For financial professionals in Denmark

Myron Scholes on Time: Efficiency in stock and option markets

In this episode, Myron, in conversation with Phil Maymin, compares and contrasts the market efficiency of stocks and options.


Philip Maymin, PhD

Philip Maymin, PhD

Director of Asset Allocation Strategies

Myron Scholes, PhD

Myron Scholes, PhD

Chief Investment Strategist

5 Dec 2022
38 minute listen

Key takeaways:

  • Rational and behavioral investors need each other to make markets more efficient.
  • Option prices contain rich information, including forecasting an entire distribution of risks, and changing over time.
  • The forward-looking options-implied information subsumes other backward-looking measures of risk and makes better forecasts.


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

Fixed income securities are subject to interest rate, inflation, credit and default risk. The bond market is volatile. As interest rates rise, bond prices usually fall, and vice versa. The return of principal is not guaranteed, and prices may decline if an issuer fails to make timely payments or its credit strength weakens.

Options (calls and puts) involve risks. Option trading can be speculative in nature and carries a substantial risk of loss.

Volatility management may result in underperformance during up markets, and may not mitigate losses as desired during down markets.

The Black-Scholes model, aka the Black-Scholes-Merton (BSM) model, is a differential equation widely used to price options contracts. The Black-Scholes model requires five input variables: the strike price of an option, the current stock price, the time to expiration, the risk-free rate, and the volatility.

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.

The Fed, or Federal Reserve is the central banking system on the United States.

The Phillips curve is an economic theory that inflation and unemployment have a stable and inverse relationship. Higher inflation is associated with lower unemployment and vice versa.

S&P 500® Index reflects U.S. large-cap equity performance and represents broad U.S. equity market performance.

The Taylor Rule is an interest rate forecasting model that suggests central banks should raise rates when inflation is above target or when gross domestic product (GDP) growth is too high and that they should lower rates when inflation is below target or GDP growth is too slow.

Phil Maymin: Welcome back to 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 they’re 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 about options and market efficiency.

Myron Scholes: Correct. Today I want to talk about option market efficiency and stock market efficiency. Many argue that the stock market prices are efficient. Fewer would agree, however, that option market prices are efficient. By efficient, I mean that unless investors have superior information than the crowdsourced information embodied in market prices, then market price is an unbiased estimate of value. That means the market price does not necessarily be exactly correct, it’s just that it has to be an unbiased estimate. It has to be a good estimate. It has to be an estimate that is on average good. The belief in the efficiency of market prices has led many to believe that buying an ETF or an index fund is superior to trying to outperform the market through selectivity or time diversification. Many empirical studies support this conclusion. Using market prices for valuation is a cornerstone of modern finance and is the underlying support for myriad products offered in the marketplace. This conclusion, however, is not a test in market efficiency. Active investors need to be paid to make the market efficient. To test for efficiency is difficult, for it is necessary to first have a model of equilibrium to know what is the market value and how it’s valued. What is the model of market equilibrium? Then you can test whether the market is in disequilibrium, or out of whack … or is it in whack? You know, without a market efficiency model or model evaluation, it’s hard to test. This is why Gene Fama was awarded the Nobel Prize in economics, because he said to test for market efficiency, you need a model. You can’t test for market efficiency looking at relative to a benchmark. Maybe the benchmark is not efficient, or not a correct model.

To estimate the value of an equity in a company is difficult. It depends not only on future cash flows including new investments and changes in capital structure and dividends payouts, but also changing discount rates. It’s very hard to estimate what the value of a stock is or a security is. Rational investors are necessary to control the behavioral tendencies of myriad investors. They need to do the hard work to value companies. The man keeps the dog in line and makes money walking the dog; they both need each other. A lot of people say the market is all full of behavioral tendencies and everyone is behavioral; they buy stocks because of noise and everything, and the stock has no value, no discernible value. It’s all noise. So all of it is determined by the dogs. The dogs are running everywhere and, basically, they determine the stock value. But without the man walking the dogs back to the home, where would the dogs be? It’d be all over the place. We’d have no equilibrium. We would not be able to do anything. So behavioralists need the man, the rational person, to walk the dogs home. The man makes money by walking the dogs. All the behavioralists pay the man to walk them home and to pay the rational people. That is how science works, with a combination of rational and irrational, and the science couldn’t work. So basically, efficiency is determined by the man understanding how to pull the dogs back and how to make the markets become more efficient.

The option market prices are derived prices and many believe they can profit by buying or selling options. Option prices are believed by many to be biased and the option market is not as efficient as the stock market. I don’t exactly know what that means to not be efficient in the stock market, because it’s hard to know whether the stock market is efficient. And it’s hard, then, to know whether the option market is efficient. It seems to me it would be much easier to value an option than a stock. The option buyer, as an insurance contract, need only focus on volatility. There is no need to forecast future cash flows. It only needs to forecast future risks. What are the risks of the road ahead? What are the risks ahead? They don’t need to have actual cash flows or know what the value is since the option price is derived from the underlying asset price. As the Black and Scholes model showed, the derivative market models are time tested as benchmark for 50 years now and they’re still used, and they continue to grow. And so, basically, the market and options now has options on over 4,000 securities.

In 1973, when Fischer Black and I published the Black-Scholes model, there was no options traded on listed securities. And from that time forward, we’ve seen the growth of options in more than 4,000 securities priced every day and traded every day and billions of dollars’ worth of valuation in options, used in myriad ways to insure portfolios, to hedge risk, and to transfer risk to others. Before the publication of the Black-Scholes model, Fisher and I were given the logbooks of an option dealer who recorded myriad actual over-the-counter option trades for many years in his diary. We published a paper in 1973 which showed that these prices were efficient. By efficient, we meant we could not use the model – which no one knew about other than Fisher and I – to hedge risk and earn a return trading at these option prices.

Since then, myriad papers have concluded that it was very difficult to find consistent profits by estimating whether an option was expensive or cheap. It is difficult to construct strategies using options on the same underlying asset with different exercise prices, different maturities, and different payoffs such as call and put options to make consistent profits. Moreover, to reduce the cost of hedging the risk portfolio, many managers undertake what are called basis trades, which rely on correlation among different asset structures to maintain themselves throughout the life of the hedge to reduce the cost of the insurance. Those seeming to reduce the hedging costs or the cost of protecting large losses, these strategies to prevent tend to provide imperfect hedges, for the relied upon correlations to reduce the costs tend to break down when needed in times of stress.

Maybe a reason why options are deemed to be inefficient is that the shape of the implied distributions of future risk as determined from option prices change over time – they’re not constant, they change over time – and in most cases, don’t forecast a distribution of risks in the future that are normal. Since many investors are used to assuming normality or normal distribution to look at the option market and saying, no, the risks of the road ahead are not normal … the risks ahead are shaped in ways that don’t look like a normal distribution causes people to tend to want to reject it because of their belief that risks should be normally distributed because all data to investors are based on the assumptions of providing experience and measurement based on normality or normal risk. The alterative, the forecasts of the risk ahead implied by option market might not seem to be accurate when judged against outcome six months or nine months or a year forward than they are maybe two months or six months going forward. So it depends what you need the option market to tell you.

Obviously, the longer the horizon in which everyone is forecasting, the more the uncertainty is. But still, it might be an unbiased forecast to risk not only two to three months hence, but six months hence or a year hence. It’s just that it’s very hard to have enough data to test whether there’s accuracy, and the more you want to test the road ahead, many miles and miles and miles ahead, the more difficult it is to forecast going forward.

Options are priced by the volatility of the underlying instruments, for they are insurance contracts. They’re also levered instruments. At the very short end of the maturity spectrum, many short-term traders are attracted to the leverage piece and not the insurance piece, which dominates the insurance component, and are willing to pay premiums to speculate on price movements. Market makers provide the leverage to clients for essentially a gambling fee. So there may not be very much information and the market might be a different market at the very short end of the option market.

The information in option prices is rich. Forecasting accuracy of the risk-neutral distribution of risks two to six months ahead dominates using historical data only alone or using combination of option-implied risk and historical data. Option prices dominate both; they dominate both using just historical data and combinations of historical data and option data. Even the tails of the distribution of risk tend to be priced efficiently using market prices of options. For every buyer of insurance, there’s a seller of insurance. The market maker sells put options, which protects against the downside. The market maker sells put options, which protects against the downside. Buyers are willing to pay more for put protection, and when they believe that the likelihood of a large drawdown is increased, more downside tail risk means they’re willing to pay more for the insurance. To survive and stay in business, however, the market maker must price these options correctly. This is a Darwinian survival of the fittest. For those market makers who think they know more than the market and don’t increase prices or protection, they then sell options too cheaply and are put out of business because they have to pay off and don’t have an ability to survive. So Darwin is correct. Over time, very successful market makers survive and know how to price these contracts. So they know how to provide value to the market, and they’re the experts.

But it’s interesting: They’re the experts in their segment of the market. They don’t have to be experts everywhere; they just have to be experts in what options their pricing. Some might be experts in U.S. equities, others in European equities, some in commodities, some in bonds. They are segmented because it takes expertise to be an expert in each of the market. They have, however, few offset possibilities available to them as they would if they were just making markets in options with exercise prices closer to marketplace prices. To survive, they know their markets, and when hedgers demand more insurance, more protection against the downside, they mark up prices. And to survive, they have to mark up prices correctly. As a result, the crowdsourced information in option prices reflects the combined knowledge of hedgers – the ones who are seeking more protection – and market makers across not only one security, but across a vast cross section of instruments around the world.

Obviously, options in the S&P 500 will exhibit much better efficiency, lower spreads, larger open interest, and greater trading volume than an option on emerging market securities; prices are not as accurate, for the crowd is missing to crowdsource those option prices. The option market forecasts of future volatility – because that, remember, is what the market is forecasting… it’s future volatility. It’s not valuation of a security, which is very difficult to do. But it’s forecasting of option prices of risk based on volatility. So-called “at-the-money” options completely dominate any prediction based on historical data using naive or sophisticated forecasting technology.

Using a sample of the top 1,000 securities by market value in the United States with liquid options, both puts and calls was a better predictor of realized volatility for the next 30 days, or 60 days, than was the market option forecast of volatility; completely dominated in forecasting future volatility for the period January 2000 to September 2021 than any historical data. Like other studies using indices on underlying securities, we found that implied volatility subsumed any information in realized volatility. Using past volatility did not add additional information or forecasting power at all.

Moreover, the option forecasts were unbiased, for the coefficient of the realized volatility on forecasted volatility was close to one. That means the forecasts were really unbiased forecasts as well. This was far from the case for just using historical volatilities alone. So the ability of the option market to focus on risk is very important because it gives us estimates of the risk the markets are forecasting and using crowdsourced information to forecast those risks. In my view, the evidence indicates that crowdsourced information in the option markets provides efficient estimates of future volatility.

Option market participants realize that volatility is not constant; it changes with changes in economic conditions and risk. Not only does it make economic sense to assume that risk is constant and unchanging, but also the empirical evidence supports this. Market participants incorporate their views on changes in risk into the prices that they are willing to pay and receive in options. Using data from the past assumes risk are unchanging, or that we can use a time slice of the past to forecast future risk, and research and finance who only rely on historical data want to believe that risks are measurable from the past and that the market is not as efficient as the past data in forecasting risk, but that is false.

Many entities use the prices of options to forecast the distribution of risk on various indices. For example, the Federal Reserve Bank in Minneapolis provides a tool that they use to determine market-based risk estimates from the option market. Important to them is the tails of the distribution, the extreme risk, either the positive or negative tails. From their description, they say, “The typical approach of trying to discern the true probability of events is typically inappropriate. Instead, policymakers should base their decisions on market-based probabilities.” End quote. A quote again: “A market-based probability is a weight that financial markets assign to a possible event. These weights are identifiable from asset prices available every day. As investors adjust their expectation, these prices change accordingly. As a result, they provide a framework for systematically considering paths the future may take.” And they are referring here to the information in the option markets.

As a last point, I am skeptical, however, that policymakers can use market prices to inform their decision-making. They can look at the market as they would from the sky, but they can’t interfere with the market’s view because if the market knows that they will do so by adjusting policy, market prices would take that information into account and prices would therefore not be as informative. For example, if market participants believe that current policy were more likely to increase downside risk and this was in fact reflected in the price of put protection and the policy market makers then change their policies to reduce downside risk, put protection prices would fall, causing losses to those acting to protect themselves. Market participants would take account of the policy reaction in advance and not bid up the prices of protection. So there’d be no information. It’d be a conundrum in the terms of a convolution.

Interesting that sustained bad central bank policies remain in prices, for macro risk increases the cost of protection. A corollary here is that market prices have options which have displayed different shaped distributions of forward risks at different points in time, warn us that policies undertaken by central bankers around the world create differential risks that market participants wish to hedge in the insurance market. It is inconceivable to me that in a global economy where interactions are nonlinear and complex, that central bankers that use simple models to estimate the path of the economy and risk will have much success in doing so. Too much time is spent using historical data to fit these models.

Maymin: That’s wonderful. I wonder, Myron, that argument, does it also apply to other things that the Fed looks at? For example, they look at unemployment. But companies choose who to hire based on what their forecast is of what the Fed will do.

Scholes: Correct. So, unfortunately, Federal Reserve policy, taking a U.S. central bank perspective, is based on models, macro models. And they’re not based on risk to start with. In a lot of science, a model is really a certainty model, and then an error term is thrown in the model. The Fed uses a lot of models, such as, you know, the Taylor Rule projections, or what’s the capacity of the economy, how much we’re deviating from the capacity. You know, what is the inflation estimates of the economy, and what’s the target inflation? Or what’s the relation between unemployment and inflation, and the like. And so the Phillips curve type of arguments, even though the empirical data is very weak on the Phillips curve argument. So they use these data models and they have a lot of macroeconomists forecasting using historical data.

And the errors are kind of large, you know, from these models. And so there is a view by the Minneapolis Fed that they should incorporate forward information into their thinking. The trouble is, how to incorporate forward information? Maybe it’s best for society if they use the information in the markets and destroy the value of the option markets to understand macro policy, but they won’t get any information from the market. That’s my problem, you know, in terms of, you know, it’s one thing to think about completely exogenous, observing the U.S. economy from the moon, and not doing anything. But once you get into trying to change the recipe for the pie, then you destroy the value of what other people are saying, how the recipe is going to turn out.

Maymin: From the perspective of a person who uses options information, it’s fine if they do that, right? You’re concerned that the Fed won’t be able to get exact enough information to make useful decisions. But from the perspective of an investor, if their information is incorporated to the options, that just makes the option prices better.

Scholes: Correct. That’s the reverse way of thinking about it.

Maymin: Nice. I really liked your analogy of the man with a dog. I had not heard that before applied to rational and irrational because, usually, those two camps are just separated from each other. People are either 100% rational or 100% irrational. But the idea that they can work together and they can coexist in the market to set prices is a nice way of looking at things. Is that your perspective, that they both exist?

Scholes: Yes. I don’t think behavioral economics or behavioral science could really do anything unless there was some rational person supporting them, because then everyone would be dogs. You know, and a lot of behavioral economics, which is a side topic here, is based on the idea of data mining. You know, it’s looking at behavior from the past and then building a theory of why that behavior existed. And I think people have irrational tendencies, and they don’t like to take losers, or whatever. And even then, I’d love to be able to sell at the high point or buy at the low point. But if you use option theory, we can design options which give you the maximum return over the last six months, if you want to buy an option before the six months to give you that.

So a lot of the behavioral tendencies are deduced. You can price that by using option technology, in theory, to do that, which is good to know what these behavioral tendencies would cost unless one were protected. But the interesting issue is that behavioral science is based on looking at people’s tendencies and the attributes they have, and not wanting to sell losers, and the like. So these models have errors to them, obviously. And there’s behavior that’s undertaken because of the models. And in life, if the reward is high enough to actually deduce whether our model, our thinking is correct, or what the cost is, then investors will tend to do that.

And so if, on the other hand, you have rational investors protecting them, they won’t have to do that as much. So they hire people who walk the dogs, you know, to actually take them on the walk and bring them home and they pay them for that service. Occasionally, however, the dogs pull in one direction in such an extreme that the leash breaks and then chaos ensues. So we get the shocks that occur and the man then has to go chase the dogs to try to get the dogs back on the leash and get them home again. So for a while, the man looks like the dogs. You can’t distinguish the man from the dog. But once they get him back on the leash, then it’s interesting, in economics, because some assume that the man will take the dogs back to exactly the equilibrium path they were on before the shock. That doesn’t happen. You know, the dogs are reconstrued back onto the leashes or what are new leashes. And then the man walks the dogs back on a new path. So the economy doesn’t return to the old path, it sets off on a new path with all the learning of why the leash broke and why the dogs are running free. So in science, it’s really the man and the dogs. Are you a man? Are you the dog? And basically, the rational person makes money by looking at the constraints of the dogs wanting to go to the flowers or off in this direction and gets paid to walk them back home.

Maymin: Very cool. Now, let’s go to the stock versus options market efficiency. One way of phrasing your argument is that whatever the efficiency level of the stock market is, the options market are probably even more efficient. Is that roughly fair?

Scholes: But we can judge what it’s doing, yes.

Maymin: Fair enough.

Scholes: Yes.

Maymin: What are some of the reasons that might come into that? Now we’ve talked, you know, the podcast is On Time. Is it fair to say that stocks… One of the dimensions is they have a time built in, right? They have a maturity. But you buy a stock, you don’t know if you win or lose. What does it mean? Over a year, over 10 years, over 100 years?

Scholes: Correct.

Maymin: But an option, there’s a clear payout, right?

Scholes: Correct. I mean, we know we can evaluate whether it’s easy to make money if you try to trade in options of various maturities, of various exercise prices, of various combinations of options. And it’s very hard to make money in the options markets. A lot of people spend time doing that, which is great. And that’s number one. And also, I talked… which is very difficult to do, make money trading in options. And in addition to that, since they have finite time, the reward or the skill level is determined very quickly, whether it’s six months or a year. In longer dated options, it’s more difficult, obviously, because you need many more replications to do that. And then, as my argument about Darwinian survival of the fittest, you know, there’s a buyer and seller of every option, and especially the ones in the tails of distribution, which I’m interested in because they give us how risks are changing over time. The option market maker, to survive, has to be pretty damn smart and know exactly what’s going on. As Warren Buffett once said, “When the tide goes out, who’s wearing bathing suits?” It’s the same thing here. You know, basically, if people are not wearing bathing suits, they’re going to go broke. And they’re going to lose a lot of money. So the smart money is always trying to figure out when to buy more protection, and the seller protection might be asymmetric, and the market maker, to survive, has to do that. That’s unlike the stock market, where you have more of a tendency to have matching of buyers and sellers than an intermediary coming in to make the market in the option market.

Maymin: Interesting. And the options market maker also has… It’s not just an arbitrary lottery ticket, right? They tether it ultimately, as you famously showed, to the underlying, right? They can replicate it to some extent with some error, whereas the stock is not really tethered to anything.

Scholes: Correct. The stock, as I said in my introduction, is based on… The value of a stock is very difficult. Because if I tell you the stock price today, it’s very hard for you to deduce much information from the stock price. I mean, you can say, okay, it’s based on earnings, it’s based on the growth prospects, it’s based on capital structure changes, it’s based on competition, which are the cash flows, and competition. It’s based on changes in discount rates or risk preferences because we’re taking a future cash flow series which, as you said, might be infinite, and try to bring that back to the present. So we have ad hoc models that do that, but they never… They came from a certainty world. You know, in a certain world, if you have cash flows, you know exactly what’s going to happen, then you can discount them back to the present. So we threw an uncertainty term on that and we try to estimate these cash flows. But you have a numerator and a denominator to estimate, you know.

Well, in some sense estimating of risk by market participants through the option market prices, which reveal risk – because that’s what an option market does, there’s no assumption about cash flows there; it’s derived from the price of the underlying asset – give you better estimates of what the insurance risks are because there’s an insurance market that you can ever get from the stock market. So you need an underlying model, as Fama said, to know what the equilibrium model is.

So for example, in recent times, we’ve had growth stocks have done worse, much worse, than value stocks. And the argument was that the duration or the risk duration was an important factor of how you valued a growth stock, because the future needed time for the growth to come to fruition. So as interest rates have increased or real rates have increased, both real rate and nominal rates have increased, that future duration, or the future value of the growth, was less, so they fell in value. But you know, that is a model that could be correct or incorrect. But you know, again, it is not necessarily the fact that that is true.

So to value a stock is much more difficult than to value an option. And the reason I said that people think the option market is not as efficient is because they’re looking for normal distributions, you know, and understanding that the normal distribution was a way in which you could price options. That was in the Black-Scholes model, it wasn’t necessarily in our technology, and others have used the Black-Scholes model – we’ll talk about that in a future podcast – to figure out how to generate the future distribution of risks.

And from that, it’s very hard to make money even if you observe this distribution. That’s why I can say there’s two ways to think about the option market. One is a way to make money by trading in options, or another is to steal the information from the option market, the signals the option market is telling you about future risk and how risks are changing over time. And that’s an important distinction.

Maymin: In fact the second one, you don’t really… It doesn’t really matter how efficient they are. Efficiency, like you said, it could be inefficient or it could be the wrong model of market equilibrium. But how much information you can put, and steal from that market, it doesn’t matter whether it’s efficient or not at the end of the day. Is that true?

Scholes: I would like it to be efficient because I would like it to be the best unbiased estimator. Because that would give me more confidence in using the option market to figure out what the distribution of risks are, and then to go from the idea of a static, one-period model or thinking about finance, to more of a dynamic model or how to think about how compound returns will be affected by using the option market prices.

Maymin: Thanks, Myron, and thanks to our listeners for joining in. If you’d like to listen to any other episodes in this series or explore our other podcasts, you can subscribe on Spotify, or Apple podcasts, or wherever you listen to podcasts. Also, check out the Insights page on for additional timely content from our investment experts.

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.


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Philip Maymin, PhD

Philip Maymin, PhD

Director of Asset Allocation Strategies

Myron Scholes, PhD

Myron Scholes, PhD

Chief Investment Strategist

5 Dec 2022
38 minute listen

Key takeaways:

  • Rational and behavioral investors need each other to make markets more efficient.
  • Option prices contain rich information, including forecasting an entire distribution of risks, and changing over time.
  • The forward-looking options-implied information subsumes other backward-looking measures of risk and makes better forecasts.