ÖAsk Dr. Risk! TM Columns
from 1999
Other columns: current 1999
1998 1997 1996
Dr. Risk Brings Peace in the Battle Over Decomposition (11/28/99)
Dear Dr. Risk – A couple of us work in the Risk mgmt dept. for a major bank and have been arguing about how to decompose an option P&L by sensitivities. I showed that technically the only way that this was possible was to use B-S 2nd order P.D.E., and that there are no changes in price due to vega or rho because of the B-S assumptions. Everyone including the Head trader disagreed, apparently there is another way to decompose B-S to show these sensitivities. Could this be true? – Tony 'Troubled' Tygar
Dear Tygar – Dr. Risk hopes the disputing parties have not come to blows, yet, and that the lion and the lamb might coexist in peace after his answer. You could both be right, which would mean that you must be saying two independent things.
The decomposition of P&L consists essentially of doing a Taylor series expansion of the change in P&L. In the B-S world only time and the underlying price can change, so we end up with terms involving theta, delta, and gamma. You (Tony) are working in the B-S world, where time elapses and only the underlying risk factor is price, a log normal, diffusion process. Black and Scholes showed that absence of arbitrage implied the PDE you mentioned. The volatility and interest rate don’t change, by assumption. So you’re right.
Allow volatility, the interest rate, and the dividend yield to change randomly, and you’re out of the B-S world and closer to the real world. You also need a more complicated model, strictly speaking. So, everyone else, including the head trader could be right.
While I can’t know for sure what the head trader and others are thinking, in my experience, people commonly continue the Taylor series expansion to include first-order changes in the interest rate and volatility, thus terms involving the rho and vega. As a practical matter, I gather that these terms have proven useful in quantifying the changes in risk, and in hedging. If that’s so, then they’re right, too. – Dr. Risk
Free the Quasi Monte Carlo Four! ((9/28/99)
Dear Dr. Risk – Since you run this wonderful 'zine' of yours it is probably the right platform for this question/discussion. How does the derivatives community view patents on pricing methods? What do you think Columbia (Traub/Paskov e.a.) plans to do with its new patent (#5940810, you can view it at http://www.uspto.gov) on (high-dimensional) low-discrepancy pricing methods? All of the sudden I feel this urge to file a lot of patents.... Doctor Risk, what do you recommend? – Eddy
Dear Eddy – Dr. Risk can't speak for the entire derivatives community, but after your message he asked for and received one opinion in a public setting. Dr. Risk was attending a presentation about option pricing using a Monte Carlo approach. During the Q&A period, Dr. Risk asked the speaker what he thought about Columbia University's patent on quasi Monte Carlo methods. The speaker responded he thought it was incomprehensible and meaningless. Coincidentally, one of the Columbia University researchers named in the patent was in the audience. Dr. Risk could have asked him what he thought about the speaker's remarks about the patent, but that would have been "ambush journalism", which would not be appropriate here. However, Dr. Risk invites his comment in this forum. Members of the derivatives community, what do you think about patents on pricing methods? Dr. Risk will print representative responses in the next issue.
Fairly obviously, Columbia plans to try to cash in on its faculty research. Universities are increasingly frequently staking a claim to the intellectual property that their faculty members create. It's hard to blame them. For-profit employers have long done the same thing. Their employees don't get patents for their inventions. This is not a new idea. For example, the University of Pennsylvania in the 1940s had a policy prohibiting its faculty from privately patenting the inventions that came out of research that Penn had funded. Mauchly and Eckert had created ENIAC while at Penn, doing research that the military had funded. Since Penn had not directly funded the research, the dean of the Moore School of Engineering made an exception and allowed Mauchly and Eckert to patent their invention. However, after WWII, the military required all universities seeking research contracts to have uniform patent policies. Penn asked Mauchly and Eckert to sign their patents over to the university, but they refused and left soon after the public announcement of ENIAC.
Perhaps it seems unusual, because much knowledge makes its way off campus and into the public domain. After that, anybody with an interest may use the knowledge for free. One reason for this is that the knowledge that scholars create tends to be difficult to claim. For example, fairly typically, if a scholar publishes an article, the journal gets the copyright. Also, academics tend to create knowledge with little or no market value, hence the expression, "it's academic". In many cases, the scholar must pay for the privilege of getting his ideas into print. Thus, even though the author of a book frequently gets the copyright, it doesn't really matter. The royalties are typically small. To a significant degree, the publication's cash value is largely as a signal that the scholar is worth having around, and his or her annual compensation tends to increase, as a result of more publications and publications of high quality. Black, Scholes, and Merton never got a nickel of direct royalty payment for their 1973 articles. However, their publications paid off richly in terms of career opportunities.
Dr. Risk is looking forward to Columbia's efforts to collect money from all the institutions who use quasi Monte Carlo methods in pricing derivatives. A cursory reading of patent #5940810, makes it clear that their patent is necessarily specific. It refers to applications with more than 50 dimensions, mentioning four kinds of quasi MC methods, such as Sobol numbers, etc. The patent is a blueprint for ways around the patent.
Dr. Risk's recommendation? Note well that a patentable invention must be a process, machine, composition of matter, etc., that is "useful", "novel", and "not obvious". These characteristics are largely subjective. Get yourself an experienced patent attorney to plead your case – and hope that you have an unsophisticated and impressionable government attorney on the other side of the application.
I sympathize with your desire to claim territory in intellectual space, particularly in the aftermath of this patent. I'm tempted to file a patent identical to theirs, except for 20-49 dimensions. Or maybe for applications of quasi Monte Carlo methods to "non financial business problems". Or maybe to all methods of quasi Monte Carlo methods, other than the ones they patented.
It's easy to laugh at such a claim, except when one realizes that they succeeded in receiving their patent. We'll have to wait to see if Columbia University is laughing, too – all the way to the bank! – Dr. Risk
Yes, Virginia, there is NO Santa Claus (7/28/99)
Dear Dr. Risk – Can you answer the following?
1) Does the 10 year note move at 2/3 the speed
of a 30 year bond?
2) If so, can you play this relationship creatively? So that even
if I lose money, it is not very often?
3) How do you create a spread between these two using futures or
options.
Here is how the sure thing trade is supposed to
set up:
Step 1: Sell an in the money 10 year straddle (put and call)
Step 2: Buy 1 out of the money 30 year Call 1 strike above and
Buy 1 out of the money 30 year put 1 strike below (buy the T bond
strangle)
The author of this trade "advice" says this is creative because it is not what most people would do – do the strangle and straddle on the same instrument. Rather the relationship between the ten and thirty year is a known relationship.
The authors experience was stated as follows:
For a two month period he never worried – he took no money into his account when the transactions were executed but took money in over the life of the trade. The author then said that this is what many of the large bond arbitrage firms do....or at least what they did now that we see the fate of Long Term Capital?
The trades should be initiated when you don't have to pay anything to put them on, and one would not want a net credit either. Does this happen frequently? Is there actually execution risk of buying the one trade while waiting for the other to be executed at a net credit. The author, to his credit seems to want to close this trade out every time the account is at a net credit of $500. Sounds like free money just for putting trades on.
As for risk profile, the commentary was a follows:
There is limited risk because you sell options in the middle, which are the slowest moving options (the straddle) and buying options on the outside which are the fasted moving options.....so if bonds move 50 points in one month, you cannot lose money because you are long the fast moving ones and short the slower ones.
Thanks for any insight – Virginia Madison
P.S. When you have more time can you elaborate on delta neutral trades?
Dear Virginia –
First, let's answer your questions:
- The speed at which the 10-year note price moves, relative to the peed of a 30 year bond is a random variable, depending on market conditions and coupon rates. If you wanted to assume that the forward curve moves with parallel shifts, then you could use a standard duration model to theorize about the relative speeds. Assuming a flat yield curve, then a parallel shift in the yield curve would produce bond price changes that were proportional to duration. Then, if the duration of the 10-year bond were 2/3 the duration of the 30-year bond, the price of the 10-year bond would move about 2/3 as fast as the price of the 30-year bond.
- If the market is efficient – typically, a safe assumption – then you can’t make money off the relationship between the relative speeds of the 10-year and 30-year, with any consistency.
- If you wanted to assume that the 10-year or the 30-year is rich or cheap, then you could use durations of the 10-year and 30-year to create a roughly market-neutral spread.
Second, let’s look at the "sure thing trade". If the underlying were the same for all legs of the trade – "what most people would do" – you would have what I call an "underwater butterfly", a portfolio that is equivalent to being short a T-bill and long a butterfly spread on the underlying. It's payoff function looks like a pointed witch's hat with an infinitely wide brim. It's maximum payoff – zero – is at the short straddle's strike. Since this trade has zero probability of paying off a positive amount, it's a credit trade, from which you generate immediate cash. I'm not sure what you mean by "he took no money into his account when the transactions were executed but took money in over the life of the trade". It seems to me that you take in the money, up front. You repay it at the end, and the only question is, "How much?"
When you allow the underlying bonds for the straddle and the strangle to differ, you could do this trade at closer to zero initial net cash outflow. The price volatility on the 30-year bond exceeds that of the 10-year note. Hence, the cost of the long strangle could approximate that of the short straddle.
As for the comment, "you cannot lose money", of course, you can lose money. It makes sense to think of the value of this trade having four parts:
| Intrinsic value | Time value | |
| Long 30-year strangle | A | B |
| Short 10-year straddle | C | D |
As time goes by, the time decay of the strangle works against you (B), the time decay of the straddle works for you (D), the price fluctuations of the strangle work for you (A), and the price fluctuations of the straddle work against you (C).
Clearly, in theoretical, perfect-market equilibrium, the market would take into account all possible moves and price the options to leave no free money on the table. My view of the market is a pretty good approximation of that perfect-market model. I'd like to hear the geniuses at LTCM explain where the approximation breaks down. – Dr. Risk
P.S. That’s enough for now. Delta neutral trades, later. Dr. Risk wouldn't want you to overdose on analysis.
Put-Call Disparity? (6/28/99)
Dear Dr. Risk – Recently a collegue asked me a question about the price of an option, concerning a put and a call option on a certain stock. His theory was that if an option was at the money, the prices of the put and call options have to be the same. This is because of the symmetrical distribution of the stock price returns. This sounds very plausible, but I know this is not true. Unfortunately, I could not explain why my collegue was wrong. Do you have an answer for this question?? – Rob
Dear Rob – Thanks for your question. Your apparently simple question raises a variety of issues, ranging from the simple to complex. One could write a chapter of a book in answer. I'll try to be more succinct.
While your colleague's intuition seems plausible, and a sort of symmetry is relevant, you state correctly that his answer and analysis are inaccurate. You might ask him why he thinks the distribution of stock returns is symmetrical. The historical distribution hasn't been symmetrical. The "risk neutral", implied distribution isn't symmetrical. The usual, Black-Scholes-Merton assumption is log normality, which is not symmetrical: The probability of price going below zero is zero, but the probability of going equally above zero is positive.
Okay, the Black-Scholes-Merton model assumes that the distribution of the logarithm of the spot price is symmetrical, but it isn't symmetrical around log(spot). It isn't even symmetrical around the log of the forward price. It is symmetrical around ln(forward price) - (1/2)var*tau, where tau = time to expiration.
Let's explore the Black-Scholes-Merton setting. First, consider European options. Then we have pricing equations for the values of European calls and puts, which you can look up in any good textbook. Under what conditions will the put value and call value be the same? A sufficient condition would be that the strike equals the forward price of the underlying – the options are "at-the-money (ATM) forward". Then, S exp(-dt) = K exp(-rt) and the natural log of S exp(-dt) / K exp(-rt) = 1 would be be zero. Then, -d2 = d1. Put this information into the pricing equations, and you'll see that the put and call have the same value.
Now, consider American options. Even if the put and call
options are ATM forward, their values may differ. Consider two
cases:
(1) Let the dividend yield equal zero and the interest rate
exceed zero. This doesn't change the equal valuation of puts and
calls for ATM forward European options. However, now there is no
reason for early exercise of the call, but early exercise of the
put may make sense. Thus, the value of the American put will
exceed that of the American call.
(2) If you let the dividend yield exceed zero and the interest
rate equal zero, then the American and European puts will have
the same value, but the American call will be worth more than the
European call. Hence, the American call will be worth more than
the American put.
If you set the dividend yield and the interest rate equal, the ATM forward American call and put have equal value. Try this in your favorite option calculator. Why? Because there is a sort of symmetry between the events that lead to value for the call and the put. Each event, including events leading to early exercise, that can lead to value for the call has its counterpart of equal value for the put.
These results don't rely on log normality. You may find it instructive to build a simple two-period Cox-Ross-Rubinstein binomial model in a spreadsheet. If you do, you'll see that that when the dividend yield equals the foreign rate, European call and put options have equal values. So do the corresponding American calls and puts. The "symmetry of value" is evident in this setting.
Perhaps, most instructive is to assume nothing about the risk neutral distribution, except that forward prices (F) exists. Then put-call parity tells us that for European options,
call value - put value = PV(F - K).
Thus, if F = K, then call value = put value. For more details, see the Mathematical Appendix. – Dr. Risk
Statistical Arbitrage (5/28/99)
Dear Dr. Risk – Where can I find more about the different methods of statistical arbitrage? – Dilip
Dear Dilip – The literature on trading strategies is vast, and much of this literature concerns statistical arbitrage, although not always referring to it by that name. You can find books in your bookstore, or on Amazon.com. I'll survey the topic, to give you a better idea what to look for.
Classic arbitrage consists of buying something cheap in one market and immediately selling it for more in market – without tying up capital or taking risk. The classic example of arbitrage is the currency dealer on the phone with two customers – a buyer and a seller. The dealer has learned that they are eager to trade, and at what price. So – within a few seconds, at most – he buys from the seller, then sells to the buyer at a higher price.
Clearly, this sort of trade is extremely attractive. Equally clearly, the existence of arbitrage is difficult to justify in any theory of economic equilibrium – or common sense. We could argue that the opportunities aren't truly arbitrage opportunities. A customer could change his mind in the middle of the arb, or stock index basket and index futures prices might move differently between the time of placing and filling the orders. If such opportunities occured predictably, then traders would show up to exploit them, which would destroy the opportunities. For example, if you and the world know in January that credit premiums will be too large during the following summer, then as soon as the excess premiums start to show up, you and the world will buy credit risky debt and sell credit riskless debt, which until the prices fall back into line. This will permanently keep credit premiums in line with reality.
Statistical arbitrage is nothing more than a spread trade that has favorable odds of becoming profitable. Other names for such trades are
- long-short strategies
- pairs trading, one long, one short
- market neutral strategies, which should make money whether the market rises or falls
- convergence trading, indicating that a price relationship that is out of line should come back in line
Often, the calculation of favorable odds comes from extensive analysis of historical data, but sometimes traders go on simple theory and casual empiricism.
My experience is mainly in the area of options, where dynamic hedging is the main form of statistical arbitrage. One family of spread trades involves being long (short) a complex, derivative instrument and short (long) the replicating portfolio of underlying instruments. A parade of traders – with David Askin in the middle – have done this with mortgages and mortgage-backed securities vs. Treasurys and Treasury options. Convertible bonds vs. shares and ordinary corporate bonds provide another example. Perhaps the most common example is equity options vs. the underlying shares and money market instruments, or currency options versus the two underlying currencies.
Other types of statistical arbitrage include
- index arbitrage, e.g., shorting the "rich" S&P 500 index futures contract and promptly buying the "cheap", corresponding basket of shares.
- event arbitrage (formerly known as "risk arbitrage", until that name lost its lustre) in the market for shares of companies involved in takeovers
- volatility arbitrage involving a forward start option and options with different expiration dates
- basis trading, involving cash and futures, or two futures contracts
- zero duration trades involving a portfolio of fixed income securities
- zero beta equity trades
- classic long-short hedge funds
- credit spreads.
Other types of arbitrage, with statistical elements, include
- tax arbitrage of the differences in tax treatment of economically identical portfolios
- regulatory arbitrage to pick the most lenient of regulators for a portfolio of risks
Wanting to know more about statistical arbitrage is like wanting to know more about the ways to prevent cancer. The types of cancer are different, and you can avoid them by different means, such as avoiding lung cancer by not smoking, skin cancer by staying inside during the summer midday, liver cancer by avoiding hepatitis, etc. Similarly, different types of statistical arbitrage call for different methods. While I don't have ready sources for most of these types of statistical arbitrage, the most readily available, authoritative resource for various option spread trades is Natenberg's book. For dynamic hedging, I'd say that Taleb's book offers a great deal.
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Once you understand a few types of statistical arbitrage, I think you have a better idea of all the rest. – Dr. Risk
Jumpin' for Joy? (4/28/99)
Dear Dr. Risk –Any good references on Jump Diffusion?Many thanks... – Lucian
Dear Lucian – I don't know your application, but a good place to start would be Merton's model of option pricing under jump diffusion, which is readily available in his book on continuous-time finance, which Amazon ships in 24 hours, and which has given me many hours of joy and a few of frustration. – Dr. Risk
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[Cubic] Spline et Ideal (3/28/99)
Dear Dr. Risk – I am a dim journalist who did this for his derivatives exam three years ago, can't remember the score and has lost his notes. I seem to recall that when cubic spline came out everyone thought it was a whizzo way of plugging gaps in their yield curve – until they lost a shed load of money. Why's it called cubic spline and what was the assumption inherent in it that didn't work? (In presenting your response please allow for addressee's room temperature IQ.) – Drew
Dear Drew – The mathematical spline that swap desks use for constructing smooth yield curves gets its name from the name (spline) for a tool that an artist or draftsman uses to draw smooth curves. The draftsman's spline (For some reason I do not associate a spline with Montmartre.) is a thin, flexible rod, ordinarily of wood, fiber glass, plastic, or steel. One way to use it is to stick push pins or nails into the surface on which the draftsman is drawing, and thread the spline through the pins, which hold it and stress it, creating the curve. Obviously, the curve is continuous and smooth, and its slope changes continuously and smoothly.
Now, suppose that we want to model this spline, mathematically. We might try to model it with a polynomial. We would need a polynomial of order 1 (linear function) to go through two points, of order 2 (quadratic) to go through three, of order 3 (cubic) to go through four, etc. The problem with such minimal polynomial functions is that they might be extremely contorted to pass through all the points, hence hard to accept visually – it flunks "the eyeball test".
A "piecewise cubic function", f(x), is cubic over each small part of its "domain" (e.g., from x=1 to x=2), although different cubic functions apply to different parts of the domain. A piecewise cubic function that satisfies the following constraints also passes the eyeball test for a model of a spline:
- adjacent cubic pieces meet at the interior pins
- the first and last pieces pass through the beginning and end points
- the slopes of the cubic pieces are the same where they meet
- the second derivatives of the cubic pieces are the same where they meet
- the second derivatives of the cubic pieces are zero at the end points (only for a so-called "natural" spline).
The usual "bootstrap" approach to estimating a yield curve gives a set of zero coupon bond prices. You might use the cubic spline to approximate the zero coupon price curve or some simple function of it, such as its logarithm. The resulting smooth curve will price the basic zeros correctly. How well the spline approximates the entire zero curve is unknowable, unless you held back some of the zeros, just to conduct a test.
The cubic spline basically ensures that the interpolated yield curve passes a single "sniff test" – the test for smoothness. The spline may be far from an ideal approximation a yield curve whenever reality is more complex than smoothness, which can be a lot of the time. The eyeball may discern some other problems. A bad data point can cause false curves in the spline. Extrapolation – always risky – is risky with a cubic spline, but so easy to do.
In all fairness to the cubic spline, no other interpolation method is always superior. I wish that I could paraphrase Winston Churchill and say, "The cubic spline ... is the worst of all interpolation methods ... except for all the rest." However, to paraphrase Richard Nixon, "that would be wrong." All I can say is that it tends to pass the eyeball test, is relatively easy to work with, and is a good tool to have in your toolbox of numerical methods. Just don't bet the family jewels on it. – Dr. Risk
Euros, Dollars, and Eurodollars (2/28/99)
Dear Dr. Risk – Is the Eurodollar in use now or is it just being traded as as commodotiy? If it is not in use, when is the planned launch of use. How can I see what the currency looks like. – Carol
Dear Carol – Eurodollars are U.S. dollar deposits in banks outside the U.S., often in British, Japanese, and other foreign, commercial banks, outside the direct control of the U.S. government. The original motivation for them was to meet the Soviet Union's need after WWII for dollar deposits that the U.S. government could not confiscate. Eurodollar time deposits are the underlying instruments for the Eurodollar futures and futures option contracts.
The Euro is the relatively new unit of account of the European Monetary Union, soon to be its currency. I draw the distinction, because one can already measure the value of goods and services in Euros, even though Euros do not circulate. One can even buy and sell goods in Euros, but any cash delivered must be in one of the existing currencies, and at the fixed exchange rate. As of 1/1/99 each of the major European currencies, except for the British pound, and each of several minor European currencies have official spot exchange rates that are fixed in terms of the Euro. Over the next two years the countries of the EMU plan to retire their national coins and currencies and replace them with coins and curency that state their worth in a number of Euros.
The motivation for the Euro is a desire to further merge the European countries, economically, as trading partners, with political ramifications. The economics is straight forward. A single currency would tend to lower the cost of trading. A lower cost of trading would lead to more trade. More trade tends to make people wealthier. The political argument is not much more complicated. Since major trading partners tend to avoid fighting with each other, the further merger of the European countries would help Europe avoid the sort of mass slaughter it has seen twice in the 20th century. At least, that's one theory.
Another, less sanguine theory is that control of the currency will lead to a bloody, European civil war within 20 years for one of two reasons: (1) Whoever controls the process of creating currency will reap the reward of seignorage, the profit that comes from issuing money that is intrinsically worthless, but worth a lot by agreement. Everybody else will resent this and fight for a piece of the action. (2) Whoever controls the currency will control monetary policy for the EMU. Whether that policy is expansionary or deflationary, it won't help everybody, because the EMU is not an optimal currency area. The people that monetary policy hurts will become angry. When they are angry enough, they will take up arms against the entity that is wrecking their economy and impoverishing them.
I have seen pictures of plans for Euro currency, but can't refer you to a web site with such a picture. Each member of the EMU will issue Euros, according to some quota. I believe that the plan is for each coin or piece of currency of a particular denomination to have one side in common and one side peculiar to the country of issue.
IBM has a web site (http://www-5.ibm.com/euro/) devoted to issues related to the Euro. This might be a good place to start your seach for pictures of the forthcoming Euro. I can tell you that the symbol for the Euro looks like a capital C, with a "equals" sign through the middle, analogous to the symbol, $, for the dollar. – Dr. Risk
Euros, Dollars, and Eurodollars (II) (3/28/99)
Dear Dr. Risk – Your reader Carol asked about Euros and what they look like. I found the following link to Westdeutsche Landesbank that presents the Euro banknotes: http://www.westlb.de/euro/ewu320.htm.
Pictures of the coins be found at: http://charon.wh10.tu-dresden.de/~jens/revers/de/revde.html.
BTW, chocolate-filled EURO-coins have been en vogue in Germany around christmas although they are not widely accepted as currency. – Thomas
Dear Thomas – Thanks for your help! – Dr. Risk
Let's Get Real (1/28/99)
Dear Dr. Risk – I am a general manager with just a rudimentary academic background in finance, however I have read some recent articles in publications like the Harvard Business Review and the McKinsey Quarterly suggesting that options pricing models have very useful applications in the "real world." Specifically, they propose that options can be used to help managers budget capital in the face of uncertainty, much better than tools like NPV and Decision Trees.
Can you review the use of option models for managerial decision-making, highlighting their advantages and limitations, as well as any practical textbooks for a manager who wants to put these techniques to use? Thank you very much. – Alex
Dear Alex – What a coincidence! Since I started running my consulting business, I've been a general manager with just a rudimentary academic background in general management. Maybe I should read more articles in HBR and MQ.
Thanks for your thought provoking question. Sounds like your reading got you thinking in the right direction. I believe that thinking about investments as complex options makes sense, and analyzing them with real option tools can be a useful exercise. I'll start with a definition and examples, then try to put real option analysis into the context of NPV, decision trees, binomial trees, and option theory. Along the way I'll touch on the strengths and weaknesses of the approaches. I'll leave you with a list of resources at the end.
Definition
A real option involves more tangible objects (such
as bricks and mortar, pipelines and equipment), not so much
financial instruments, dividends, and coupons, and physical
actions (such as excavation, construction, demolition, physical
movement, and hard work), rather than simply tendering notice of
exercise of an option. I think that the boundary between real
options and standard stock and bond options is a little fuzzy,
and that some options are hybrids.
Examples and applications
Every person faces real option problems in his or
her daily life, such as these decisions:
- go out for football or spend your time studying
- attend college or join the marines
- go for an MBA or for a law degree
- accept (or offer) a marriage proposal or keep looking for a better proposal
Many business decisions are real option problems, for examples, the decisions to:
- build a large or small apartment building today or wait until next year to decide
- buy a more flexible and more expensive production process or a cheaper one with fewer applications
- test pharmaceuticals, most of which will be worthless, in hopes of finding a huge money maker
Even government faces real options:
- scrap ships (airplanes) that the Navy or merchant marine (Air Force) takes out of service, or "mothball" a fleet, paying the cost of taking a unit out of service and preserving it, so the organization can can put the units back into service during a later emergency, rather than waiting for new construction.
The main business application for real options seems to be capital budgeting, i.e., business investment, often related to strategic planning. One investment may open doors to other opportunities that may grow or not, and neither net present value (NPV) nor simple decision tree methods are up to the task of evaluating such sequential investment decisions. Real option analysis combines elements of NPV, decision trees, and option pricing in an effort to make better decisions.
Net present value
The NPV approach to investment involves
simplifying an investment opportunity into a sequence of cash
flows (in and out), converting all the future cash flows into
present cash value, and adding up all the present values to see
whether the entire project is in the red or the black. This is
analogous to looking into your crystal ball to see how much money
you would make if you paid a fee, walked along a row of corn,
picked every ear, took the harvest to market, and sold it.
The NPV approach was a great advance over previous methods of capital budgeting, including such methods as payback period, internal rate of return, and even benefit/cost ratio. Essentially, it allows us to apply standard techniques in the theory of choice to choices made about consumption at different calendar dates. However, in its common form the net present value approach doesn’t easily allow for "stop or go" decisions along the way and handles uncertainly awkwardly.
Decision tree
In essence, a decision tree is a like the map of a
road system that starts at a point, then forks repeatedly. At
each fork, one deliberately chooses which way to go, and one
picks up a foreseeable quantity of fruit at various points along
the way. Where one ends up and how much fruit one collects
depends entirely on choices made. A simple decision tree has no
randomness to it, and time value of money is not ordinarily part
of the process. A sophisticated decision tree lets Mother Nature
make the decision at some forks by "flipping a coin",
reflects the time value of money, uses something like dynamic
programming to work back through the tree to make optimal
decisions – and looks a lot lot real option analysis.
Binomial price tree
A binomial price tree looks like a decision tree,
but at each fork Mother Nature essentially flips a coin to decide
which way the price goes. You may be able to make a decision at
each node, not about which way to proceed, but perhaps about
whether or not to proceed (i.e., to exercise the option early, or
not). The binomial price tree in option pricing fully embodies
the idea of time value of money. In the limit, as steps in time
and space approach zero in the right way, the binomial price tree
turns into a continuous-time diffusion process. The binomial tree
allows us to extend the theory of choice from consumption at
different dates to consumption at different points in the (date,
state) space.
The real option approach
The real option framework is a combination of the
most useful elements of the decision tree, the binomial tree, and
NPV analysis. Consider the simple "discrete time, discrete
state" case. As we move along the decision/binomial tree and
come to a fork, we might be able to choose freely which path to
take (as in the decision tree), we might have to pay cash or do
something to head in one direction (as in NPV analysis), or we
might move randomly in one direction (as with the binomial tree).
As we move along, we might collect cash or pay cash at any given
point, as with NPV analysis. We might have a compound option (an
option on an option), and one of those options might be the
option to exchange one real asset for another. Lenos Trigeorgis,
a founder of the field of real options, says, "... almost
all real options are special cases of compound exchange
options." Where we end up and what we end up with would be
partly random, but would also depend on choices we made. This is
an extremely powerful way of looking at things. Tools for making
decisions in this sort of framework include option pricing
theory, stochastic control theory, and stochastic dynamic
programming. Binomial pricing of American options is a special
case.
Example: "the "secretary
problem"
For example, consider a simple, illustrative
"real option" scenario, known as "the secretary
problem." The boss wants to hire a secretary and an
employment agency sets up 50 candidates. For simplicity, suppose
that the boss can hire any candidate on the spot, or can reject
all candidates, until the last. If the boss has not hired a
secretary by the time of the last interview, that candidate gets
the job.
Each interview has a cost, certainly in the boss’s time, perhaps also in cash. After each interview the boss makes a decision to either continue the search or hire the secretary. The boss can "buy" future interviews by giving up the immediately preceding candidate and calling in the next one. At the end, the boss has a payoff – a secretary – whose value depends on the random opportunities he faced, as well as how well he played the game.
More applications
We’ve hardly scratched the surface of
applications. Here are a few more.
- A company can build a plant this year or forgo the immediate benefits of the plant in order to take advantage of potential technological advances or shifts in the market.
- A high school graduate must choose between getting a liberal arts education, in order to keep his options open, or to get a technical or business education and start a promising career.
- ConEd bought and keeps gas-fired electricity generators on barges in the East River, so it has the option of putting them into service on hot summer days when it needs peak capacity.
- Parents hire a tutor for their five-year-old, so he can excel in kindergarten and gain admission to a better private elementary school, where he can choose to goof off or work hard to get into a better private high school, where he can choose to goof off or work hard, in order to qualify for admission to a better college, in order to qualify for better entry level job offers, in order to achieve a higher career trajectory, in order to attract a more intelligent wife, in order to produce higher quality children, who will be able to gain admission to a really good kindergarten, … At every point along the way the parents and child can pay a price in money and effort to create better opportunities in the future, and any slacking along the way closes doors – eliminates options. People do this!
I’ve attached some resources to take you more deeply into this subject. Also, you might want to attend one of the conferences on the subject, such as the conference in the Netherlands, in June 1999.
You asked about putting these techniques to use. I mention books, below, with comments about practicality. My gut feeling is that the approach is essential for thinking about many problems in business and everyday life. I would want to critically evaluate spreadsheets or other applications that take inputs and crank out answers, because the data requirements for this approach are relatively large and rigorous. However, professionals say they can get out useful numbers, so I could be wrong. Tom Copeland of Monitor Company (formerly with McKinsey) has applied real options analysis to about a dozen clients.
– Dr. Risk
P.S. Do you have a specific real option in mind in your line of business?
Resources
Books (Are they "practical"? Depends on what you need. I bought them all, because Dr. Risk needs to have a complete research library. See my comments, below.) on the subject include –
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Web resources include:
- Third Annual Conference on Real Options. Includes abstracts and some papers in .pdf format.
- Real Options Tutorial. (http://www.puc-rio.br/marco.ind/non-tabl/tutorial.html) An introduction.
- Options Bibliography. (http://www.eur.nl/few/indec/litlist.htm) A good place to find references.
- Real Options in Petroleum. (http://www.puc-rio.br/marco.ind/non-tabl/main.html) An application.
- "Real Options" vs. EVA. (http://www.businessinnovation.ey.com/journal/issue2/features/stunt/abstract.html) Why the real options approach is better than the Economic Value Added approach.
– Dr. Risk
Classic "Ask Dr. RiskTM" columns from Previous Years: 1998 1997 1996
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