For financial professionals in Italy

Myron Scholes on Time: Time diversification

In the first episode of the series, Myron explores time diversification and its importance in effecting investment outcomes. Myron, in conversation with Phil Maymin, explains why targeting a specific level of risk over time is equally, if not more important, than cross-sectional diversification.


Philip Maymin, PhD

Philip Maymin, PhD

Director of Asset Allocation Strategies

9 Sep 2022
27 minute listen

Key takeaways:

  • Time diversification is as important as cross-sectional diversification in effecting investment outcomes yet is seldom mentioned. It also takes on more importance in periods of market stress.
  • Time diversification is not the same as avoiding market timing: a static allocation portfolio that does not do market timing still has time-varying risks. This is especially applicable to benchmarks.
  • Managing the risk of a portfolio to a target level over time can enhance compound return by reducing uncompensated, excess volatility.
Philip Maymin: Welcome to the first episode of the Myron Scholes’ podcast, On Time. Chief Investment Strategist at Janus Henderson, Professor of Finance at the Stanford Graduate School of Business, and Nobel Laureate in Economic Sciences, among many other accomplishments and responsibilities that would take too long to list. Myron shares his unique insights with us here.

My name is Phil Maymin and I have the pleasure of working with Myron here at Janus Henderson. These podcast episodes are aimed at sophisticated investors and those who wish to be sophisticated investors and are intended to be thought-provoking – and perhaps even controversial. We hope you leave each episode with more questions than you started, and we invite you to send feedback or questions to Myron at Today’s episode is, “Time Diversification.”

Myron Scholes: Thank you very much, Phil. Today I want to talk about time diversification. Although many of us study and understand cross-sectional diversification, which is buying myriad securities and holding them in a portfolio in a weighted or unweighted way, time diversification is diversification across time, and it’s seldom mentioned, time diversification is seldom mentioned. Diversification across time however, is an important … it’s as important or maybe even more important than cross-sectional diversification in effecting investment outcomes.

Diversification is a fundamental investment principle. Diversify investments by holding many securities in a portfolio to reduce random noise and to eliminate the effects of only holding a few stocks on the volatility or the risk of an investment portfolio, especially for investors who lack skills to select winners and avoid losers. When James Tobin, a famous Yale economist, was awarded the Nobel Prize for work on understanding risk, the press asked what he would prove to win the prize in economics? What did he prove? His reply was, “Don’t put all your eggs in one basket.” [Eugene F.] Fama, another Nobel Prize winner, has claimed that just buying 20 stocks or 20 securities will achieve a diversified portfolio and that holding a non-diversified portfolio produces inferior results. Burton Malkiel, in his famous book, A Random Walk Down Wall Street, has claimed that the only free lunch in finance is cross-sectional diversification. You diversify, you get rid of risks, you make your returns. That’s free. They, as others, believe that it is difficult to pick securities consistently that will produce sufficient abnormal returns to overcome the costs of giving up the benefits of diversification.

And as we will discuss, uncompensated excess volatility reduces the investor’s compound return. So there’s two dimensions of returns: lack of diversification increases risk and non-diversifying over time increases risk. Unless you have skills to overcome the lack of diversification either cross-sectionally or over time, your returns will not be as good as diversifying fully.

The theory and supporting empirical evidence has led to the growth of index funds and ETFs and factor investing. In the late 1960s, I was a major innovator and proponent of this line of thinking. And important to time diversification, the corollary belief that buy-and-hold strategies dominate alternatives, such as time diversifying a portfolio. When I proposed passive investments way back in the 1960s, there was no signals, however, as to the risks of forward risks in the marketplace. We were left to make the assumption that the only alternative was to assume the world was normally distributed and risks were not changing over time. We had no evidence to the contrary that we could substantiate the opposite belief. We believed that that was a good approximation to reality, just assume the risks were constant and normally distributed.

As Milton Friedman said, however, and he told us and informed us in his famous dictum, “There is no such thing as a free lunch.” Why, therefore, is cross-sectional diversification not a free lunch? Unfortunately, although it works most of the time, it fails badly at the times of shock when we most need it. When good or bad shocks occur, all assets tend to move together. The correlation among the returns on assets approach one; they’re all moving together. For example, all equities, domestically, internationally, moved together during the COVID crisis in March of 2020 and again during the recent inflation shock and Russia/Ukraine war.

It is at these times, the time of shocks, that the free lunch becomes awfully expensive. Diversification is lost; one does not have diversification. If everything is moving together, the only factor is the market volatility or the market volatility that individuals have to hold. Equity volatility increases, and because diversification is lost with high correlation among assets, the volatility of portfolios increased dramatically.

Forecasting risk over time, however, to keep risk closer to target, has a greater impact than does the extent of cross-sectional diversification and should command much more attention than it does. An example of time diversification that is bad – and most equate the bad with market timing – will help: Assume that a portfolio manager assumes that he has market-timing skills and, however, unfortunately, he has no skills at all and he randomly times the market. That means he places, for example, 100% of his money in bonds 50% of the time and 100% of his money in stocks the remaining 50% of the time. Since the manager has no skills and is a random timer, bang-bang, in and out of the market, into bonds and the stock … no skills at all, his expected return experience is exactly the same as the person who’s a “Steady Eddie” and doesn’t do anything other than hold 50% in stocks and 50% in bonds all the time. The return would be exactly the same. If 50% of the time, I make the stock return, 50% of the time I make the bond return, versus 100% in stocks 50% of time, and make the stock return the remaining 50% in bonds, gives you exactly the same expected return.

So the timer who goes bang-bang in and out of the market essentially has to overcome the fact that the volatility will be much greater in that timing strategy. In fact, the mathematics and the results show that the volatility is actually 70% of the risk in the market because you have 100% of your risk in stocks half the time, which are very volatile, and volatility is a squared term, and while the 50/50 strategy is only 50% of the risk all the time. So to time the market is very expensive; if you’re a random or a bad timer of the market, the volatility increases. The example here rises even if the underlying volatility of the market investment is constant. The market risk is not changing. So timing has a bad reputation because it increases risk. Unless you’re a good timer, it’s uncompensated increases in risk.

Are there any benefits, however, to time diversifying if the volatility of the market portfolio does change? And we’ll talk more about this over our time in the podcast. The answer, yes. If changes in future risks are measurable, why so? If volatility is bad, increasing volatility is bad; if you incur excess volatility that is bad. And so we want to figure out ways to reduce the excess volatility and try to keep your volatility closer to target. The empirical evidence and the mathematics and the economics suggest that there are ways, in measuring the future volatility of the market, the return experience can be enhanced for an investor that can do it by using this market information to control or manage the risk of the volatility over time.

The compound return on a portfolio is different from the average return. The compound return is the growth of the portfolio, how it grows over time, and investors want to maximize their compound return, the growth of their portfolio, their terminal wealth for the risks they take. Most investors are encouraged to consider average return – on average, how am I doing? But in life, averages are not your friend. You don’t consume averages; you consume the end result, which is the compound return, and that’s very important.

Einstein said that the most powerful force in the universe is compound returns. I agree with him. Compound returns should be the major focus of all of activities, not only investing but in life generally. As I said, we do not consume averages, we consume file outcomes or compound return results. Our compound returns have many more dimensions than do average returns. Risk affects compound returns. In the short run, risks are everything in life, and risks are everything in the market. Risks dominate average returns. If I’m at the dinner table with my family, we don’t talk much about average return, we talk about why did the market go up a lot today? Or why did the market go down a lot today? That’s risk in the market.

Volatility reduces compound returns. So, this is oftentimes called the drag in returns. The average return or expected return exceeds compound returns. So we have to think about, how do we manage the drag? We’ll talk about that more. And assuming excess volatility around a target risk level reduces compound return even more. We can accept the drag for a target risk level; however, why assume much more volatility? Experiencing a large loss reduces compound return and the tails of the distribution – the bad outcomes or the good outcomes – are the most important than the middle of the distribution, which is not that important. Middle of the distribution tends to be noisy. Reducing the bad tails and participating in the up tails enhances compound return.

Great investors invest this way. Investors who are great ignore the risks of the middle of the distribution. Life is all noise in the middle. Everyone fusses about the middle of their life, but the most important thing and the things we remember are the great good things that occurred in life.

Recovering from a bad outcome or a big loss might take myriad years, or many years, to overcome. Missing a big win also may take a very great number of years to overcome. Although cross-sectional diversification – that is, pick a value-weighted or equally weighted group of stocks and give up the benefits of having superior skills – and investment management will achieve cross-sectional diversification. Time diversification, however, takes more skills and discipline. The amazing part of time diversification, however, is that it is free. Basically, reducing excess volatility reduces the drag on compound return. And that is true as well for cross-sectional diversification, [which] reduces excess volatility that is not compensated as well. Thank you.

Maymin: Well, that was wonderful. Myron, could you combine two of those thoughts? One, cross-sectional diversification doesn’t work in moments of stress, and the other is that the middles are the noise? Is it the case, that cross-sectional diversification is just a function of the middles? That’s the only place it exists?

Scholes: That’s correct. Cross-sectional diversification gets rid of the random noise of security A and security B moving in opposite directions. So the more you diversify, the more you move to the middle, or the systematic factor, the remaining factor, of the risk of the portfolio. And the risk of the portfolio sometimes dominates and sometimes it’s the idiosyncratic risk that dominate. When things are quiescent in the world, you know, then idiosyncratic things occur more frequently, the ups and downs. When things are moving together at times of good or bad shocks, then it’s the market effects or the factor effects that tend to dominate everything. And the middle is completely washed away because the big macro events, the COVID effect in March of 2020, dominated everything. All our securities tend to go down together, for example.

Maymin: And to do time diversification, you’ve alluded to using information from option prices, of course. But one could just use recent historical volatility, right, as a proxy.

Scholes: Correct. Any investors who could use anything, also any information they have, if they concentrate on forward information and signals, [investors] can use historical data such as using historical estimates of volatility. They could use historical estimates of association or correlation, how things are moving together to obtain what that recent market is telling us. And if there’s momentum or the market has a continuation of its past, then that would be a good forecaster of the future. It would have information and many investors use historical data to, in various combinations, to forecast future risks and changing risks. So some, ignore the changing risk, could use 40 years of historical data to attain the risk, some might use the most recent 60 days of data to estimate what the risks will be over the next 60 days or the next period of time. On the other hand, there are information in the markets that people can incorporate into their decision-making, such as that, as you mentioned, contained in risk markets, such as the option market, estimates of what crowd-sourced information is suggesting through the prices of options.

Maymin: Makes sense. And whatever signals they’re using, the actual process of doing time diversification is really easy, right? It’s when the risk seems to be – by whatever signals – higher, you scale back, and vice versa.

Scholes: Correct, that’s correct.

Maymin: Like it’s not a complicated thing to do. It’s why … why do you think so few people do it, if it’s that mechanically easy at least?

Scholes: Well, it’s …. as I said in my introduction to time diversification, it is the timing stigma that many people believe, and have been educated and taught that timers do not do well. Those people who, in my extreme example of randomly going in a noisy way with no skills between bonds and equities, that timer, all the timer does is create excess volatility, which is uncompensated. Just the same way as the stock plunger dominates by holding a few stocks and has no skills will increase their volatility as well, reducing two things. One is taking extra risk; this extra risk is uncompensated so, therefore, one took more risk for no reward. In our investment paradigm, we want to achieve the highest reward for any level of risk. Why not? That’s the model. And so, secondly, that it also reduces compound return. So the timing is a problem.

And then another problem is knowing how much historical data to use. Should you use 60 days of historical data, three years of historical data, five years of historical data? And given that the world does change and that the risks we see today are not the same way as the risks we saw five years ago, this conundrum or puzzle as to what mode of data to use has tended to force people away from the idea of trying to measure or incorporate time diversification into their strategies.

There are many other reasons for concentrating on cross-sectional diversification. It’s because it is easier to find a numerator or a benchmark. Many investors compare their advisors or managers to a benchmark. So that’s the same as relative investing or the idea of investing in comparing yourself to a benchmark. It’s the same thing as … in our school issues, we have, “Do I want my child to get A’s and be the best student in the class?” Yes, I do, but at the same time, I absolutely want to know how well they’re doing. What is that John Keeler said? Camp Lake Wobegon, “Everyone is above average in their performance.” And basically the problem with that is that there’s better gravitation because the science of measurement has improved over time to do relative comparisons or to grade managers or to grade performance relative to a benchmark, and it’s been harder to gauge in a compound return space. My mantra, or my belief, is I want people to move away from relative to compounding. Relative performances are averages relative to benchmark, to compounding. The world needs compounding as a focus in our thinking. And so maybe we can move back or think of ways to measure the effects of time diversification on portfolio performance in addition to looking at our ability, to say, “Should we diversify, or should we concentrate by looking at the significance of relative performance?”

Maymin: Wonderful. So it’s, in a sense, you’re saying people who are not changing their weights over time, they think they’re being so great, right? We’re avoiding market timing. Good for us. But in fact, even though their allocations aren’t changing because the risk is, they’re actually taking real market timing bets.

Scholes: That’s correct. So when I initially had thought of the concept of the index fund, you know, it was the case that I thought of that, as I said, the distribution of risks being best approximated by a normal distribution. In that case, the risks are not changing. You take the first step to develop a science, you make assumptions and you move forward. So the index fund, ETFs, etc., which grew out of those, and various forms of factor investing or constant portfolio investing, is all based on the assumption that risks are constant, or risks that are changing are not measurable, or they’re not measurable in a way to help in the time diversification aspects.

I think that’s false. I think we can have ways to measure how risks are changing. And I think that we can redirect our attention to the compound return experience or the growth of the portfolio and away from the relative comparisons. Just the same way, in schooling or education, we don’t want to always say, is the student doing well, relative to their peers, but absolutely, how is the student doing, and can they compete in the world around us? Or they cannot compete because, even though they’re relatively better off, they’re not really adding value to themselves and their human capital.

Maymin: Wonderful. Thank you so much, Myron.

Scholes: You’re welcome.


Equity securities are subject to risks including market risk. Returns will fluctuate in response to issuer, political and economic developments.

Diversification neither assures a profit nor eliminates the risk of experiencing investment losses.

Volatility measures risk using the dispersion of returns for a given investment.

Correlation measures the degree to which two variables move in relation to each other. A value of 1.0 implies movement in parallel, -1.0 implies movement in opposite directions, and 0.0 implies no relationship.

Idiosyncratic risks are factors that are specific to a particular company and have little or no correlation with market risk.

These are the views of the author at the time of publication and may differ from the views of other individuals/teams at Janus Henderson Investors. Any securities, funds, sectors and indices mentioned within this article do not constitute or form part of any offer or solicitation to buy or sell them.


Past performance does not predict future returns. The value of an investment and the income from it can fall as well as rise and you may not get back the amount originally invested.


The information in this article does not qualify as an investment recommendation.


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Philip Maymin, PhD

Philip Maymin, PhD

Director of Asset Allocation Strategies

9 Sep 2022
27 minute listen

  • Time diversification is as important as cross-sectional diversification in effecting investment outcomes yet is seldom mentioned. It also takes on more importance in periods of market stress.
  • Time diversification is not the same as avoiding market timing: a static allocation portfolio that does not do market timing still has time-varying risks. This is especially applicable to benchmarks.
  • Managing the risk of a portfolio to a target level over time can enhance compound return by reducing uncompensated, excess volatility.