(Bernstein 2005)

Summary and Comments

Markowitz calculates the value of diversification. Tobin shows that an investor can get all good combinations of risk and reward by combining a risk-free asset such as a T-bill with a portfolio of risky assets – and that there must be one and only one preferred efficient portfolio. Sharpe shows that this portfolio is just the whole market. And so: the passive index fund that doesn’t try to pick stocks but instead invests in the whole market basket – and as of 2024, it is the discipline of more than half of all mutual fund assets[1].

Bernstein starts with the clubby investing world before 1950 – one in which he himself was a professional investment advisor – and works through these and the other major ideas developed in the second half of the 20^th century that put finance on a mathematical and statistical foundation. All in a very approachable, non-mathematical exposition laden with context and biography of the founders themselves.

Quotes of Interest

Rhea on Stock Picking (Technical Analysis)

An example of an early market technical analysis investor was Robert Rhea, who took Hamilton’s “Dow Theory”, developed and popularized by William Peter Hamilton (editor of the Wall St. Journal starting in 1903) and structured it – and offered this via a popular newsletter Dow Theory Comment started in 1932. Hamilton had said a central idea of Dow Theory – that prices on the NYSE reveal everything worth knowing about business conditions (a key to the Technical Analysts’ focus on prices rather than value) (p. 29). Bernstein quotes Rhea as saying:

Those who try to profit from the advance and decline of security prices are perplexed 90% of the time. And it seems the perplexity increases with experience… Unvarying cocksureness on the part of traders or investors is a badge of incompetence. There is, nevertheless, a time and a place for certainty where the market is concerned, but such times and places are few and far between (p. 30).

Hamilton’s Success

William Peter Hamilton wrote many editorials in the Wall Street Journal offering financial advice. Alfred Cowles examined the impact of that advice (Cowles 1933). Bernstein notes:

William Peter Hamilton called the peak of the bull market in 1929, but apparently was lucky to do so. True, the portfolio of an investor who had followed Hamilton’s timing recommendations would have done all right in absolute terms: Cowles calculated that the portfolio would have grown nineteen-fold during the years from 1903 to 1929 when Hamilton was making his recommendations, a return that lead Robert Rhea to remark, “I for one would not complain at such a gain.” But an investor who had simply bought the market in 1903 and held on for twenty-six years would have ended up twice as wealthy as an investor who had followed Hamilton’s advice. Hamilton made twenty-nine bullish forecasts, of which sixteen turned out profitable, and twenty-three bearish forecast, of which ten were profitable. These results are about what one could do calling heads or tails on the toss of a coin. (p. 34)

But, Goetzman (Brown, Goetzmann, and Kumar 1998) takes exception, claiming that Hamilton’s advice was in fact positive when adjusted for risk – “…Hamilton’s forecasts were based on a momentum strategy…during the first three decades of the [20^th] century, it appeared to work.”

Markowitz’ Portfolio Selection article

Bernstein provides a pithy summary of the article:

Despite its formidable appearance, the true meaning of Markowitz’s article is also homey. It boils down to nothing more than a formal confirmation of two old rules for investing: Nothing ventured, nothing gained. Don’t put all your eggs in one basket. (p. 44)

He later elaborates

Markowitz for example threatens the private preserve of portfolio managers by stressing the dominance of the portfolio over its individual components. That means hat managers should not blithely stuff portfolios with their favorite picks, ignore the overwhelming importance of the diversification. In fact, the diversification Markowitz calls for often requires managers to hold stocks they do not like in order to balance out the ones they do like. (p 234)

And imperfections notwithstanding, Markowitz sums up the market he seeked to optimize:

Granted that the invisible hand is clumsy, heartless, and unfair, it is ever so much more deft and impartial than a central planning committee. (p. 306)

John Burr Williams on Cash Flow Analysis without Diversification

Bernstein notes that John Burr Williams wrote a 1937 book The Theory of Investment Value that predates the discounted cash flow model:

Williams’ model for valuing a security calls for the investor to make a long-run projection of a company’s future dividend payments and then to test that projection against his own confidence in its accuracy. Forecasting future dividends for a public utility, for example, is easier than forecasting dividends for General Motors, and forecasting the long-run outlook for General Motors is easier than forecasting the outlook for a start-up company in a highly competitive business. Williams then shows how to combine the long-run projection of dividends with the expected degree of accuracy of that forecast to estimate the intrinsic value of the stock. Williams called the model the Dividend Discount Model. (p. 47)

But he didn’t explicitly consider diversification:

Williams seemed to be recommending that the investor should buy the one stock that has the highest expected return – and shun all the rest. (p. 47)

And another popular business book of the time deliberately downplayed diversification (Gerald Loeb’s The Battle for Investment Survival, first published in 1935 with a last edition in 1965). What Loeb said was:

“Once you obtain confidence, diversification is undesirable….Diversification [is] an admission of not knowing what to do and an effort to strike an average.” (p. 49)

And Bernstien also credits antipathy towards diversification to Keynes who among other things said “To carry one’s eggs in a great number of baskets, without having time or opportunity to discover how many have holes in the bottom, is the surest way of increasing risk and loss.”

Of course, Markowitz contribution was to quantify and justify diversification. The tension between Markowitz and Keynes really is the usual core tension of the efficient market hypothesis – Keynes emphasizes only investing where one has privileged insight (that is, the arbitrageur’s role in earning profit from information) and Markowitz emphasizes what is true if one doesn’t believe one has privileged information (the arbitrageurs have already done their work; what do you do now?).

Paul Samuelson on Stock Pickers

Samuelson takes a dim view of most portfolio managers. He has only scorn for those who claim that their skill in selecting stocks enables them to outperform investors who simply buy and hold a well-diversified portfolio of equities. In the first issue of the Journal of Portfolio Management in the fall of 1974, he minced no words:

They also serve who only sit and hold; but I suppose the fees to be earnes by such sensible and prosaic behavior are less than from essaying to give it that old post-college try…

But a respect for evidence compels me to incline toward the hypothesis that most portfolio decision makers should go out of business – take up plumbing, teach Greek, or help produce the annual GNP by serving as corporate executives. Even if this advice to drop dead is good advice, it obviously is not counsel that well be eagerly followed. Few people will commit suicide without a push.

(p. 113)

Or has he put it to me in an interview, “When the broker calls to say ‘Hurry, hurry, hurry!’ that’s nonsense. If the stock were sure to go up, it would already be up.” (p. 120)

But can there be investors who truly are expert – who can consistently outperform the market? First, we have to deal with survivorship bias.

Consider this set of coin-tossing possibilities, proposed by Warren Buffer. Suppose 225 million Americans all join a coin-tossing contest in which each player bets a dollar each day on whether the toss of a coin will turn up heads or tails. Each day, the losers turn their dollars over to the winners, who then stake their winnings ont eh next day’s toss. The laws of chance tell us that, after ten flips on ten mornings, only 220,000 people will still be in the contest, and each will have won a little over $1,000. After that, the game heats up. Ten days later, only 215 people will still be playing, but each of them will be worth over $1,050,000.

Buffet suggests that this small group of winners will marvel at their own skills. Some of them will write books on “How I Turned a Dollar into a Million in Twenty Days Working Thirty Seconds a Morning.” Or they will tackle skeptical professors of finance with “If it can’t be done, why are there 215 of us?” But, Buffet goes on to point out “…then some business school professor will probably be rude enough to bring up the fact that if 215 million orangutans had engaged in a similar exercise, the results would be much the same – 215 egotistical orangutans with 20 straight winning flips.”

But what about the Buffets, Baruchs, Grahams, Neffs, and Lynches? Are they in the same class as the Orangutans? Paul Samuelson admits that such market geniuses must exist, even in a totally efficient market. “It is not ordered in heaven, or by the second law of thermodynamics, that a small group of intelligent and informed investors cannot systematically achieve higher mean portfolio gains with lower average variabilities. People differ in their heights, pulchritude, and acidity. Why not in their P.Q. or performance quotient?

But

…the few with an extraordinary P. Q. are unlikely to rent our their talents “to the Ford Foundation or to the local bank trust department. They have too high an I.Q. for that” They are more likely to invest their own money and keep their systems to themselves. Otherwise, others would copy them and spoil their advantage by making the market more efficient. (p. 143)

On the Role of Information

But skepticism about market expertise doesn’t mean you can ignore information…

Jack Traynor, long-time editor of the Financial Analysts Journal, once said that you may not get rich by using all the available information, but you surely will get poor if you don’t. (p. 120)

And Bernstein elaborates:

When information dries up and gives way to uncertainty, the markets go dead. But just a drop a hint about a company that some conglomerate is eyeing, or about the weather in Peru, or the mindset of Japan’s new finance minister, and volume will pick up and markets will move. Like a pebble dropped in a still pond, a scrap of information will send ripples in every direction.

Although new information is what triggers a change in prices, it arrives with no predictable pattern. One day the papers are bulging with it. Another day there seems to be nothing happening to report. Some information is world-shattering. Some is trifling. No wonder properly anticipated prices fluctuate randomly. (p. 120)

There is evidence that information is being incorporated faster and faster:

In a range of zero to one, the correlation between a stock’s change in price at one moment and its change over the next fifteen minutes was 0.4 in 1983; today [2005] it is essentially zero. Similar measures of daily and weekly correlations over the past twenty years have also fallen. If the walk is more random than ever, information must be moving faster, prices must be holding closer to intrinsic values, an outguessing the market must be growing increasingly difficult. (p. 304)

On Whether It’s a Zero Sum Gain

Under these conditions, what can an investor expect to earn by buying an asset? The answer, to repeat the conclusion reached by Bachelier and Osborne, is – zero! Or as Samuelson puts it, “No easy pickings, no sure-thing gains.”

This is something of an oversimplification. Samuelson recognizes that people will not invest without hope of a least some minimal return on their investment – higher on risky securities, lower on safer ones. It has to be a positive-sum game to some extent, or else no one would play. The issue is not whether a positive sum exists, but whether we can predict who is going to end up possessing it. Samuleson maintains that is ultimate ownership is a random outcome. (p. 121)

On Whether an Efficient Market Eliminates Bubbles

This is something of a contradiction; it would seem that efficiency precludes a bubble, but they do seem to exist anyhow. Samuelson narrows them to aggregate effects:

If investors were for some reason to put to high a value on Bristol Myers or IBM, Samuelson is convinced that the aberration would be extremely short-lived, because the professional analysts would sharpen their pencils and call it to the attention of their clients. Bit if all the 500 stocks in the Standard and Poor’s Composite were to soar because investors became euphorically optimistic about the future, Samuelson believes that they would lose their shirts arguing with the tape. The Bachelier-type forces that make individual prices so difficult to predict do not necessarily operate on aggregate equity values. The history of markets demonstrates that those kind of bubbles – bloated and burst – are all too common. (p. 123)

Although this does seem to mirror the difference between individual (diversifiable) and systemic (non-diversifiable) risk in a portfolio, it doesn’t seem all that logical. If all the components of the market are correctly priced, how can the market as a whole not be correctly priced? It also gives some succor to technical analysis as an investing strategy, as long as it is applied at the aggregate level, although sizing and timing of bubbles is notoriously difficult.

On the Role and Value of Noise Trading

Black contrasts noise with information. Noise arises as people buy and sell on what they believe is information but is really rumor, badly analyzed information, misinformation, or hunch. Confused by the noise, investors respond to their brokers’ urgings to “Hurry, hurry!” Black suggests that many people trade on noise simply because they enjoy fooling around and trading on hunches. Others are not even aware that they are trading on noise – they believe that they are trading on reliable information.

“Noise is what makes our observations imperfect,” Black points out. Noise gets in the way of keeping observed prices in line with shadow prices or intrinsic values. Research leads to reliable and relevant conclusions only rarely, “because of the noise that creeps in at every step.” Even people who have accurate information are uncertain about whether they are trading on information or noise. The whizzes themselves seldom pass on recommendations to their clients without including qualifications and escape clauses.

This state of affairs has two important consequences, one bad and one good.

First, nose obstructs rational decision-making. “Because there is so much noise in the world, people adopt rules of thumb. They share their rules of thumb with each other, and very few people have enough experience with interpreting noisy evidence to see that the rules are too simple.” …

The good news is that noise trading is the primary motivation for market activity. When traders act on noise, they push prices away from intrinsic values. And when this happens, people with reliable information have an advantage. It may even pay them to spend money, time and effort, to seek good information to guide them. Noise trading makes the market lively and liquid. People who need cash can raise it readily and those with cash to invest can put it to work promptly. (p. 125)

The idea that noise trading creates liquidity is quite interesting, as liquidity, or more importantly lack of liquidity, seems to play a big role in market collapse (fat tail events).

Bernstein elaborates in the context of Modigliani and Miller..

In the Modigliani and Miller model, conscientious investors make judgments about the riskiness of each corporation and then meticulously apply John Burr Williams’s rules to the expectations of the corporation’s future earnings stream. Most players are not so painstaking, but the essential principle is valid. Noise traders who take their tips from stories told at cocktail parties, chase only what is hot, and dump their stocks in a panic lose out in the long run, no matter how smart they seem in the short run. They end up selling too cheaply to better-informed, more patient investors, or else they pay too dearly for stocks that more systematic investors are kind enough to sell them. (p. 181)

But addresses equilibrium and deviations from equilibrium (and the role of noise traders):

Thus, Modigliani and Miller put investors back in the catbird seat, with corporate managers at their mercy. Through arbitrage, profit-seeking investors can eliminate discrepancies in the perceived risk/return trade-offs of one security relative to another to the point where no one has any incentive to buy or sell. Trades take place only when investors disagree about the future of a company or when new information surfaces. Modigliani and Miller’s market is a market in equilibrium.

And yet equilibrium is only a rough approximation of reality, because information pours into the marketplace constantly, in every shape and form. Most investors are restless, and even those who are more relaxed are beset by brokers hurrying to tell them what stocks are hot. Fischer Black suggests that most investors are noise traders at least part of the time, whether they think so or not. Nevertheless, persistent forces are constantly driving the market towards MM equilibrium. That is what the massive evidence in support of market efficiency is telling us. (p. 182)

On Backtesting

Eugene Fama had a job earning extra money at college trying to find buy and sell signals for a stock market letter.

Although Fama’s efforts to develop profitable trading rules were by no means unsuccessful, the ones he found worked only on the old data, not on the new. He did not realize it at the time, but his frustrating experience was shared by many highly motivated investors seeking ways to beat the market. All too often, backtests give every promise of success but prove disappointing when investors try to apply them in real time. The environment shifts, market responses slow down or speed up, or too many people follow the same strategy and end up competing away one another’s potential profits. (p. 127)

The last phenomenon is known as “a crowded trade.”

Fama and Mandelbrot on Chaos and Fat Tails

Cootner’s book also contained a short article by Fama (Fama 1963), reprinted from the Journal of Business for October 1963, in which Fama expanded on an analysis of market behavior conducted by Benoit Mandelbrot, a French mathematician living in the Unite States whose work was published in the same issue of the Journal. Mandelbrot proposed that stock prices fluctuate so irregularly because they are not sufficiently well behaved to submit to the kind of rigorous statistical analysis recommended by Bachelier and Samuelson.

Mandelbrot’s research implied that stocks are riskier than had been assumed, that diversification might not work as well as Markowitz had indicated, that measures like variance could be highly unstable, and that major price movements would cluster more closely than anticipated. Mandelbrot’s view of the stock market was the genesis of what is know today as Chaos Theory, of which Mandelbrot himself is an articulate proponent. The events of October 1987 and less dramatic but quantitatively similar episodes lend some credence to Mandelbrot’s warnings. Despite those events, however, Mandelbrot remains on the periphery of financial theory, both because of the inconvenience to analysis of accepting his arguments and because of the natural human desire to hope fluctuations will remain within familiar bounds. (p. 132)

Modigliana and Miller and Financing the Corporation

In equilibrium, in an efficient market, and ignoring taxes, transaction costs and asymmetry in information, the value of a company depends only on its future cash flows, not the split in its capital between equity and debt.

Although the owners of a company that borrows money are in a riskier position than the owners of a debt free company, the value of the company’s bonds and stock, taken as a totality, will still depend on the company’s’ overall expected earning power and the basic risks the company facies. This is the essence of William’s law of the Conservation of Investment Value….No other outcome is possible when the market is functioning as Samuelson theorized it should as research into the efficiency of capital markets has demonstrated that it does. (p. 170)

This means that borrowing increases both the return to stockholders (the upside of leverage) but also increases their risk (the downside to leverage) exactly the same amount.

There is no “right” level of debt in terms of how potential stockholders would see the company.

This is undermined by first order effects, especially the fact that interest payments on debt are deductible for corporate income tax purposes (though note that they become taxable to the lender).

Similarly, there is no change in the value of the company based on whether it pays out a dividend.

The value of the corporation will be the same whether the corporation pays a big divided, a small dividend, or no dividend at all… The real issues, [Modigliana and Miller] argue, is how dividend payments affect the way the corporation finds the money to finance its growth, which they assume is independent of dividend policy. A company’s investments in its future competes with the demand of stockholders for dividends; attending to one will either constrain the other or force the company into the capital markets to raise funds. Stockholders like to receive cash dividends. But dividends paid today shrink the assets of the company and reduce its future earnings power. The cash must be replaced either by borrowing money or by issuing new shares of stock. Paying dividends will influence how the company finances its growth, but it will have no lasting effect on the company’s value in the marketplaces; that will still depend on its growth potential and its riskiness. (p. 177)

But again, taxes can undermine the finding, in particular where the tax rate on dividends versus deferred and potentially different tax rates on capital gains. The latter can, for example, suggest buying back shares rather than paying dividends…

Once taxes come into the picture, even borrowing money to repurchase shares can have positive consequences for corporate valuation. (p. 179)

The Dominant Portfolio

Bernstein notes:

Sharpe’s major breakthrough came in 1964, with what is known as the Capital Asset Pricing Model (CAPM). CAPM starts out from the basic idea of the single-index model that returns are related “only through common relationships with some basic underlying factor,” but it ends up a long way from there.

The model concludes with the startling but inescapable conclusion that Tobin’s super-efficient portfolio is the stock market itself. No other portfolio with equal risk can offer a higher expected return; no other portfolio with equal expected return will be less risky….If the market itself is the super-efficient portfolio, no one can beat it without taking on an unwarranted amount of risk.

Heresy. Totally inadmissible. Most investors believe that they can read the tea leaves that stock prices leave in the cup of fortune. They ask one another, over and over, “How’s the market? Hoe do you like the market?” They call their brokers, sometimes every day, even every hour. They hang on the news reports, study the stock listings in the daily papers, and faithfully watch the TV show, Wall Street Week. They act on the notion that knowing what happened today will somehow tell them what will happen tomorrow. And if they do not themselves know what is going to happen, there must be somebody, somewhere, who does know and will share that information with them, or will sell it to them. (p. 87)

Tobin’s separation theory says that all investors choose the same “super-efficient” portfolio and then mix it with owning a risk free asset or borrowing at the same rate to satisfy their particular appetite for risk and reward.

As the expression “Separation Theorem” has not yet been introduced to describe Tobin’s concept, Treynor used the term “dominance” for the one combination of risky assets that is dominant, because, quoting Tobin, “it gives the investor the highest possible expectation of return available to him at that level or risk.” Optimal portfolios will always include that dominant combination of risky assets, and “an investor’s attitude toward risk will be reflected in the faction of the portfolio held in cash, rather than in the …composition of the non-cash [risky] assets.” (p. 186)

Later

The implications of the [Capital Asset Pricing] model’s links to efficient market theory are especially important. At an equilibrium such as Sharpe describes, all stocks are appropriately priced. Each promises a reward in accordance with its riskiness; no stock is relatively more attractive than any other. This means that a rational investor will want to own all stocks; anything less would be less than optimal. Thus, the market as a whole – or the market portfolio as it has come to be known – is Tobin’s super-efficient portfolio that dominates all others, and the super-efficient portfolio of Sharpe’s single-index model as well. (p. 192)

The Single Index Model and Portfolio Risk

The single index model is a simple linear asset pricing model that assumes the asset value is partially predicted by the movement of some index or factor – typically “the market as a whole.” Regression determines how much the asset’s return is predicted by this factor (beta), how much seems to be consistently independent of this factor (alpha), and how much seems to be random variation.

The efficient market hypothesis implies that alpha will be arbitraged to zero. The assumptions lead to a powerful conclusion:

Sharpe takes off from the propositions that underlie both Markowitz’s position and the Single Index Model: the results of the securities are related “only through common relationships with some basic underlying factor.” In diversified portfolios, the riskiness of any single asset is submerged by the behavior of the portfolio as a whole. This insight leads Sharpe to the same conclusion that Treynor and Markowitz had reached: The only thing investors should worry about is how much any asset contributes to the risk of the portfolio as a whole. (p. 188)

The riskiness of the portfolio as a whole is systematic risk and cannot be diversified away.

We can – as usual – attempt to reconcile the contradiction in the efficient market hypothesis:

Betting against the market is not doomed to be a losing proposition, but an investor’s appetite for unsystematic risk should reflect the quality of the information that leads to that decision. (p. 190)

Limitations to Modern Portfolio Theory

Homo economicus and information transparency are necessary:

Luckett told Sharpe that his assumption that all investors made the same predictions was so “preposterous” as to make his conclusions “uninteresting.” Yet that assumption is the logical consequence of a market in which information is freely available to all and in which all investors are rational risk-averse diversifiers. Treynor recently remarked “Assuming, as Sharpe and I did, that all investors had the same expectations was merely an analytical convenience, like Newton assuming away air resistance in theorizing about falling bodies. One tackles the world’s complexities one at a time.” (p. 195)

And

Despite the undeniable importance of the Treynor-Sharpe-Lintner-Mossin Capital Asset Pricing Model, I do not mean to suggest that it opened up the surest route map to the road to riches. Investors are not always rational beings. Taxes and transaction costs often prevent them from trading freely enough to price all assets precisely as they should be priced. Information is not always freely available, nor does everyone understand it in the same way and act on it as soon as it appears.

That is not all. In a world where the future purchasing power of money is uncertain, how does one determine a risk-free rate of interest? Is the capital market the only “basic underlying factor” that influences the value of the assets traded there? What about inflation and the distribution of wealth, to name just two possible factors that might come into play as well? And how do we defined and measure “The market” when capital assets exist all over the world and included everything from cash, stocks, bonds, and real estate to art, gold, venture capital, and even intellectual capital lie education and acquired skills?

Time plays a critical role in all aspects of investing, yet CAP, as originally conceived, described how investors ant only at a given moment rather than over continuous time. (p. 200)

This later was addressed to some extent by applying stochastic differential equations and Ito’s Lemma.

Empirical tests have found many flaws. Improvements to address them include Merton’s intertemporal model to get past a single time period, muti-factor models to include driving forces other than the market alone such as Arbitrage Pricing Theory, and better statistical methods for estimating beta.

Black-Scholes

The derivation of the classic options pricing formula relies on the assumption of the Capital Asset Pricing model (that price increases with riskiness):

With differences in risk cancelling out differences in expected gain for all securities, Black and Scholes concluded that the expected gain on a stock option or warrant is irrelevant in calculating what the current price of an option or warrant should be.   This insight allowed them to solve the option equation and derive their formula for setting a value on the option. But they arrived at this original derivation by building their structure on the foundations of the Capital Asset Pricing Model. (p. 213)

…

How can two securities, each of which is risky in its own right, be combined to mimic the behavior or an asset that has no risk at all?   Suppose an investor buys a stock and at the same moment buys a put….[Merton] pointed out that investors will seek out combinations of stocks and options in which the good news will outweigh the bad. If the prices of the stock and the put option are out of line with each other, the stock might rise in price by more than the value of the put falls.   The news, in other words, would be net good, with more gained from the rising stock price than lost from the shrinking value of the put.   Such strokes of luck are to be taken advantage of…. As arbitrageurs rush to take advantage of such an opportunity by buying the stock and selling the put, the stock will become more expensive while the put gets cheaper.   The free lunch will disappear and the symmetry between the two assets will return as they move back into proper alignment.

If the gain on one side of the combination is precisely offset by a loss on the other, the investor will be holding a riskless position that is the equivalent of holding a Treasury bill or some other liquid asset with a certain return knowing in advance. If the combination of stock and option offered more than this risk-free rate, investors would compete for the opportunity to win and would bid the opportunity away. If it offered less, investors would shun it and its value would fall to a point where it once again offered the riskless rate of return.   (p. 218)

The only remaining step is to solve for the option price.

Applying options pricing analysis to value corporate liabilities is called Contingent Claims Analysis.

Note that the Black Scholes continuous time pricing analysis can be made more general in a discrete time approximation, the Binomial options pricing model (or Cox-Ross-Rubenstein model).

Portfolio Insurance

The idea is to limit downside loss on a portfolio.

Leland decided that the put option was just the instrument he was looking for. The trick was to make it serve as protection for the whole portfolio of stocks, not just one stock. But in 1976 there was no organized market for put options on individual stocks, much less for options on a whole portfolio. Leland then recalled that Black and Scholes had created the equivalent of a risk-free asset by combining shares of a stock with an option. If you could combine stock and an option to create something that performed like cash, why not combine cash and stock to create something that would perform like an option? …

Portfolio insurance and a conventional put option would be identical twins. The owner of a portfolio would set some minimum value, or “floor”, below which the portfolio would not be allowed to go – the equivalent of the selling prices specified in a put option contract. The idea would be for the owner to sell stocks and invest in cash as the market fell and to switch from cash to stocks as the market rose…The program would be set so that the portfolio would consist of virtually 100 percent cash and zero stocks at the precise moment when the portfolio reached the specified floor value.

The difference between the value of the portfolio at the outset and the floor value would be the “deductible” for the insurance policy…The “premium” would be what the investor would sacrifice if the portfolio was less than 100 percent in stocks when the market started to go up.

But the process of moving back and forth between the portfolio and cash was complicated (especially if it involved multiple brokers) and laden with transaction costs. Hence “The opening up of the market for futures in the major stock indexes in 1983 was a godsend.” (P. 282)

Now the purveyors of portfolio insurance could change the mix of the overall portfolio without ever disturbing the clients’ managers. As the market declined, portfolio insurance called for the investor to sell futures; as the market rose, the investor would repurchase the futures. (p. 283)

But things didn’t work out quite as hoped.

Leland and Rubenstein were also concerned about what would happen if stock prices fell far enough to trigger selling from $50 billion to $60 billion of insured portfolios that would hit the market all at once. An act of faith in the efficiency of the capital markets eased LORs’s worries about this dire possibility. Although some skeptics continued to raise the question, the purveyors of insurance, and the big brokerage firms that enjoyed their busy trading activities, asserted confidently and repeatedly that other investors would be delighted to absorb these liquidations at only a minimal discount from the current prices. After all, the insured sellers would be offering stocks for sale, not because they had some kind of negative information, but simply because they wanted to protect their portfolios from further loss. Experience up to that point had demonstrated that the market stood ready to accommodate such “informationless” sellers at much better prices than sellers who were suspected of “knowing something.” The rationalizations about the ability of the market to absorb the concentrated and heavy selling persisted right up to the day of reckoning that arrived on October 19, 1987. (p. 283)

Bernstein argues that portfolio insurance actually increased volatility and the “bubble” in stocks heading up to 1987 because, without it, more investors would have sold to lock in profits, dampening the peak of the bubble. But when the 1987 crash happened, the synthetic nature of portfolio insurance became problematic:

At this point, the difference between portfolio insurance – a synthetic put option – and the real thing turned out to be fateful. A conventional put option commits the seller of the put to buy the underlying shares at a specified price; the contract to do so is secured by cash collateral. The arrangements at to price and purchase are set in advance and are secured by an agreement enforceable in a court of law. …[but in 1987] The investors without portfolio insurance flatly refused to play the part of the seller of the put. They had madne no advanced commitment whatsoever to oblige the investors by taking stock off their hands at the current price, and they had no intention of putting up the cash to do so….Market liquidity evaporated. (p. 285)

And in the crash, fear captured even the professionals

The arbitrageurs who would normally have supported the futures market by buying the futures when they were at such a large discount from the stock market failed to make their usual appearance. Some of them had run out of money during the decline of the preceding week. Those who stayed in the game on Monday found that they could buy the futures all right, but they were unable to execute to offsetting sales on the stock market at prices anywhere near what they expected to receive. Like everyone else, they were just plain scared. So, the prices kept dropping on the futures market, pulling stock prices down with them, and adding to the fright suffered by everyone. (p. 288)

The results were damning:

Even the most enthusiastic proponent of portfolio insurance cannot deny its disappointing performance during this critical test of its capabilities. The problem was not in a failure to keep portfolios above the promised minimum value – the minimum values were seldom penetrated by more than 1 percent or 2 percent. The problem was the unexpected failure of market liquidity, which made the effective premium much more expensive than has been anticipated: under more normal conditions, the necessary selling would have been executed at significantly higher prices. (p. 290)

Bibliography

Bernstein, Peter L. 2005. Capital Ideas: The Improbable Origins of Modern Wall Street. New York: John Wiley & Sons.

Brown, Stephen J., William N. Goetzmann, and Alok Kumar. 1998. “The Dow Theory: William Peter Hamilton’s Track Record Reconsidered.” The Journal of Finance 53 (4): 1311–33. https://doi.org/10.1111/0022-1082.00054.

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[1] According to Avantis Investors (quoting Morningstar 5/31/24 but also see Morningstar 2/13/24), the fraction of assets in passive vs. actively managed mutual funds has changed from 6% vs. 94% in August 1996 to 59% vs 41% in May 2024. They also report that they hold 18% of all U.S. stocks as of the end of 2023.

Notes on Capital Ideas – The Improbable Origins of Modern Wall Street