In this essay, Dartmouth finance professor Kenneth R. French explains five investment principles that he uses as the foundation for a holistic approach to portfolio design.
The essay is directed at individual investors and financial advisors who work with them.
French develops a flexible and comprehensive framework for portfolio design using the global average of all investors and the global portfolio of all stocks, bonds, and other financial assets as reference points.
I have been passionate about investing since I started studying finance in 1977. The first investmentclass I took was dominated by the Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner(1965). The CAPM says every investor’s ideal portfolio is some combination of the risk-free asset and the value-weight (VW) market portfolio of all stocks, bonds, and other investible assets, and every portfolio’s expected return is a linear function of its beta, which is its sensitivity to the market return. The academic view of investing is far more complicated today.
In this essay, I focus on five concepts that capture much of what I know about investing and that drive my approach to portfolio design.
Risk is uncertainty about lifetime
The average dollar invested holds the
Chance dominates realized
Active investing is a negative sum
Most investors should diversify their
This is a vibrant time for investment research. There is much that we don’t know and lots of controversyabout what we do know. Although we may disagree on other issues, I think most researchers who study investing and portfolio design will agree that the five concepts in my list are true, so I will call them facts.
I explore the implications of each fact for the investment strategies and portfolio designs of individuals. The essay does not explore the interesting challenges corporate managers face when trying to evaluate potential projects. It is also not directed at the investment problems of hedge fund managers, venture capitalists, or private equity activists, although I hope former students in these areas agree with what I say. The emphasis on individuals, and financial advisors who work withindividuals, simplifies the discussion and keeps what is already a long essay from getting longer.
1. RISK IS UNCERTAINTY ABOUT LIFETIME CONSUMPTION.
Most investors are risk averse. Given the expected return, they prefer lower risk, and given the level of risk, they prefer higher expected return. Most investors understand that the expected return on an investment is essentially the best guess of what the return will be. There is a lot more confusion about risk. When I ask students, investors, and friends what risk means I get conflicting answers. Some say itis the potential for loss. Others suggest it’s the volatility of the return. And others say it’s beta, from the CAPM. Good portfolio design requires a clear understanding of risk.
I define risk as uncertainty about lifetime consumption broadly defined. People invest because they wantto use their wealth in the future. Some might plan to spend all the money on themselves for things like food, shelter, travel, recreation, and medical care. Others may plan to spend some of their wealth on political contributions, charitable donations, or gifts and bequests to their children. My definition of lifetime consumption includes all these and any other anticipated uses of wealth. Investors like a high expected return because it increases theexpected wealth that will be available to spend or give away. And everything else the same, risk averse investors prefer less uncertainty about their future wealth.
If people don’t like uncertainty about future wealth, shouldn’t we measure each investment’s risk by its potential for losses or the volatility of its returns? No. Those definitions miss important interactions within an investor’s portfolio and, even more important, between the portfolio return and the investor’s other sources or uses of future wealth.
My goal is a portfolio I can justify to myself today, based on the information available now. Because unexpected returns will dominate the outcome, I won’t judge my choice on what the portfolio delivers tomorrow.
Think about homeowner’s insurance. If we consider only the policy, this investment is as bad as a lottery ticket. First, there’s lots of uncertainty about the outcome. Typically, the policyholder pays the premium and gets nothing back, but there is always the chance of a big payoff. Second, if theinsurance company rationally expects to make money on the contract, a rational policyholder’s expected return must be negative. Why would a risk averse homeownerchoose a volatile investment with a negative expected return? Because insurance reduces the uncertainty of his or her lifetime consumption. The probability that a disaster will destroy any specific policyholder’s house is tiny, but if it does, the loss to that homeowner can be catastrophic. Most homeowners are happy to pay the annual insurance premium to eliminate this potential hit to wealth and lifetime consumption.
In that same spirit, it is particularly risky to invest most of your savings in your employer’s stock. As theformer employees of Enron might warn us, this can be a remarkably unfortunate way to put all your eggs in one basket. Enron was an energy and trading company based in Houston, Texas. After roughly a decade of phenomenal success, Enron filed for bankruptcy in 2001. Many employees had most if not all their 401(k) in Enron stock and lost their job and retirement savings at the same time. A better understanding of risk might have led them to a retirement portfolio that reduced their uncertainty about lifetime consumption.
Liability driven investing is another way to manage the uncertainty about lifetime consumption. My friendJeff Coyle is a financial advisor in Southern California who has spoken to most of the classes I have taughtover the last 25 years. He describes a client who hired a shipyard in Italy to build a large yacht. The amount and timing of the payments were known, but the obligations were in euros. Jeff took this liability off the table by buying government bonds that delivered the euros needed when each payment was due. Thoseof us with more mundane obligations can use the same approach. If you are stretching to buy your firsthome, for example, you might move the savings you will need at closing into a safe money market accounttoday.
The general takeaway here is to think about risk holistically. How will a potential investment vary with yourexisting portfolio and with your other sources and uses of wealth? More succinctly, how will it affect the uncertainty about your lifetime consumption?
2. THE AVERAGE DOLLAR INVESTED HOLDS THE MARKET.
I use a top-down approach when designing my investment portfolio. (My wife’s tastes and preferences also affect our portfolio. To respect her privacy, I leave her out of this discussion.)
I start with the fact that all investors must collectively hold the global market portfolio of all stocks, bonds, and other financial assets. Simple arithmetic then says the average dollar invested holds the global marketportfolio. And if we weight by investment wealth, so Bill Gates gets more weight than I do, the averageinvestor also holds the global market. As a result, the average investor and the global market portfolioprovide useful reference points for my portfolio.
My pro rata slice of the global market portfolio would probably be a fine choice for my portfolio if mypreferences and circumstances matched those of the global average investor. But they don’t. Thedifferences help me think about how my portfolio should differ from the global market portfolio. I illustratethis framework with a few examples of how I differ and the implications of the differences for my portfolio.
I live in the United States, almost everything I buy will be denominated in US dollars, and I may not betreated as well as local investors in foreign markets. All three facts lead me to overweight US investments.First, economists talk about something we call “keeping up with the Joneses” and younger readers know asFOMO, fear of missing out. If your neighbors overweight US investments, you can reduce your risk ofsuffering while they prosper by also overweighting US investments. Second, since the things I expect toconsume are priced in dollars, investments denominated in other currencies have an extra risk; the dollarpayoff from a foreign investment will be smaller if the foreign currency depreciates. Third, local investorshave an advantage over foreigners in some markets. Foreigners sometimes pay higher effective tax ratesthan locals, and in some countries capital controls make it difficult for foreigners to repatriate their wealth. Argentina, for example, instituted restrictions on the flow of capital in 2019 that continue to challenge foreign investors. These and similar factors push me and other US investors to overweight US investments and underweight foreign investments. And this seems to be a universal result. As a group, locals overweight the investments in their home market.
Let’s look at another factor. I am substantially older than the average investor, even after weighting people by their investment wealth. When I was young, most of my wealth was anticipated income, so the volatility of my investment returns contributed little to the uncertainty of my lifetime consumption. The return on my investment portfolio had almost no effect on my anticipated wealth or lifetime consumption. I also had a lifetime of real options ahead of me. If my investments did poorly after I had accumulated someretirement savings, I could adjust, perhaps by deferring the purchase of a vacation home or by moving to a higher paying but less attractive job. At my current age, the return on my investment portfolio pretty much determines the wealth I will have available to spend or give away. As a result, my age pushes toward less risk, with a bigger allocation to fixed income and a smaller allocation to equities than the global market portfolio.
A third factor is my risk aversion. I think I’m less risk averse than the average investor. While my agepushes toward more fixed income, my low risk aversion pushes toward equity. Low risk aversion iswinning for now, so I hold more equity and less fixed income than the global market portfolio.
The top-down global-market approach draws attention to many of the issues that are important when designing an investment portfolio. In addition to domicile, age, and risk aversion, one should consider how personal financial circumstances, including anticipated and potential sources and uses of wealth, tend to vary with the components of the global market portfolio. Other issues, such as transaction costs, tax considerations (including unrealized capital gains and losses in one’s taxable portfolio), environmental, social, and governance concerns, and perceived informational advantages anddisadvantages, may also be important.
The top-down approach helps me think about the direction I should move away from the global VW market—should I overweight value stocks and underweight growth stocks or vice versa. It also gives me a general sense of how much each of my portfolio allocations should differ from the global market’s. Theapproach does not tell me, however, exactly how much to deviate unless I am trying to match a specificliability, such as locking in a big down payment. Someone clever may be able to determine my “ideal”portfolio, but I would not trust a precise analytical solution to a problem as complicated and poorly defined as this.
3. CHANCE DOMINATES REALIZED RETURNS.
Perhaps because the evolutionary cost of false negatives—failing to see real patterns—was high relativeto the cost of false positives, people seem hardwired to identify patterns, whether they are real or not (e.g.,Shermer 2008). Who hasn’t seen a ship in the clouds or human figures in a dirty window? Those of us whogrew up in New Hampshire in the 20th century have fond memories of the Old Man of the Mountain, arock formation that looked like the silhouette of, well, an old man. We mourned when he fell from themountain in 2003 and are proud to honor his memory on our road signs and license plates.
Given the importance of financial markets and the human inclination to identify patterns, it is notsurprising that researchers and investors have found patterns in asset prices and returns for centuries and continue to do so now. It is also not surprising that a nontrivial fraction of the patterns are false positives.
We can split an asset’s return into its expected return, which is our best guess of what will happen based on all theinformation currently available, and its unexpected return, which is the surprise—the difference between what actually does happen and what was expected,
R = E(R) + U. (1)
The goal of most who study stock returns is to predict the future, not describe the past. In the context of equation (1), researchers are trying to identify persistent differences in expected return across assets orasset classes. Differences in the cross-section of expected returns, however, are usually small relative to the volatility of unexpected returns, so realized returns are mostly the result of chance. Over reasonable investment horizons—three, five, ten, even 20 years—realized returns are typically dominated by the unexpected component and inferences from realized returns are often false positives.
The performance of FAANG stocks—Facebook, Amazon, Apple, Netflix, and Google—over the decadefrom 2012 to 2021 illustrates the importance of unexpected returns. (I know, some of the names havechanged, but FAANG sounds better than MAANA.) The 2012-2021 average annual return on a VW portfolioof these five large stocks is 30.09% and the cumulative ten-year return is 1166%. (The FAANG portfolio andvalue-weight market returns here and below are computed using monthly data from Chicago Booth’sCenter for Research in Security Prices, CRSP, and are denominated in US dollars.) Should we expect theportfolio to deliver 1166% over the next decade? No. Strong unexpected returns are a better explanation for the great return and, by definition, the expected value of future unexpected returns must be zero.
Those who use the recent returns on the FAANG portfolio to predict its future returns will probably be disappointed.
The FAANG portfolio’s return in 2020 is a remarkable 61.47%, almost three times the solid 20.99% return on the CRSP VW market portfolio. The success of the five technology stocks in the first year of the pandemic makes sense. The companies were selling entertainment, social interaction, and home delivery to a world of people isolated in their houses. The huge increase in the demand for FAANG services could have been anticipated only by someone whose crystal ball forecast COVID-19 and its consequences. Those who use recent returns on the FAANG portfolio to predict its future returns will probably be disappointed.
The incentives to identify new patterns in stock returns or to improve existing patterns are strong: degrees are awarded, papers are published, tenure is granted, and new investment products are sold. The set of potential patterns or improvements a researcher might test is huge. There are thousands ofstocks, an almost unlimited list of attributes, and many ways to combine the candidates. With a good search algorithm and enough time, a clever empiricist should be able to find big patterns in any reasonable sample of realized returns. Ideally, the winning pattern describes expected returns, but evidence that it doesn’t is not likely to arrive before the successful researcher is rewarded. If we are notalready, we may soon be facing an onslaught of unconstrained search, the cardinal sin of financial economists.
How can an investor tell whether the winning pattern is gold or pyrite? Start by considering the modelthat justifies the pattern. If there is none, presume you are looking at the winner of a massive,uninformed search. A winning pattern is more likely to persist if the model that predicts it is compelling. For example, a model motivated by greed, fear, and transaction costs has potential. A model that works only if all returns are first converted to Turkish lira does not. Finally,the credibility of both the model and the pattern are enhanced a lot if the model obviously came first.
Be suspicious about unusual procedures, a peculiar sample period, or strange variable definitions.Researchers constructing factors, for example, often follow the procedure in Fama and French (1993), notbecause (ahem) it is obviously the best, but because doing so eliminates potential users’ concerns about one type of overfitting. Everything else the same, almost all researchers want a long sample period. As aresult, the start dates for most empirical research are driven by data availability. Three typical start dates inresearch on US stock returns align with key dates for the widely used monthly CRSP data, January 1926,July 1962, and January 1973. Other databases drive other start dates. Be suspicious when there is noobvious link between the start of the available data and the start of the sample. Similarly, expect the sample to end no more than four or five years before a paper is circulated. Finally, Novy-Marx (2014)emphasizes that unusual variable definitions are ominous. Don’t be surprised if the patterns they producedo not persist out of sample, especially if standard definitions destroy it in sample.
In short, when designing a portfolio, investors are typically interested in future differences in expectedreturns. Because expected and unexpected returns come in pairs, however, it is easy to misinterpretdifferences in unexpected returns as differences in expected returns. Many years ago, my colleagueGene Fama convinced me that the best way to manage this problem is to start with the null hypothesisthat any pattern in realized returns happened by chance.
When testing the chance hypothesis, look for (i) a compelling story that predicts the pattern in expectedreturns, (ii) strong in-sample evidence that the pattern is more than noise, and (iii) robust out-of-sampleevidence that reinforces that conclusion. Be particularly wary of patterns identified by uninformed and unconstrained search.
4. ACTIVE INVESTING IS A NEGATIVE SUM GAME.
Dick Roll is a friend, finance professor, and pilot who flies his own plane. Many years ago, when we werecolleagues at UCLA, I asked him whether his hobby was risky. He said the data imply it’s about as dangerous as driving a motorcycle. Dick is a smart and careful man, so I suggested the averagesoverstate the risk when he flies. His response changed the way I see the world: “Ken, every pilot thinks he’s better than average.”
Bill Sharpe published a great paper in the Financial Analysts Journal in 1991 that implies Dick’s insight aboutoverconfidence extends to active investors. Sharpe’s paper, “The arithmetic of active management,” makes a simple point. The average dollar invested actively loses to a passive investment in the value-weight market portfolio.
Sharpe’s argument is straightforward. Suppose I hold a passive VW market portfolio, that is, I hold mypro rata slice of all stocks, bonds, and other financial assets in the aggregate market portfolio. Since I hold the VW market, my return is the return on the market minus the low costs of maintaining my buy-and-hold portfolio, RM– CL. And since I hold the market portfolio, the combination of all other investors—passive and active—must also hold the market, and their combined return is the return on the market minus their higher costs, RM– CH. Why are their costs higher? Because the active investors in the group pay extra management fees, transaction costs, and the other expenses of investing actively. My costs CLare lowerthan the VW average costs of all other investors CH, so over every period—every year, day, minute, andeven every instant—my return RM– CLis higher than the VW average return of all other investors RM–CH.
When choosing my own investments, I remind myself that most overconfident investors don’t realize they are, and that client fees pay formost investment managers’ yachts.
There is another way to see Sharpe’s logic. If some investors choose to hold more than their pro rata slice of Apple stock, others must hold less than their pro rata slice. The over- and underweights in Apple are side bets. Whatever one group wins, the other loses. And both groups pay to play the game.
If active investing is a negative sum game, why does it persist? The most likely explanation is investor overconfidence combined with the fog of volatility. See, for example, Odean (1998) and Barber and Odean (2000). Given the high volatility of unexpected equity returns, active strategies and managers typically produce almost as many good monthly or annual returns as bad ones, which allows investoroverconfidence to persist. There has been a gradual shift from active to passive since at least 1980 (e.g.,French 2008), but as the meme stock events of 2021 remind us, seemingly uninformed and overconfident new investors enter the market every day.
Most investors also seem overconfident about their ability to evaluate managers. Suppose that after fees and expenses, the expected outperformance or alpha of the world’s greatest hedge fund manager is 5%per year. If her fund has equity-like volatility of 20% per year, how long should we expect to wait before confidently inferring (with a t-statistic of 2.0 or greater) that her alpha is positive? The answer is 64 years. When I ask others this question, most are surprised that it will take two or three investment lifetimes to determine that this great hedge fund manager more than covers her costs. Why does it take so long to evaluate the manager? First, the highly volatile unexpected returns that let many underperforming active investors believe they are beating the market also obscure the great hedge fund manager’s skill. Second, hedge funds rarely track benchmarks and without a benchmark, 100% of the unexpected return is noise.
Index funds are easier to evaluate because each fund’s target index is a perfect benchmark, providing direct evidence of whether the fund is delivering as promised. Active equity mutual funds are typicallyeasier than hedge funds to evaluate and harder than index funds. Although a benchmark or asset pricing model may eliminate some noise, it can still take decades to decide whether an active fund’s under- or overperformance is the result of luck, skill, or a failed model.
Investor overconfidence about what one can learn from prior hedge fund or mutual fund returns causes returns chasing, with new money flowing in after a relatively short period of good returns and flowing out after a similar period of poor returns. Some institutional investors have their own version of returns chasing, using only three to five years of returns to assess anactive manager’s performance, with unlucky managers fired if the next few years’ returns are not better. The resulting portfolio churn is driven more by random unexpected returns than by meaningful information.
In short, high equity volatility and investor overconfidence combine to explain much investor behavior in equity markets.
5. MOST INVESTORS SHOULD DIVERSIFY THEIR PORTFOLIOS.
Warren Buffett and his partner, Charlie Munger, argue that academics are wrong when they advise investors to diversify. I think their argument reflects Buffett and Munger’s innate humility. If I had their abilities and circumstances, I would probably diversify as little as they do. But that is a big “if”. Buffett and Munger’s argument against diversification makes sense only if they believe most investors share their ability to identify investments with extraordinary expected returns. That’s not what Sharpe’s (1991) arithmetic predicts or what empirical research finds. It’s possible a few great stock pickers would be hurtby the recommendation to diversify, but it seems unlikely they pay any attention to academic advice anyway.
For the rest of us, diversification can be a powerful tool. It is important to remember, however, that the goal is not to reduce the volatility of any particular investment. It is to reduce the uncertainty about lifetime consumption. Imagine diversifying your investment in homeowner’s insurance by using your premium to insure a tiny slice of every house in the state. The diversification almost eliminates uncertainty about the return on your insurance premium, but it also eliminates the reason you buy insurance—to reduce the uncertainty about your lifetime consumption.
Similarly, if much of your wealth is in executive stock options on the small growth company where you work, diversifying your retirement portfolio with the stock of other small growth companies probably doesn’t reduce your uncertainty about lifetime consumption.
SUMMARY
When thinking about my investment portfolio, I start with a clear objective. Given the level of expected return, I want to minimize the uncertainty about my lifetime consumption, which includes what I spend on things for myself, like food, travel, and health care, and what I give away as political donations, charitable contributions, and gifts and bequests to my children and others. Holding the level of uncertainty about lifetime consumption fixed, I prefer more expected wealth to less.
I use a top-down approach to organize the tradeoffs involved in my ideal portfolio. How do mytastes, preferences, and circumstances differ from those of the investment-weighted average of all investors, and what do the differences imply about how my portfolio should differ from the global market portfolio? This approach does not give me an exact solution, but I’m sure it puts me in the right neighborhood. I would not trust a precise solution to such a complex andpoorly specified problem anyway. My goal is a portfolio I can justify to myself today, based on the informationavailable now. Because unexpected returns will dominate the outcome, I won’t judge my choice on whatthe portfolio delivers tomorrow.
Finally, when choosing my own investments, I remind myself that most overconfident investors don’t realize they are, and that client fees pay for most investment managers’ yachts.
REFERENCES
Barber, Brad M., and Terrance Odean, 2000, Trading is hazardous to your wealth: The common stock investment performance of individual investors, Journal of Finance 55, 773-806.
Fama, Eugene F., and Kenneth R. French, 1993, Common risk factors in the returns on stocks and bonds, Journal of Financial Economics 33, 3-56.
Fama, Eugene F., and Kenneth R. French, 2018, Volatility lessons, Financial Analysts Journal 74, 42-53. The preferred version of this paper is available at FamaFrench.Com.
French, Kenneth R., 2008, Presidential address: The cost of active investing, Journal of Finance 63, 1537-1573.
Lintner, John, 1965, The valuation of risk assets and the selection of risky investments in stocksportfolios and capital budgets, The Review of Economics and Statistics 47, 13-37.
Novy-Marx, Robert, 2014, Predicting anomaly performance with politics, the weather, global warming, sunspots, and the stars, Journal of Financial Economics 112, 137-146.
Odean, Terrance, 1998, Volume, volatility, price, and profit when all traders are above average, Journal of Finance 53, 1887-1934.
Sharpe, William F., 1964, Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance 19, 425-442.
Sharpe, William F., 1991, The arithmetic of active management, Financial Analysts Journal 47, 7-9.
Shermer, Michael, 2008, Patternicity: Finding meaningful patterns in meaningless noise, Scientific American 299.
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Five Things I Know about Investing
KEY TAKEAWAYS
I have been passionate about investing since I started studying finance in 1977. The first investmentclass I took was dominated by the Capital Asset Pricing Model (CAPM) of Sharpe (1964) and Lintner(1965). The CAPM says every investor’s ideal portfolio is some combination of the risk-free asset and the value-weight (VW) market portfolio of all stocks, bonds, and other investible assets, and every portfolio’s expected return is a linear function of its beta, which is its sensitivity to the market return. The academic view of investing is far more complicated today.
In this essay, I focus on five concepts that capture much of what I know about investing and that drive my approach to portfolio design.
This is a vibrant time for investment research. There is much that we don’t know and lots of controversyabout what we do know. Although we may disagree on other issues, I think most researchers who study investing and portfolio design will agree that the five concepts in my list are true, so I will call them facts.
I explore the implications of each fact for the investment strategies and portfolio designs of individuals. The essay does not explore the interesting challenges corporate managers face when trying to evaluate potential projects. It is also not directed at the investment problems of hedge fund managers, venture capitalists, or private equity activists, although I hope former students in these areas agree with what I say. The emphasis on individuals, and financial advisors who work withindividuals, simplifies the discussion and keeps what is already a long essay from getting longer.
1. RISK IS UNCERTAINTY ABOUT LIFETIME CONSUMPTION.
Most investors are risk averse. Given the expected return, they prefer lower risk, and given the level of risk, they prefer higher expected return. Most investors understand that the expected return on an investment is essentially the best guess of what the return will be. There is a lot more confusion about risk. When I ask students, investors, and friends what risk means I get conflicting answers. Some say itis the potential for loss. Others suggest it’s the volatility of the return. And others say it’s beta, from the CAPM. Good portfolio design requires a clear understanding of risk.
I define risk as uncertainty about lifetime consumption broadly defined. People invest because they wantto use their wealth in the future. Some might plan to spend all the money on themselves for things like food, shelter, travel, recreation, and medical care. Others may plan to spend some of their wealth on political contributions, charitable donations, or gifts and bequests to their children. My definition of lifetime consumption includes all these and any other anticipated uses of wealth. Investors like a high expected return because it increases theexpected wealth that will be available to spend or give away. And everything else the same, risk averse investors prefer less uncertainty about their future wealth.
If people don’t like uncertainty about future wealth, shouldn’t we measure each investment’s risk by its potential for losses or the volatility of its returns? No. Those definitions miss important interactions within an investor’s portfolio and, even more important, between the portfolio return and the investor’s other sources or uses of future wealth.
Think about homeowner’s insurance. If we consider only the policy, this investment is as bad as a lottery ticket. First, there’s lots of uncertainty about the outcome. Typically, the policyholder pays the premium and gets nothing back, but there is always the chance of a big payoff. Second, if theinsurance company rationally expects to make money on the contract, a rational policyholder’s expected return must be negative. Why would a risk averse homeownerchoose a volatile investment with a negative expected return? Because insurance reduces the uncertainty of his or her lifetime consumption. The probability that a disaster will destroy any specific policyholder’s house is tiny, but if it does, the loss to that homeowner can be catastrophic. Most homeowners are happy to pay the annual insurance premium to eliminate this potential hit to wealth and lifetime consumption.
In that same spirit, it is particularly risky to invest most of your savings in your employer’s stock. As theformer employees of Enron might warn us, this can be a remarkably unfortunate way to put all your eggs in one basket. Enron was an energy and trading company based in Houston, Texas. After roughly a decade of phenomenal success, Enron filed for bankruptcy in 2001. Many employees had most if not all their 401(k) in Enron stock and lost their job and retirement savings at the same time. A better understanding of risk might have led them to a retirement portfolio that reduced their uncertainty about lifetime consumption.
Liability driven investing is another way to manage the uncertainty about lifetime consumption. My friendJeff Coyle is a financial advisor in Southern California who has spoken to most of the classes I have taughtover the last 25 years. He describes a client who hired a shipyard in Italy to build a large yacht. The amount and timing of the payments were known, but the obligations were in euros. Jeff took this liability off the table by buying government bonds that delivered the euros needed when each payment was due. Thoseof us with more mundane obligations can use the same approach. If you are stretching to buy your firsthome, for example, you might move the savings you will need at closing into a safe money market accounttoday.
The general takeaway here is to think about risk holistically. How will a potential investment vary with yourexisting portfolio and with your other sources and uses of wealth? More succinctly, how will it affect the uncertainty about your lifetime consumption?
2. THE AVERAGE DOLLAR INVESTED HOLDS THE MARKET.
I use a top-down approach when designing my investment portfolio. (My wife’s tastes and preferences also affect our portfolio. To respect her privacy, I leave her out of this discussion.)
I start with the fact that all investors must collectively hold the global market portfolio of all stocks, bonds, and other financial assets. Simple arithmetic then says the average dollar invested holds the global marketportfolio. And if we weight by investment wealth, so Bill Gates gets more weight than I do, the averageinvestor also holds the global market. As a result, the average investor and the global market portfolioprovide useful reference points for my portfolio.
My pro rata slice of the global market portfolio would probably be a fine choice for my portfolio if mypreferences and circumstances matched those of the global average investor. But they don’t. Thedifferences help me think about how my portfolio should differ from the global market portfolio. I illustratethis framework with a few examples of how I differ and the implications of the differences for my portfolio.
I live in the United States, almost everything I buy will be denominated in US dollars, and I may not betreated as well as local investors in foreign markets. All three facts lead me to overweight US investments.First, economists talk about something we call “keeping up with the Joneses” and younger readers know asFOMO, fear of missing out. If your neighbors overweight US investments, you can reduce your risk ofsuffering while they prosper by also overweighting US investments. Second, since the things I expect toconsume are priced in dollars, investments denominated in other currencies have an extra risk; the dollarpayoff from a foreign investment will be smaller if the foreign currency depreciates. Third, local investorshave an advantage over foreigners in some markets. Foreigners sometimes pay higher effective tax ratesthan locals, and in some countries capital controls make it difficult for foreigners to repatriate their wealth. Argentina, for example, instituted restrictions on the flow of capital in 2019 that continue to challenge foreign investors. These and similar factors push me and other US investors to overweight US investments and underweight foreign investments. And this seems to be a universal result. As a group, locals overweight the investments in their home market.
Let’s look at another factor. I am substantially older than the average investor, even after weighting people by their investment wealth. When I was young, most of my wealth was anticipated income, so the volatility of my investment returns contributed little to the uncertainty of my lifetime consumption. The return on my investment portfolio had almost no effect on my anticipated wealth or lifetime consumption. I also had a lifetime of real options ahead of me. If my investments did poorly after I had accumulated someretirement savings, I could adjust, perhaps by deferring the purchase of a vacation home or by moving to a higher paying but less attractive job. At my current age, the return on my investment portfolio pretty much determines the wealth I will have available to spend or give away. As a result, my age pushes toward less risk, with a bigger allocation to fixed income and a smaller allocation to equities than the global market portfolio.
A third factor is my risk aversion. I think I’m less risk averse than the average investor. While my agepushes toward more fixed income, my low risk aversion pushes toward equity. Low risk aversion iswinning for now, so I hold more equity and less fixed income than the global market portfolio.
The top-down global-market approach draws attention to many of the issues that are important when designing an investment portfolio. In addition to domicile, age, and risk aversion, one should consider how personal financial circumstances, including anticipated and potential sources and uses of wealth, tend to vary with the components of the global market portfolio. Other issues, such as transaction costs, tax considerations (including unrealized capital gains and losses in one’s taxable portfolio), environmental, social, and governance concerns, and perceived informational advantages anddisadvantages, may also be important.
The top-down approach helps me think about the direction I should move away from the global VW market—should I overweight value stocks and underweight growth stocks or vice versa. It also gives me a general sense of how much each of my portfolio allocations should differ from the global market’s. Theapproach does not tell me, however, exactly how much to deviate unless I am trying to match a specificliability, such as locking in a big down payment. Someone clever may be able to determine my “ideal”portfolio, but I would not trust a precise analytical solution to a problem as complicated and poorly defined as this.
3. CHANCE DOMINATES REALIZED RETURNS.
Perhaps because the evolutionary cost of false negatives—failing to see real patterns—was high relativeto the cost of false positives, people seem hardwired to identify patterns, whether they are real or not (e.g.,Shermer 2008). Who hasn’t seen a ship in the clouds or human figures in a dirty window? Those of us whogrew up in New Hampshire in the 20th century have fond memories of the Old Man of the Mountain, arock formation that looked like the silhouette of, well, an old man. We mourned when he fell from themountain in 2003 and are proud to honor his memory on our road signs and license plates.
Given the importance of financial markets and the human inclination to identify patterns, it is notsurprising that researchers and investors have found patterns in asset prices and returns for centuries and continue to do so now. It is also not surprising that a nontrivial fraction of the patterns are false positives.
We can split an asset’s return into its expected return, which is our best guess of what will happen based on all theinformation currently available, and its unexpected return, which is the surprise—the difference between what actually does happen and what was expected,
R = E(R) + U. (1)
The goal of most who study stock returns is to predict the future, not describe the past. In the context of equation (1), researchers are trying to identify persistent differences in expected return across assets orasset classes. Differences in the cross-section of expected returns, however, are usually small relative to the volatility of unexpected returns, so realized returns are mostly the result of chance. Over reasonable investment horizons—three, five, ten, even 20 years—realized returns are typically dominated by the unexpected component and inferences from realized returns are often false positives.
The performance of FAANG stocks—Facebook, Amazon, Apple, Netflix, and Google—over the decadefrom 2012 to 2021 illustrates the importance of unexpected returns. (I know, some of the names havechanged, but FAANG sounds better than MAANA.) The 2012-2021 average annual return on a VW portfolioof these five large stocks is 30.09% and the cumulative ten-year return is 1166%. (The FAANG portfolio andvalue-weight market returns here and below are computed using monthly data from Chicago Booth’sCenter for Research in Security Prices, CRSP, and are denominated in US dollars.) Should we expect theportfolio to deliver 1166% over the next decade? No. Strong unexpected returns are a better explanation for the great return and, by definition, the expected value of future unexpected returns must be zero.
The FAANG portfolio’s return in 2020 is a remarkable 61.47%, almost three times the solid 20.99% return on the CRSP VW market portfolio. The success of the five technology stocks in the first year of the pandemic makes sense. The companies were selling entertainment, social interaction, and home delivery to a world of people isolated in their houses. The huge increase in the demand for FAANG services could have been anticipated only by someone whose crystal ball forecast COVID-19 and its consequences. Those who use recent returns on the FAANG portfolio to predict its future returns will probably be disappointed.
The incentives to identify new patterns in stock returns or to improve existing patterns are strong: degrees are awarded, papers are published, tenure is granted, and new investment products are sold. The set of potential patterns or improvements a researcher might test is huge. There are thousands ofstocks, an almost unlimited list of attributes, and many ways to combine the candidates. With a good search algorithm and enough time, a clever empiricist should be able to find big patterns in any reasonable sample of realized returns. Ideally, the winning pattern describes expected returns, but evidence that it doesn’t is not likely to arrive before the successful researcher is rewarded. If we are notalready, we may soon be facing an onslaught of unconstrained search, the cardinal sin of financial economists.
How can an investor tell whether the winning pattern is gold or pyrite? Start by considering the modelthat justifies the pattern. If there is none, presume you are looking at the winner of a massive,uninformed search. A winning pattern is more likely to persist if the model that predicts it is compelling. For example, a model motivated by greed, fear, and transaction costs has potential. A model that works only if all returns are first converted to Turkish lira does not. Finally,the credibility of both the model and the pattern are enhanced a lot if the model obviously came first.
Be suspicious about unusual procedures, a peculiar sample period, or strange variable definitions.Researchers constructing factors, for example, often follow the procedure in Fama and French (1993), notbecause (ahem) it is obviously the best, but because doing so eliminates potential users’ concerns about one type of overfitting. Everything else the same, almost all researchers want a long sample period. As aresult, the start dates for most empirical research are driven by data availability. Three typical start dates inresearch on US stock returns align with key dates for the widely used monthly CRSP data, January 1926,July 1962, and January 1973. Other databases drive other start dates. Be suspicious when there is noobvious link between the start of the available data and the start of the sample. Similarly, expect the sample to end no more than four or five years before a paper is circulated. Finally, Novy-Marx (2014)emphasizes that unusual variable definitions are ominous. Don’t be surprised if the patterns they producedo not persist out of sample, especially if standard definitions destroy it in sample.
In short, when designing a portfolio, investors are typically interested in future differences in expectedreturns. Because expected and unexpected returns come in pairs, however, it is easy to misinterpretdifferences in unexpected returns as differences in expected returns. Many years ago, my colleagueGene Fama convinced me that the best way to manage this problem is to start with the null hypothesisthat any pattern in realized returns happened by chance.
When testing the chance hypothesis, look for (i) a compelling story that predicts the pattern in expectedreturns, (ii) strong in-sample evidence that the pattern is more than noise, and (iii) robust out-of-sampleevidence that reinforces that conclusion. Be particularly wary of patterns identified by uninformed and unconstrained search.
4. ACTIVE INVESTING IS A NEGATIVE SUM GAME.
Dick Roll is a friend, finance professor, and pilot who flies his own plane. Many years ago, when we werecolleagues at UCLA, I asked him whether his hobby was risky. He said the data imply it’s about as dangerous as driving a motorcycle. Dick is a smart and careful man, so I suggested the averagesoverstate the risk when he flies. His response changed the way I see the world: “Ken, every pilot thinks he’s better than average.”
Bill Sharpe published a great paper in the Financial Analysts Journal in 1991 that implies Dick’s insight aboutoverconfidence extends to active investors. Sharpe’s paper, “The arithmetic of active management,” makes a simple point. The average dollar invested actively loses to a passive investment in the value-weight market portfolio.
Sharpe’s argument is straightforward. Suppose I hold a passive VW market portfolio, that is, I hold mypro rata slice of all stocks, bonds, and other financial assets in the aggregate market portfolio. Since I hold the VW market, my return is the return on the market minus the low costs of maintaining my buy-and-hold portfolio, RM – CL. And since I hold the market portfolio, the combination of all other investors—passive and active—must also hold the market, and their combined return is the return on the market minus their higher costs, RM – CH. Why are their costs higher? Because the active investors in the group pay extra management fees, transaction costs, and the other expenses of investing actively. My costs CL are lowerthan the VW average costs of all other investors CH, so over every period—every year, day, minute, andeven every instant—my return RM – CL is higher than the VW average return of all other investors RM –CH.
There is another way to see Sharpe’s logic. If some investors choose to hold more than their pro rata slice of Apple stock, others must hold less than their pro rata slice. The over- and underweights in Apple are side bets. Whatever one group wins, the other loses. And both groups pay to play the game.
If active investing is a negative sum game, why does it persist? The most likely explanation is investor overconfidence combined with the fog of volatility. See, for example, Odean (1998) and Barber and Odean (2000). Given the high volatility of unexpected equity returns, active strategies and managers typically produce almost as many good monthly or annual returns as bad ones, which allows investoroverconfidence to persist. There has been a gradual shift from active to passive since at least 1980 (e.g.,French 2008), but as the meme stock events of 2021 remind us, seemingly uninformed and overconfident new investors enter the market every day.
Most investors also seem overconfident about their ability to evaluate managers. Suppose that after fees and expenses, the expected outperformance or alpha of the world’s greatest hedge fund manager is 5%per year. If her fund has equity-like volatility of 20% per year, how long should we expect to wait before confidently inferring (with a t-statistic of 2.0 or greater) that her alpha is positive? The answer is 64 years. When I ask others this question, most are surprised that it will take two or three investment lifetimes to determine that this great hedge fund manager more than covers her costs. Why does it take so long to evaluate the manager? First, the highly volatile unexpected returns that let many underperforming active investors believe they are beating the market also obscure the great hedge fund manager’s skill. Second, hedge funds rarely track benchmarks and without a benchmark, 100% of the unexpected return is noise.
Index funds are easier to evaluate because each fund’s target index is a perfect benchmark, providing direct evidence of whether the fund is delivering as promised. Active equity mutual funds are typicallyeasier than hedge funds to evaluate and harder than index funds. Although a benchmark or asset pricing model may eliminate some noise, it can still take decades to decide whether an active fund’s under- or overperformance is the result of luck, skill, or a failed model.
Investor overconfidence about what one can learn from prior hedge fund or mutual fund returns causes returns chasing, with new money flowing in after a relatively short period of good returns and flowing out after a similar period of poor returns. Some institutional investors have their own version of returns chasing, using only three to five years of returns to assess anactive manager’s performance, with unlucky managers fired if the next few years’ returns are not better. The resulting portfolio churn is driven more by random unexpected returns than by meaningful information.
In short, high equity volatility and investor overconfidence combine to explain much investor behavior in equity markets.
5. MOST INVESTORS SHOULD DIVERSIFY THEIR PORTFOLIOS.
Warren Buffett and his partner, Charlie Munger, argue that academics are wrong when they advise investors to diversify. I think their argument reflects Buffett and Munger’s innate humility. If I had their abilities and circumstances, I would probably diversify as little as they do. But that is a big “if”. Buffett and Munger’s argument against diversification makes sense only if they believe most investors share their ability to identify investments with extraordinary expected returns. That’s not what Sharpe’s (1991) arithmetic predicts or what empirical research finds. It’s possible a few great stock pickers would be hurtby the recommendation to diversify, but it seems unlikely they pay any attention to academic advice anyway.
For the rest of us, diversification can be a powerful tool. It is important to remember, however, that the goal is not to reduce the volatility of any particular investment. It is to reduce the uncertainty about lifetime consumption. Imagine diversifying your investment in homeowner’s insurance by using your premium to insure a tiny slice of every house in the state. The diversification almost eliminates uncertainty about the return on your insurance premium, but it also eliminates the reason you buy insurance—to reduce the uncertainty about your lifetime consumption.
Similarly, if much of your wealth is in executive stock options on the small growth company where you work, diversifying your retirement portfolio with the stock of other small growth companies probably doesn’t reduce your uncertainty about lifetime consumption.
SUMMARY
When thinking about my investment portfolio, I start with a clear objective. Given the level of expected return, I want to minimize the uncertainty about my lifetime consumption, which includes what I spend on things for myself, like food, travel, and health care, and what I give away as political donations, charitable contributions, and gifts and bequests to my children and others. Holding the level of uncertainty about lifetime consumption fixed, I prefer more expected wealth to less.
I use a top-down approach to organize the tradeoffs involved in my ideal portfolio. How do mytastes, preferences, and circumstances differ from those of the investment-weighted average of all investors, and what do the differences imply about how my portfolio should differ from the global market portfolio? This approach does not give me an exact solution, but I’m sure it puts me in the right neighborhood. I would not trust a precise solution to such a complex andpoorly specified problem anyway. My goal is a portfolio I can justify to myself today, based on the informationavailable now. Because unexpected returns will dominate the outcome, I won’t judge my choice on whatthe portfolio delivers tomorrow.
Finally, when choosing my own investments, I remind myself that most overconfident investors don’t realize they are, and that client fees pay for most investment managers’ yachts.
REFERENCES
Barber, Brad M., and Terrance Odean, 2000, Trading is hazardous to your wealth: The common stock investment performance of individual investors, Journal of Finance 55, 773-806.
Fama, Eugene F., and Kenneth R. French, 1993, Common risk factors in the returns on stocks and bonds, Journal of Financial Economics 33, 3-56.
Fama, Eugene F., and Kenneth R. French, 2018, Volatility lessons, Financial Analysts Journal 74, 42-53. The preferred version of this paper is available at FamaFrench.Com.
French, Kenneth R., 2008, Presidential address: The cost of active investing, Journal of Finance 63, 1537-1573.
Lintner, John, 1965, The valuation of risk assets and the selection of risky investments in stocksportfolios and capital budgets, The Review of Economics and Statistics 47, 13-37.
Novy-Marx, Robert, 2014, Predicting anomaly performance with politics, the weather, global warming, sunspots, and the stars, Journal of Financial Economics 112, 137-146.
Odean, Terrance, 1998, Volume, volatility, price, and profit when all traders are above average, Journal of Finance 53, 1887-1934.
Sharpe, William F., 1964, Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance 19, 425-442.
Sharpe, William F., 1991, The arithmetic of active management, Financial Analysts Journal 47, 7-9.
Shermer, Michael, 2008, Patternicity: Finding meaningful patterns in meaningless noise, Scientific American 299.
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