Category: General Finance

Celebrating Black-Scholes-Merton

Two Nobel Prize winners look back, and forward, as they reflect on their famous model

Professor Robert Merton, in the classroom, 1980

“There are very few academic papers that you have a 40th anniversary for,” said MIT Sloan finance professor Stewart Myers. And yet, in honor of the anniversary of the Black-Scholes-Merton options pricing model, MIT Sloan did just that, with a two-day symposium celebrating the famous model and its widespread adoption and influence.

Capping off a day of talks featuring finance professors including Deborah Lucas and Stephen Ross as well as alumna Judy Lewent, SM ’72, was a fireside chat between Robert Merton and Myron Scholes, moderated by Myers. The group spoke to MIT Sloan students, alumni, and fellow faculty in a packed house that included the daughter of the late economist Fischer Black, as well as at least one former master’s student of Merton’s.

Merton and Scholes won the Nobel Memorial Prize in Economic Sciences for their work on the model, which provides a way to value options and dynamically hedge risk. The model, which can be applied to financial products ranging from interest rate swaps to mortgages as well as to a wide array of corporate investment decisions or “real options,” is notable not only for its ability to solve a challenging problem, but also for its rapid uptake by practitioners and its many uses.

“It isn’t just that they had a formula for a particular thing, it’s that the methodology can be applied so broadly. The range of things it can be applied to is amazing,” said Myers recently.

“The Black-Scholes-Merton option pricing model is probably one of the most successful theories in all of the social sciences,” said finance professor Andrew Lo in an interview before the anniversary event. “It is an idea that has come out of academic research that has been adopted in practice. The approach they created, not just the formula but the theoretical framework they created, launched a thousand additional research papers as well as a lot of industry practices that rely on that framework.”

Entire industries, including the exchange-traded options market, the over-the-counter derivatives market, and the market for credit derivatives, evolved based on Black-Scholes-Merton. “There are multiple trillions of dollars in each of those industries, and at the heart of each of them is the analysis pioneered by Black, Scholes, and Merton,” said Lo, who added that he “uses their ideas all the time” in his own work on quantitative models in financial economics.

Lessons learned

At the event, Merton and Scholes shared good-natured ribbing and humorous anecdotes about the model’s evolution, including a story Scholes told about giving an early public presentation of the work together with Black and waiting for Merton to reveal the grand finale—only to find that Merton, who did not appear, had overslept.

The pair agreed that they could not have imagined the model’s impact when they published their work in 1973. Indeed, the now famous paper was initially rejected by multiple academic journals whose editors deemed it “too arcane.” It was only when friends at the University of Chicago—Eugene Fama and Merton Miller—pressed their contacts at the Journal of Political Economy that the model finally made it into print.

When discussing the model’s use in practice and their own early trading experience applying it, Merton and Scholes advised the audience that even the most sophisticated model is no match for a trader with inside information. “The market knows things that the models don’t,” said Merton. “One ounce of non-public information is going to clean the clock of the smartest person with the model and no information. You have to ask yourself, ‘Is there somebody who knows more?’ Use the model, use history, but also use what the market is telling you.”

Looking ahead to the next 40 years, Scholes said corporate managers could use the model as they decide how to structure their companies in an increasingly technologically advanced world. The Black-Scholes-Merton approach could help determine whether or where to manufacture goods, for example, or which products to develop or innovations to pursue and which to abandon.

Merton added that the model could also be applied to risk management in emerging markets and that it could help central bankers better understand their risks as they strive to avoid another financial crisis. Developing financial markets like China’s could also rely on the model to build a stronger, safer financial system that appropriately transfers risk.

“I think it will be expanded and extended in many different ways,” said Lo. “One hundred years from now, people will still be reading about Black-Scholes-Merton.”

Videos from the events can be found at the MIT Sloan Finance TechTV site here: http://techtv.mit.edu/collections/mitsloanfinance/videos

Understanding the Role of Financial Constraints in the M&A Market

Professor Andrey Malenko

A decision to expand by acquiring another business is one of the important decisions that a firm’s stakeholders make. Consider a mature firm, such as a big pharmaceutical company, contemplating an acquisition of a growing company, such as a small biotech firm. This decision has three aspects to it: (1) whether to initiate a bid for the target now or later; (2) how much to bid; and (3) what form should the bid take (cash, stock of the combined firm, or more exotic forms). In a recent research paper, Alexander Gorbenko from London Business School and I develop a theoretical framework to analyze how these decisions are interconnected. Within this framework, we explore a number of research questions. First, what role does bidders’ ability to pay in cash play in acquisition activity? The M&A activity has experienced a boom-and-bust pattern, and our goal is to understand whether fluctuations in financial constraints of the bidders could be linked to these dynamics. Second, what determines whether the firm gets acquired, and if it does, at what stage of its life-cycle does it occur? In particular, how are acquisitions of small targets different from acquisitions of targets that have already grown? Finally, how do deals done in cash and in stock differ?

In the perfect world with no frictions, bids in cash and in stock would be equivalent both for the bidder and for the target. If both parties agree on the monetary value of the bid in stock, there is no difference between getting paid in stock and getting an equivalent payment in cash. This is no longer true in the presence of information asymmetries between the bidder and shareholders of the target. To see why, consider the following simple numerical example. Suppose there are two bidders, A and B, who compete to acquire company X. Both bidders have assets in place worth of $100, but differ in their ability to add value to firm X. Specifically, firm X will be worth $25 if it is acquired by A, and $100 if it is acquired by B. These values are private information of each bidder.

Suppose that A and B compete by making cash bids in an open ascending-bid auction. Then, A is willing to bid up to $25 – the price at which A breaks even. Similarly, B is willing to bid up to $100. As a consequence, B wins the auction and acquires X for $25 – the price that A is no longer willing to increase. Now, instead, suppose that A and B compete by making bids in the form of stock of the combined company. In this case, A  is willing to offer up to 20% of the combined entity – this is the offer at which shareholders of A are indifferent between owning the remaining 80%  of the combined firm worth $125 and owning 100%  of the stand-alone firm A worth $100. By a similar logic, B is willing to offer up to 50% of the combined entity. As a result, B acquires the target and pays the maximum bid of A, which is 20% of the combined entity. The value of this bid is $40 (20% of $200), which is 60% higher than $25 that B would pay if it bid in cash.

By this reasoning, the ability of bidders to pay cash helps bidders to pay less and hence capture more value from acquisitions. Does it imply that more cash-constrained bidders make fewer acquisitions? It turns out that not necessarily. In particular, the answer depends on whether the bidder is expected to stay cash-constrained for a sufficiently long time, and how high its synergies with targets are. To see why, consider, first, a transitory negative shock to cash constraints: Suddenly, a bidder is no longer able to pay its bids in cash, but it is expected to become less constrained in the near future. In this case, it clearly benefits from postponing bidding for the target until financial conditions get better. Thus, a short-term tightening of cash constraints indeed reduces acquisition activity.

Instead, consider now a permanent shock to cash constraints: Suddenly, a bidder is no longer able to pay its bids in cash, and it is expected to stay constrained until, perhaps, distant future. Or, equivalently, consider a bidder that is constrained because of the nature of its ownership, for example, if it is a private company. In this case, postponing bidding can be less beneficial for the constrained bidder than for the unconstrained bidder. Intuitively, by acquiring the target while it is still small, the bidder can capture a higher fraction of surplus generated in the takeover. This is because by how much bidding in stock is more expensive than bidding is cash depends on how large the target is. If the target is small, there is little difference between cash and stock bids. This is not the case if the target is large, when stock bids can be considerably costlier than cash bids. In the example above, if the target were twice bigger, the winning cash bid would be $50, but the value of the winning stock bid would be $100.[1]

Thus, when deciding whether to bid for a target a constrained bidder faces the following trade-off. On one hand, bidding in stock generates less value than if the bidder were unconstrained. This factor discourages the bidder from bidding. On the other hand, there is a benefit to acquiring the target preemptively, while it is still small, which encourages the bidder to bid. We show that the latter effect dominates if the target grows very quickly and if synergies that a bidder realizes from acquiring the target are large enough. If one of these two conditions does not hold, the former effect dominates, and permanent cash constraints discourage acquisitions.

Our analysis implies that “mega-mergers” are rarely successful for shareholders of the acquirer. This happens due to a combination of two factors. First, because such deals are so large, even the most unconstrained acquirers bid, at least partially, in stock. However, bids in stock make it hard for the acquirer to capture value in the deal if the target is large. Second, such deals tend to be low-synergy, simply because if they were high-synergy, they would have happened in the past.

The analysis also has implications for the relation between means of payments in a deal, total value created in it, and the split between the acquirer and the target. Empirically, acquisition premium in deals done in stock is on average lower than in deals done in cash. This is consistent with our theory. Intuitively, high-synergy targets are acquired early when they are still small. Because they are small, acquirers can usually afford paying cash for them. In contrast, low-synergy targets are acquired, if at all, after they grow enough, in order to outweigh the cost of doing the deal. Because such targets are large, bidding in cash is often not an option for acquirers, so such deals are often done, at least partially, in stock. Thus, cash deals tend to be high-synergy, while stock deals tend to be low-synergy, so average premium paid in cash deals is often higher than in stock deals, despite the fact that a bidder in any given deal may find it more expensive to pay in stock.

Andrey Malenko is an Assistant Professor of Finance at MIT Sloan School of Management.


[1] A offers up to 50/100+50 of the combined company. Hence, the value of B’s winning bid is 50/100 ($100+$200) = $100. Hence, the value of the winning stock bid would exceed the winning cash bid by 100% , not by 60% , as before.

Stimulus or austerity: an economist’s search for answers

New finance faculty member Jonathan Parker examines the effects of 2008 stimulus payments

Professor Jonathan Parker

In February 2008, Congress passed a $100 billion stimulus bill aimed at shoring up an an economy on the edge of freefall.

The stimulus awarded a tax rebate of up to $600 per person or $1,200 per couple in hopes that recipients would spend the money and prop up the sagging economy.

Jonathan Parker, one of MIT Sloan’s newest professors, said he believes the 2008 Economic Stimulus Act offers a promising opportunity to study a vexing question: Is household stimulus effective and good public policy?

“My research suggests that the stimulus payments did increase spending, and the extent to which they did informs us about the effects of similar policies on the economy.” Parker said. “We now have a reasonable idea about the spending responses to hitting the Fiscal Cliff or to a proposed tax change.”

“Whether the stimulus bill was good public policy, some will say ’yes,’ others will say ’no,’” he said. “That’s one of the things I’m studying.”

Parker joins MIT Sloan from Northwestern’s Kellogg School of Management, where he wrote several papers examining the impact of stimulus spending. He says at MIT he expects to continue to study stimulus spending versus austerity.

“My view is there is not a great case for either,” Parker said. “A convincing quantitative picture is still murky. A requisite for clarifying that picture is a better understanding of how firms and households behave. That’s what I’m continuously chasing.”

Parker’s path

This fall, Parker returns to MIT, where he received his doctorate in 1996. He joins an impressive roster of finance faculty at MIT Sloan, which is home to Nobel laureate Robert Merton and 2012 Time 100 honoree Andrew Lo.

“It’s a great institution with fantastic colleagues, from the grad students to the most senior faculty member,” Parker said. “It’s an exciting place to be.”

It is also a personal homecoming for Parker, who was born in Portland, Ore., but raised in the Boston suburb of Newton.

As a child, Parker couldn’t avoid being influenced by the academic life. Both parents worked at Boston University—his mother was an administrator, his father a professor of ancient Near Eastern languages and religion specializing in the ancient language Ugaritic.

While he didn’t choose economics until college, Parker’s studies began at the kitchen table.

“My mother was continuously coming up with mechanisms to make sure things were reasonably fairly divided between me and my brother,” he said. For instance, one brother sliced a piece of cake and the other brother got to pick which slice he got. “There’s something about that in economics, determining allocations in reasonable ways, understanding incentives, and thinking about how to make mechanisms that efficiently allocate resources,” said Parker.

His parents sent him to the rigorous Roxbury Latin School in the West Roxbury neighborhood of Boston. Parker went on to earn a bachelor’s in economics and mathematics from Yale University in 1988, and later a PhD in economics from MIT. The longtime headmaster at Roxbury Latin, F. Washington “Tony” Jarvis, an Episcopal priest who oversaw the school from 1974 to 2004, left a lasting impression.

“He was an inspirational figure for thinking about living for more than a house in the suburbs and the 2.5 kids and a minivan,” Parker said. “It was about doing something bigger, better, and beneficial to other people rather than measuring success in life by income.”

Work and public service

Parker studies household economics and asset pricing—the big economic questions that touch on people’s everyday lives.

After posts at the University of Michigan and the University of Wisconsin, Parker taught at Princeton University.

In 2009, while at Northwestern, Parker was tapped to join a team of economists charged with devising a way to attach values to the assets in the government’s Troubled Asset Relief Program (TARP) portfolio. It was critical to find ways to help the government pin values to assets to protect taxpayers. There were many challenges, Parker said.

“How do we value claims the government holds against AIG, Citigroup, and most of the smaller banks in the U.S.?” Parker asked. “Many of the claims on these institutions held by the U.S. government—and so taxpayers—were not traded in the marketplace, so how do you figure out their worth? Given that some may not pay the government back, and the government controls policies that influence whether they will be able to, how do you price the risk in these banks?”

Parker’s work studying the efficacy of stimulus spending started at Princeton with the tax rebates of 2001, and continued at Northwestern. There he set out in several studies to measure exactly what households did with their stimulus checks, and why, with an eye toward influencing future policy.

In 2012, Parker wrote “The Economic Stimulus Payments of 2008 and the Aggregate Demand for Consumption,” with Christian Broda of Duquesne Capital Management. The pair used consumer purchase scans to see how the tax rebates were spent.

What they learned was that after rebates arrived, households raised spending 10 percent in the first week and 4 percent in the following seven weeks, then the spending trailed away. Almost all consumer spending was by households with incomes of $35,000 or less and with two months or less of liquid assets.

Parker said it is tough to sell stimulus programs if households believe they don’t work and are costly because they add to the nation’s long-term debt.

“The $64,000 question is, ’What do we do now—with the US debt to GDP as high as it is and a perceived need to increase spending for demand?’” Parker said. “There’s a tough trade-off because household spending reflects not just cash flow, but also future concerns about who’s going to pay, and will there be a default crisis?”

His research so far doesn’t give a clear answer—stimulus or austerity. But then again, no one has the answer yet.

“Economists who get on TV and say ’I’m sure we should do more stimulus’ or claim that the only way forward is austerity, they are not getting there from the academic evidence they’ve read,” Parker said. “They’re getting there from somewhere else.”

“I’m always humbled by how little we know,” Parker said. “The world is infinitely more complex than our economic models. So we’re continuously learning. Some of the biggest questions in economics are still up for grabs.”