s *A Random Walk Down Wall Street* is probably the best of those in the mainstream, but it too has some serious problems. Malkiel’s key insight is that you are better off passively owning an index rather than paying for a mutual-fund manager to trade stocks on your behalf.

Unfortunately, he goes off the rails when it comes to constructing an overall portfolio that includes shares, bonds, and other assets because he relies on the valuable but incomplete Modern Portfolio Theory (MPT).

MPT provides the basic analytical tools for determining how you ought to construct a portfolio. Its key insight is that diversification can improve a portfolio’s risk-reward tradeoff. This discovery has been called the one free lunch in all of economics. The problem is that MPT does not really tell you *how* you can diversify a portfolio. I will.

Let’s see how diversification works with a simple, stylized example. Imagine we have two assets, A and B. The following chart shows the monthly returns of the two assets as well as the monthly total return of a portfolio that is composed of equal parts A and B:

The total return of the portfolio is exactly the same as it is for each of the individual assets (actually it is slightly *higher* because of compounding) but the combined portfolio has literally no risk. Another way of visualizing this is to look at how much money you would have over time after putting $100 in A, $100 in B, and $50 each in A and B:

Diversification sure is great. Of course, this was a heavily stylized example—the two assets moved exactly opposite each other all the time. That is not how the real world works. The real world looks more like this:

How are you supposed to figure out the best combination of C and D? C is an upward-sloping random walk with some extra volatility thrown in for realism. D, meanwhile, looks like a great investment every single month except for that one time when it loses half its value.

Fortunately, MPT can help. It tells you how you can calculate the expected volatility of a portfolio of assets (expressed as a standard deviation of returns) if you know their correlations with each other and their individual expected volatilities.

Below is a table illustrating how this works, with new assets:

Read the link above for details on how to calculate the expected volatility and return of the total portfolio.

Before I start my critique of MPT, you should notice that the capital weights in the portfolio do not correspond with the risk that each asset contributes to the risk of the total portfolio. Putting aside, for now, the question of correlation, you can see that assets E and F contribute three times as much risk as assets G and H.

The relatively high correlation between E and F makes this problem even more acute. You think you have a balanced portfolio of four unique assets but you actually have a portfolio heavily skewed towards two assets that are pretty similar.

If you adjust for this you can increase your returns/risk (Sharpe) ratio significantly. I asked Excel to maximize my Sharpe ratio using Solver and it pushed it up from 0.37 to 0.50. My total portfolio return was the same (3%) but my expected volatility dropped from 9% to 6%. In case you are wondering, Excel put 76% of my capital in asset G and 24% in asset F. The free money came from the robust negative correlation between those two assets.

Great, what’s the catch?

There are two major problems with MPT. First, there is no reliable method for predicting either the future excess returns or the future volality of an asset. This problem can be worked around if you are willing to accept a few big caveats.

Over very long periods of time, the volatility of an asset class (stocks, bonds, commodities, etc.) tends to be stable. Similarly—over very long periods of time—there is a very robust relationship between the returns you earn from owning a risky asset (above and beyond what you could make from parking the money in a bank account) and the risk to which you expose yourself. Over very long periods of time, the ratio of the returns above cash to risk ranges from 0.2 to 0.3. If you have enough good historical data, you can in fact predict the future excess returns and future volatility of any asset class—over an extremely long time horizon—with a reasonable degree of confidence.

I stress the length of time required for the analysis to make sense because most people (including Malkiel, not to mention David Swensen or Siegel) think like this:

- Investors are paid for risk
- The amount you are paid is proportionate to the risk you take
- The proportion is more or less the same for all assets
- Therefore you can maximize your return by buying the riskiest assets

See the problem?

The S&P 500 outperformed cash in the bank over the past 100 years. During that century, however, there were very long periods when the opposite was true. Forgetting that little detail can ruin the life savings of actual people, who do not have the luxury of letting the “long run” take care of their portfolios.

For example, the S&P 500 did not reach its September, 1929 peak again until 1954. After adjusting for inflation, the bear market did not end until 1959. The Depression is far from the only example. After adjusting for inflation, U.S. equities were in a long bear market from the end of 1968 until the beginning of 1993. And of course, there is more recent history. In real terms, the S&P 500 is currently below its price in early 1997, just before the second edition of *Stocks for the Long Run* was unleashed on the investing public. It is 40% below the all-time peak it reached in 2000.

(Data courtesy of Professor Shiller)

Don’t forget that the United States was one of the most successful countries in the world in the 20th century. A robust historical analysis would look at other countries, including those where “stocks for the long run” was a great way to be poor for the long run.

After acknowledging these big caveats, we have overcome the first problem with MPT. That leaves the second one: correlations between assets are not constant over time. This is actually far more serious than the first. Unfortunately, I do not have access to data on the historical returns an investor could have earned from owning assets but I do have access to data on the historical price changes of U.S. stocks and bonds, which should still give a pretty good picture.

This is the rolling 6-month correlation between the monthly changes in price of the S&P 500 against the monthly changes in the price of a 10-year Treasury note (roughly calculated by taking the inverse of the change in yield and multiplying by the average duration of a 10-year note, which is about 7) since 1900:

To me, this illustrates that there is no stable mathematical relationship between price changes in bonds and stocks. Over a six-month time horizon, there were plenty of periods when stocks and bonds moved exactly opposite each other and exactly together. But perhaps you think my timeframe was too short.

This is what it looks like when you look at the correlation of monthly price changes in rolling two-year periods:

The line is a lot less squiggly (to use a technical term) but it still moves around a lot. There were some two-year periods when stocks and bonds moved in sharply opposite directions and some where they almost moved in lockstep. What about over a five-year time horizon?

Again, the volatility of the correlation is reduced, but it takes some impressive stretches of the imagination to suggest that there is a stable relationship between price changes in stocks and bonds that can be represented mathematically.

So much for MPT. If the correlations change—and change in a way that cannot be predicted with an equation—we cannot make a covariance matrix or optimize a Sharpe ratio. Does this mean we are stuck at the beginning?

No. Remember, the lesson about diversification is real. MPT fails because it assumes static relationships between different asset classes. This is woefully unrealistic but that does not mean there are no better approaches. In fact, if you think about the problem of portfolio construction as one of basic economics rather than mathematical finance, you can come to some pretty powerful conclusions.

As I mentioned in an earlier post on investing, markets try to predict the future but are often wrong. An active investor can make a lot of money by betting against the markets’ expectations if the markets come around to his point of view. As I said at the beginning, this is really hard to do consistently. That does not mean, however, that a passive investor cannot take advantage of the market’s propensity to be bad at predicting the future. I will tell you how.

Start with a reasonable assumption: while markets are always either over-optimistic or overly pessimistic about the real economy, they have no long-term bias in one direction or the other. That means you want to create a portfolio that is equally biased to do well when the markets are needlessly melancholic as when they are irrationally exuberant.

To make an even better portfolio, remember that the markets get upset and excited about different things. The 1970s were terrible for stocks and bonds but great for commodities. They probably would have been great for inflation-linked bonds (ILs) had they existed back then. On the other hand, the 1930s were a terrible time to own stocks and commodities (except gold) but a wonderful time to own nominal bonds.

To visualize how you can put these thoughts together into an actual portfolio, here is an illustrative diagram showing how to conceptually allocate risk (not capital) across these different scenarios:

The way to read this is that 37.5% of a portfolio’s *risk* (roughly) ought to be in nominal government bonds, 25% in inflation-linked bonds, about 20% in commodities, and the rest evenly split between stocks and spreads (mortgages, corporate bonds, Brady bonds, etc.)

Given the relative volatilities, you will need to put the vast majority of your capital in bonds of one sort or the other and very little in the riskier assets in order to get the right risk balance. For perspective, my 403b (the 401k for people who work at think-tanks) is 50% ILs, 35% nominal bonds, and 15% equities. I slightly over-weighted ILs because we don’t have the option to invest in commodities. I’m guessing this is a bit different than what you are doing with your portfolios.

The main criticism of this approach is that your long-run expected return will be far lower than someone who just punts on risky stocks. This is true, but it is easy to overcome. All you need is some mild leverage and you can target the total risk of the portfolio to match whatever you want. Thanks to all the ETFs out there nowadays, this is easier than ever, although you won’t do as well as a big investor that has lower costs and no taxes.

So now you know how to think about passive investing. Hopefully this will make you richer, or at least, less likely to end up poor.

Endnote:

Bridgewater Associates, one of the very best investment firms around, developed a product using this logic (called All Weather) in the 1990s. Its historical ratio of excess returns divided by volatility is near 0.7, far better than anything else you could have achieved in the period through passive asset allocation. Moreover, they have simulated this portfolio going back to the 19th century and across the developed world. In all cases, it delivered superior returns to risk when compared to a more typical portfolio allocation.