MARKOWITZ INTERVIEW - American Finance Association

Interview at Rady School of Management at the University of California San Diego
(edited for clarity and readability)
I am Steve Buser, and on behalf of the American Finance Association, I welcome
you to this first of a series of interviews with the founding contributors to the academic
discipline of finance. Our hosts this evening are Dean Sullivan and the students of the
executive MBA program at the Rady School of Management of the University of
California, San Diego. The series is entitled “Masters In Finance”, and our first founding
contributor is none other than Dr. Harry Markowitz.
Dr. Markowitz is best known as the father of modern portfolio theory. But he has
made a number of other contributions as well. In 1989 he received the John Von
Neumann Prize for contributions in the area of operations research. In 1990 he shared the
Nobel Prize in Economics for his contributions in portfolio theory and other areas. If that
were not enough, Pension Magazine declared him not just the man of the year, and not
just the man of the decade, but indeed the man of the century. So tonight I give you Dr.
Harry Markowitz, the man of the century.
The cardinal rule of journalism is, do not bury the lead. So with
that I will ask, what was it like to win the Nobel Prize?
It was great. It was a surprise. Jim Tobin got the prize a few years
before. It was announced at that time that he got it for portfolio theory, period. It turns
out he got it for many good works in macro economics. But at the time I thought, well
that’s it. They have given the prize for portfolio theory, and I didn’t get it.
I was at a meeting at the time, and I had given my paper the day before. When I
heard the announcement I told my wife, Barbara, that I didn’t feel like going to the
meeting that day. So we went for a long drive, it was down in Maryland, we went past
farms with those white fences with the horses behind. We came to a little town with a
department store and each of us had a big ice cream cone. When I finished my ice cream
cone I said, okay, now I’m ready to go back. So it was a big surprise when the
announcement came.
Do you remember where you were and the circumstances, how did
you hear about it?
We were in Japan. The Nobel committee didn’t know where we
were, and we were sitting down to dinner. I was giving a course on portfolio theory for
the math department at Tokyo University. The head of the math department called me
and said, “You just won the Nobel Prize in Economics, and this fellow at the public
television station would like to interview you.”
You mean you’ve already done one of these interviews? Where’s
the tape?
Well it showed on Japanese television. That was a very short one.
The head of the math department wasn’t a kidder, but we wanted to check for ourselves.
Once an hour there would be news, in English, from the Armed Forces station. We heard
that Markowitz, Sharpe and Miller had gotten the Nobel Prize. We called the guy at the
public television station and he said he’d like to do an interview. I said, well I think I
have a little time sometime tomorrow afternoon about 2:00 p.m. He says no, no, no, we
want to be on the 9:00 o’clock news this evening. So he came out and everything moved
very fast.
You mentioned you shared the prize with William Sharpe and
Merton Miller. What was your reaction to learning that you were going to share the
Well, the Nobel’s fine. I didn’t quite do a mental calculation.
Nobody asked me that question so far. We sort of felt that Bill and I really had worked
on the same thing, and Miller should have shared the prize with Modigliani.
So Franco owes you 1/6th of something ?
Yeah, but it’s too late.
You received your PhD from University of Chicago, and Dr.
Miller was at the University of Chicago. But I guess did not overlap with you?
Was there at least professional pride in the fact that it was a
professor from your institution, your alma matter, that shared it with you? And then, of
course, there was William Sharpe who worked very closely with you. So the three of you
at least had some ties.
Right. Bill and I had worked together on things. And, a lot of
Nobel Prizes have come from the University of Chicago. My Professor had gotten a
Nobel Prize for work that had a certain kind of influence on portfolio theory. When this
idea came to me, I was a PhD candidate and was taking a course under T.C. Koopmans
called Activity Analysis. He distinguished between efficient and inefficient allocations
of resources. And I had efficient and inefficient portfolios. So the term efficient portfolio
was the result of my taking a course under Koopmans.
Tell us a little bit more about how you got this idea for your
dissertation topic.
You were a graduate student at the time?
Right. I was at the stage where I had to pick a dissertation topic.
So I went to my advisor, Professor Jacob Marschak. He was busy when I got there, so I
waited in his ante room. There was another fellow in the ante room who turned out to be
a broker waiting for Marschak. We chatted while we were there, and he suggested that I
should maybe do a dissertation on the stock market. So I went in.
A stockbroker gave you the idea?
That’s right, a stockbroker.
A tip that paid off.
Yeah. Some biographer of mine said this was the best advice a
stockbroker has ever given. And I agree. Anyway, I went in and told Professor
Marschak, the guy out there suggested that I do a dissertation on the stock market.
Professor Marschak was very receptive. I was a student member, and he was a former
head and now currently a member of the Cowles Commission, as it was called at that
time. Alfred Cowles had actually endowed the Cowles Commission with the hope that
there would be econometric research done in the stock market.
I did not know that.
Well in fact there’s a book by him called Cowles Commission
monograph 3, I think, that has a time series which then later linked up with the S&P 500.
And he did early research about how good financial advisors were not when it came to
prediction versus actual. So Marschak thought it was a good idea.
He didn’t know the literature in finance so he sent me to a professor in the
business school, Professor Marshall Ketchum. Professor Ketchum gave me a reading list.
I went to the library and went through the reading list. The reading list included Graham
and Dodd of course. And the next one of the readings was John Burr William’s Theory
of Investment Value.
When I was reading Williams in the library, it must have been in the afternoon in
roughly 1950. I don’t know the exact date, but some afternoon in 1950, I was reading
John Burr Williams, and Williams said that the value of a security should be the present
value of its future dividends. He understood that future dividends were uncertain. So he
said it should be the expected value of future dividends. Now I thought to myself, well if
you only are interested in the expected value of the return on a security you must be only
interested in the expected value of the return on the portfolio as a whole. And if you are
only interested in the expected value of the portfolio, you maximize that by putting all
your money in one security, whichever has the highest expected value. And that’s not
right. Everybody knows you are not supposed to put all your eggs in one basket. At that
point it was obvious that people diversified because they are interested in avoiding risk as
well as earning return. I was a budding young economist with two things, expected
return and risk. So I drew a graph with expected return on one axis and risk on another
axis. And I called that an efficient frontier, the very first efficient frontier. All this in that
same day.
Oh, this is all happening in real time?
The notion of just using standard deviation or variance was the
first idea that popped into my head, because that is a commonly used measure in
statistics. I knew that the expected return on a portfolio is the weighted sum of the
expected returns on individual securities. And I knew what the expected value of a
weighted sum was. But I did not know what the variance of a weighted sum was. So I
got a book off the library shelf, Uspensky, “Introduction to Probability”. I don’t
remember the guy I met yesterday or the day before, but I remember Uspensky’s
“Introduction to Probability”. I looked for the formula for the variance of the weighted
sum. It had all those covariances in it, and I thought, this is wonderful! The riskiness of
the portfolio depends on covariances. So that all happened in one afternoon. There was
still a lot to do, like figure out how you actually compute efficient frontiers, but the basic
idea was there in one afternoon.
You had an epiphany?
Right, epiphany, that’s right.
And without the benefit of any training in finance at all?
No. I had statistics and little linear programming from Koopmans,
and I was well trained.
How about on the personal side. Did you have any experience as
an investor?
No, none. I was a poor student…I’m going to rephrase that…I
wasn’t quite destitute, but I was improvised as a student.
I heard you describe elsewhere that at the time of your dissertation,
there was some doubt not only that you might not win the Nobel Prize for the effort, but
that you might not even get a PhD. At the risk of drudging up old painful memories,
would you care to go through that for us?
That’s fine. It wasn’t a fun experience at the time, but it has been a
fun experience to relive ever since. I was working at Rand Corporation in Santa Monica,
and I had been on a trip for Rand in Washington, D.C. On the way back, I stopped off in
Chicago to defend my dissertation. I remember landing at Midway Airport and thinking
to myself, I know this field cold, not even Milton Friedman will give me a hard time.
Tempt not the devil.
So about five minutes into my defense, Friedman says, well Harry
I’ve read this. I don’t find any mistakes in the math, but this is not a dissertation in
economics, and we cannot give you a PhD in economics for a dissertation that is not in
economics. He kept repeating that for the next hour and a half. My palms began to
sweat. At one point he says, you have a problem. It’s not economics, it’s not
mathematics, it’s not business administration, and Professor Marschak said, “It’s not
literature”. So after about an hour and a half of that, they send me out to the hall, and
about five minutes later Marschak came out and said congratulations Dr. Markowitz.
Well, on behalf of the American Finance Association, I would like
to thank your committee for giving you a hard time. If they had not treated you so badly,
and in particular if the economics profession had not been so slow to recognize you, then
the finance profession might not have as great a claim on you as we allege that we now
have. In particular, you elected to publish the first article from your dissertation in the
Journal of Finance. I happened to have brought the issue with me, 1952. One of the
interesting numbers on this particular issue is seven. This is volume seven, meaning it
was only the 7th volume that the Journal of Finance had published. There is normally
one volume per year. However I also brought with me the very first publication of the
Journal of Finance which combines volumes one and two. It includes two years worth of
proceedings from the annual meetings plus all of the articles that the profession produced
in the two years of 1946 and 1947. By way of contrast, the single volume you elected to
publish your Nobel Laureate address in is even bigger. At the risk of getting a hernia,
this is now going to be…this year’s volume… of the Journal of Finance. In addition,
there are now many finance journals, as we all know. But at the time you elected to place
your article in the Journal of Finance, it was really a very new and relatively untested
journal. So I have to ask why? What made you think of the Journal of Finance?
It was a finance contribution, and I heard there was something
called “The Journal of Finance”. Fred Westin was the publisher. I was at Rand, so I was
in Santa Monica, and he was at UCLMARKOWITZ: I can’t remember whether that had
any influence. It’s a complete blank, why I decided. But somehow it seemed to me that
this little 1952 article was something that belonged in The Journal of Finance. It was
about finance.
There is another name you have mentioned, who was also an
editor. You might want to read the names of the two coeditors of the Journal of Finance.
Oh well, Marshall Ketchum. I didn’t know. That’s wonderful.
I’m learning all sorts of things.
Stick with me kid, and you’ll do all right. So you had another
connection there to the journal. And as I said, we are delighted that you elected to
publish in the Journal of Finance.
I wonder if Marshall Ketchum suggested that. I have no idea. You
know, it’s a complete blank.
In the movie version we’ll say he suggested it.
Right, absolutely right. We’ll clean it up.
You also elected to publish your Nobel address in the Journal of
Finance. And by the time 1990 rolled around the Journal had advanced as we have
indicated. I was one of the coeditors of the Journal at that time and can attest that we
were receiving a thousand papers per year, about three a day. That is why I’m no longer
one of the coeditors. And there are many more journals around, so there is a lot of
competition for top papers. The economics journals were hot after the top papers as well.
But the thing that strikes me about your decision to publish in the Journal of Finance was
that until this time every presentation for the Nobel Prize in Economics had been
published in the American Economic Review. Why did the three of you decide to honor
the Journal of Finance?
Well, you folks requested it.
I told you not to say that.
And it seemed perfect. I mean, I don’t know if AER requested it,
but if the AER and AFA had both requested The Journal of Finance was the obvious
We thank you. Because the AER had presumed, even if they did
not request, they presumed.
Yeah and we got into a little trouble … but never mind …
Oh, oh. Did they presume that we would publish…?
I didn’t realize that.
But we are delighted that you stuck with the Journal of Finance,
which again strengthens our claim, the finance claim, to you although we have already
said that the operations research people regard you as one of them, the economists regard
you as one of them. I’m sure the statisticians regard you as one of them. I’m not sure
about the literature people yet.
Certainly not the literature. It’s definitely not the literature people.
But you’ve still got a chance on the literature side. Tell us a little
bit more about this topic of modern portfolio theory. I am intrigued by the title. When
was the first time you heard that phrase, modern portfolio theory?
Many years later. I did not call it modern portfolio theory. I’m not
sure who did.
You’re not sure who did?
Well, it’s a little over 50 years old now.
Yes. And I am glad something 50 years old can be modern because
I am 77 years old.
And you’re not modern any more?
Well, it would nice; it would be nice to think I was.
If we accept the designation of modern portfolio theory, then prior
to 1952 was there something called classical portfolio theory, or more generally what was
the state of the art regarding portfolio section in 1952?
Okay. Let’s go back to John Burr Williams. He said that if you
are in doubt, if something’s uncertain, you should act according to the mean. I have an
article which I published in the Financial Analyst Journal, you’ll excuse the plug for
another journal, on the early history of portfolio theory 1600 to 1960.
I just happen to have that with me as well.
I go into more detail than I can go into here. But what Williams
said was that if something had risk in it, well you don’t have to really worry about that
because with sufficient diversification you can eliminate the risk. Now if risks were
independent, if returns were uncorrelated with each other, then if you diversify enough
you can make the variance of the portfolio go away. But when risks are correlated, they
don’t go away. There is something in Chapter 5 of my 1959 book called “The Law of the
Average Covariance”. It says that if risks are correlated then if you equal-weight a
portfolio, variance does not go to zero. Variance goes to the average covariance, and that
can be very substantial. Even if correlations are just 0.1, 0.2, or 0.3 among all securities
on the average, the variance of the portfolio can still be very substantial. So while
Williams did believe in diversification, he thought that diversification would eliminate
risk, and so your job was just A) to pick out whichever investments had the highest
expected return, and B) diversify among lots of things, and then you would get the mean.
So that was the basic difference between portfolio theory as it existed in 1952,
prior to the simultaneous work of two people. In that year A.D. Roy published something
called safety first investment. He also recommended action in terms of expected return
and variance or standard deviation of a portfolio. But he recommended a specific
portfolio, namely the portfolio whose expected return was as many standard deviations
above some catastrophic level as possible. Instead, I presented an efficient frontier and
said let the person choose. The difference between Roy and me, on the one hand, and the
theorists that preceded us was they thought the law of large numbers would get rid of risk
if you diversified enough.
You are very kind to Roy. First, I want to point out that his paper
was published in 1952, but in July.
Oh was it?
Whereas yours came out in March.
Oh I never knew that. Okay. I’m learning all sorts of things.
And a second thing about Roy, when I read his work and your
work at the same time, as a student, what struck me even then was that, as you have
noted, prevailing theory emphasized expected return first. Once you did the best you
could with expected return, you diversified as best you could as a secondary strategy.
Roy proposed reversing that logic. He wanted safety first and then subject to that safety
constraint, do the best you can on expected return. You blended the two concepts very
clearly, and proposed equal consideration of expected return and risk. Do the best you
can on both, and whatever you do, do not choose an inefficient combination. So I think
you’re selling yourself a bit short.
Well I think basically the reason Roy did not get the prize and I did
You don’t want to split it four ways?
No, no. You can’t. You can’t split it four ways. Three is as far as
it’ll go. But the reason that Roy did not get the prize was that he did not do anything else
in finance. That was his one and only contribution. He never showed up at a meeting,
never as far as I know wrote another paper or anything like that. So by the time it came
time to hand out the prizes Roy wasn’t on their radar screen and I was.
Again you are very generous. Your initial contribution not only
beat him by three months, but I think was a stronger contribution as well.
Thank you.
By the way, the title of your paper on the early history of portfolio
theory has a curious starting date. Do you remember what the starting date was?
And do you remember the author of the original work?
I have a quote which I stole from William Shakespeare. Act one,
scene one. Somebody says why are you sad? Is your business going bad? And he says,
[reading from paper supplied] “My ventures are not in one bottom trusted, nor to one
place, nor is my whole estate upon the fortune of this present year. Therefore my
merchandise makes me not sad.” That means that not only did he know that you’re not
supposed to put all your eggs in one basket, but that there are covariances in a
By the way, that wasn’t only your opinion of the state of portfolio
theory at the time. There was also a paper by J.L. Leavens. Are you familiar with
Yes, right.
He did a survey at the time, actually in 1945, about the state of
portfolio theory, and you are quite right. Diversification was somewhere in there. It was
just not very specific.
I talk about Leavens in that early history paper. Leavens say that a
lot of people talk about diversification but they do not tell you why it is good. He does an
example to explain why it is good, but he uses the law of large numbers and comes to the
conclusion that he can make risk disappear. Then he says in his next to last paragraph, of
course this assumption that risks are independent is subject to question. There is the
possibility all stocks in a given industry will go bad together. So you really have to
diversify across many industries. There is also the possibility that all industries will go up
or down, and so you cannot diversify completely. So in his next to last paragraph he
intuitively understood that covariance counts. However his formal analysis still assumed
Many of the early writers must have intuitively understood because
they must have diversified on their own. Although I am puzzled, as are you, that anyone
would think you could eliminate risk. It doesn’t seem they could have invested very
much, or gone through very many ups and downs of the market and still think they could
eliminate all risk.
Or that somebody writing in the 1930s would think you can ignore
things going up and down together, that you can assume independence after 1929 through
Perhaps they had short attention spans or perhaps they weren’t paid
very well as professors and did not invest much. With respect to diversification, how
many securities did you use to illustrate the basic principles?
Well I didn’t do any computation, but I remember Peter Bernstein
commenting on the example I used, and since I had absolutely no experience with
finance, it was a silly example. I think I said that if you put all your money in 60
railroads or something like that, it wouldn’t be well diversified. And he pointed out
many years later that there weren’t 60 railroads around. So a pure theoretician should not
give examples. By the time the 1959 book came out I presented a 10 security case, 9
risky securities plus cash. I had somebody collect time series on nine securities. I had
actually planned a 25 security example--maybe that’s something you don’t know about—
I thought that the way you got inputs was to ask security analysts or
You got your first tip from them also?
Right, well that too. Well that was a broker. So I wanted to use
security analysts. These were actually the CFO and assistant CFO or something like that
from Yale that filled out these forms. I was going to do a 25 security example, but we
could never get it to work. We did the ten security example on a 602A, which had a
punch card reader.
Can you all hear that, a 602A? That was before you all were born.
[speaking to an audience of MBA students]
Right. It read a deck of cards, and it had lots of wires that would
sense where the punches were. The wires indicated where you wanted to pick up the
numbers and what to add or subtract or multiply or transfer. And then you make a pass
through the deck of cards and punch another deck of cards, and you make a pass through
that deck of cards and you have another board. You’d sit there reading a book, and it
would go chuggedy chug, chuggedy chug, and then finally it would stop. And that was
how I got the first efficient frontier.
So going from nine securities to 25 securities was a remarkable
computational feat, and you didn’t make it?
We didn’t make it, that’s right. So I figured the book would be
fine without it.
Does that conclusion have anything to do with your deciding you
had written everything there was to write about portfolio theory?
Well I said what I had to say, and I went on to work on other
We will get to the other things in a bit, but the part I find
remarkable was that at precisely that point in time much of the finance profession was
deciding that portfolio theory was the thing to be working on. I’d heard that your original
paper launched a thousand dissertations. And by now I think it’s more than a thousand,
including my own dissertation. But you did move on to other things.
This was about 1960. I don’t know whether there were a lot of
dissertations actually in process during the 50s.
Not in the 50s, no.
I think they started in the 60s.
Right. After your 1959 book.
Well maybe after my 1959 book and after Bill Sharpe’s one factor
model and after Bill Sharpe’s capital asset pricing model, then I think the wave hit.
And I am counting that as part of the wave, yes.
Okay. I think once that hit 11
But you were on to other things.
I was on to other things.
One of the things you moved on to was Simscript. Would you care
to define that for us?
Simscript was, and still is, a programming language that is
particularly designed for programming asynchronous discrete event simulation models,
like air force logistic systems or manufacturing systems. Those kinds of things. Rand
was the first to finance the thing, and in its day it was very widely used. It is not as
widely used now, but it was at one time widely used.
How about your work on sparse matrices? Can you define those
for us?
I had the good fortune of going to Rand shortly before George
Dantzig who was my mentor at Rand for many years. A group of us, Allan Manne and
others, some at Rand, some outside of Rand, were working on very large linear
programming models of economic capability, economy-wide capabilities. They were
very aggregate models, on the one hand, but as linear programming models they were
still very large for that day. I observed that while those models were very large, most of
the coefficients in the models were zero. If you picked your pivots right you could invert
these things by hand even though it took the computer a long time to do it. Well I
couldn’t quite keep up with the computer, but the trick was to get the computer to use the
sparsity. I coined the term sparse matrix, and then Bill Orchard-Hayes, who usually
programmed for George Dantzig, programmed this for me and we published the first
sparse matrix code. I am told that the Markowitz method of picking the pivots to keep
the inverse sparse is still used in big production codes. So I claim that as one of my
What other work have you been doing since 1959?
Well those are the big things since 1959. The prize from the
Operations Research Society was for Simscript, sparse matrices and portfolio theory. I
haven’t done anything else which, so far, is recognized as a big block buster. But I keep
busy. One of the things I am doing with some colleagues, Bruce Jacobs and Ken Levy, is
that we are building a large asynchronous market model where there are entities like
statisticians, portfolio analysts, investors and traders. The investors periodically
recompute their efficient frontiers and place orders with traders. Prices are then set
endogenously by the order book with people trying to either pick up something from the
book or put it on the book. It turns out that if you do not have any news coming in, any
volatility is just due to the market itself.
We have basically two kinds of investors. Those who tend to be price insensitive,
and those who tend to be price sensitive. If you get the right mixture of those two kinds
of investors, you can get volatility in the market that looks very much like real markets
even when there is no news. I mean the guys at CNN could be telling all sorts of stories
as this market goes up and down, but it is just the market itself. So this is great fun, and
we will be putting that out. There is an article coming out describing that in the Journal
of Portfolio Management. [“Financial Market Simulation” by Jacobs, Levy, and
Markowitz appeared in the special 30th Anniversary Issue of the Journal of Portfolio
Management in 2004.] Pretty soon we will have it on a Jacobs Levy Equity Management
website so you can go in and change parameters such as how many investors you want,
and various types of investors, and so do simulations yourself. So that is something that
has been going on.
Very good. At this point we are going to open up the floor for
questions. Do any of you have a question you would like to ask of Dr. Markowitz? And
can you stand up and speak real loudly please?
Dr. Markowitz. How do you feel about putting the Social Security
funds into stock and diversifying?
I am in favor of that being an opportunity. I have worked with the
Chilean pension system, and they have certainly done a lot better than I did with Social
Security. There is a legitimate worry that some people won’t be able to handle it. So it
should be an optional thing. But hopefully most young people should be able to handle
The question mentioned diversification. Should diversification be
required? Or would you allow individuals to go pre-Markowitz and just chase expected
Yeah, that is a problem. Should they be allowed to pick individual
stocks? In the Chilean system, there is good and bad. They can only invest in certain
approved pension funds. These pension funds are not told what to invest in. However,
they are told that if they perform too far below the median pension fund they will be
penalized, and money will be taken out of their fees and put back into the fund. So that’s
good and bad. It keeps people from going off the deep end, but it also tends to make
everybody invest in lock-step. Maybe the right thing would be to have people pick
among a list of pension managers that offer sufficient diversification, but allow some
variety as to whether individual managers are a little bit more aggressive or a little less,
either higher on the frontier or lower on the frontier. So you raised some good questions.
Takes some thought.
Hi Dr. Markowitz. As our ability to collect large data sets, stream
information in real time, and create large complex computations and models continues to
increase exponentially, and as our economic models and our understanding of the
markets continue to evolve, what do you see for the future of market prediction and
Well, I usually try to avoid predicting things. But I think one safe
prediction is that the future will be uncertain just like the past and present. So we are in
the information age, and we have all this information zipping around. Some of it gets into
print, and a lot of it gets into databases. For example, we have a piece of information like
the earnings of a company, which of course might be a lie. Or it might be a misprint.
Or it might be an honest error. Or it might be even correct. I am not saying they
are all lies but, you know, somehow we have to advise people on how to invest their
401(k)s despite the fact that it is an uncertain world. Not only is information about
individual stocks uncertain, but the average return over the long run of stocks as
compared to bonds is still subject to quite a bit of controversy. Some people look at the
past and say, stocks did 10 percent on average before or after inflation. Other people say
that during the same period the price earnings ratio increased considerably and you would
not expect it to go up that much in the future. Therefore you will not have as much return
in the future as in the past. So there’s a range of uncertainty as to what the stock market
as a whole will do over the next many years. And I think that’s good. The world is
uncertain and we have to continue to act in the face of uncertainty.
Are there any financial modeling simulation experiments that are
going on right now that you find interesting?
The experiment I am doing with Jacobs and Levy certainly
interests me. I think it is perfectly reasonable for people to ask what about the real
behavior of investors as distinguished from rational behavior. I do not necessarily
subscribe to each article by the behavioral economists, but I think it is a reasonable
activity to pursue. I am especially interested in simulations that involve asynchronous
time, which means that time does not go by steady increments necessarily and need not
be continuous, but can advance to the most imminent event of various kinds. If you make
assumptions about how people in the market behave, and put those assumptions inside
the simulation, you can see whether behavioral theories at the micro level add up to
observable market behavior.
A lot of academic research has focused on the issue on how to
define risk. You even suggested the measure of semi-variance in your 1959 book. You
observed using variance as a risk measure assumes symmetry. For example, if there is a
potential for a very large positive return, the variance of an asset might increase. But that
is not to say that the probability of incurring a loss is higher for that asset. Where do you
see future work on modeling risk going now that people are talking about things such as
value at risk, skewness, fat tails, or even the entire probability distribution? Do you think
that there is something that will turn out to be valuable and will become feasible as
computing power improves?
Let me tell you what my view was, and has been from 1959 to
approximately the present, about justifying mean and variance, or selecting among
alternate criteria for measures of risk. As of 1959 I was convinced that the proper way a
rational decision maker should act was to maximize expected utility using personal
probabilities. In other words, I had been thoroughly brainwashed by Leonard J. Savage’s
Foundations of Statistics. I say to approximately the present as I haven’t really stopped
and decided what to think about some of the recent objections to expected utility such as
that presented by our colleague Mark Machina.
As a working hypothesis let me continue right to this moment, and will on to my
dying day believe in expected utility and personal probability. So if I really believe in
personal probability, what probability distributions are we talking about? And if I believe
in expected utility, how come I’m out peddling mean and variance?
As you say, in Chapter 9 of my 1959 book I propose semi-variance as an alternate
to mean and variance. However in Chapters 10, 11, 12, and 13, I explain to the reader
what expected utility and personal probability are. I then do some experiments where I
say, suppose you only knew the mean and variance of a portfolio, how good would you
do at guessing what expected utility was? If the probability distribution wasn’t spread
out too much, for example, if most of the probability distribution was between a 30
percent loss and a 40 percent gain, then the quadratic approximation to the utility
function was quite close and the mean variance guess is quite close to the actual expected
I once gave that response at Hebrew University and Marshall Sarnat said, let’s test
Harry out. Let’s get lots of historical distributions of returns, and lots of utility functions
and see if the quadratic guess is close. That effort resulted in the 1979 Haim Levy and
Markowitz paper which reached the conclusion that for many historical distributions of
returns, if you know mean and variance you can guess expected utility quite close. But if
you look at the actual approximation, if you draw the quadratic approximation and the
utility function, you see that the thing that makes this work is that, again, over a range
from 30 percent loss to 40 percent gain the approximation is quite good. However, if you
imagine a situation where somebody could lose more than 30 percent of a portfolio or
could gain more than 40 percent on the portfolio, then the mean variance approximation
breaks down.
Is there is something we can replace it with which is convenient and
understandable? People understand mean variance. They may understand it for the
wrong reason, but you know they feel warm and fuzzy about mean variance and use it.
So if you could get something else like mean and semi-variance, or value at risk-although value at risk is usually just mean and variance again. This is an exciting
question that you asked. I don’t know the answer, but if I were starting all over I might
want to do another dissertation in that field.
I am wondering if there are any weaknesses in the current
economic structure to bring about a catastrophe like we saw in 1929?
You know, we just don’t know. Every now and then I get a letter
where somebody will say, I am with a brokerage firm, and I give financial advice based
on the efficient frontier. I am having a discussion with another broker who also uses the
efficient frontier to give financial advice. The guy thinks they should only use returns
from 1950 onward, and his colleague thinks they ought to use the whole history from
1926 onward that is available, including 1929, 1930, and so on. I reply that I am not one
to predict, but I feel that nature is picking from a probability distribution, and somewhere
in that probability distribution there is another 1929. Maybe it doesn’t have exactly the
same frequency as its historical frequency. But I would feel happier to do an analysis
based on some kind of an estimate that there is a 1929 still in the bag.
Dr. Markowitz. One of the interesting things is that you used your
background in statistics to work in other areas, like finance, which ultimately led to your
Nobel Prize. In that spirit, do you have any advice for this generation as to how they
should proceed in terms of finance? Are there any particular areas that you think should
be associated with the world of finance, economics and statistics that might not be
explored yet?
Yes. In the first place, as a practical matter if you’re going to be a
professor of finance these days and publish in the best journals, like the Journal of
Finance, you better know a lot of continuous time mathematics. And that, I must
confess, is very difficult for me. I wasn’t taught it, and it was very hard for me to learn it.
I am still not very good at it. I am not facile with lots of subjects that people publish
these days. But you should be adept at that.
On the other hand, while it is all very nice to have that facility, I hope you do not
lose sight of philosophical issues when dealing with uncertainty. I recommend that you
read Descartes’ first Meditation, Hume’s On Human Understanding, and certainly you
have to read Leonard J. Savage’s Foundation of Statistics. You should know about those
kinds of things. I think technique is great and important, and I am sorry I am having
trouble keeping up with the big kids these days on all this continuous-time math.
However I think we should also remember that the basic subject is how to deal with
It is tricky enough to come up with an efficient frontier if you’ve got historical
time series. But from a practitioner’s perspective, how do you deal with something that is
totally new. And, in particular, China. Assume you are trying to advise people on what
to invest in there. You have very risky investments where you do not know the expected
returns, standard deviations or covariances. Well let me tell you what you’re supposed to
do in theory, what Leonard J. Savage’s rational man would do, and then let me suggest
approximately what you should do in practice. Savage would say that somehow you
would make estimates of likely return and standard deviation and then do an expected
utility analysis. I would do a mean variance analysis with those beliefs, and then
somehow the result would reflect the fact that there is an investment opportunity but also
a huge uncertainty. Presumably the answer would be to put a little here and a little there.
So that is how it goes in theory. In practice, I just put a little here and a little there.
I would second that and note that in the Merchant of Venice, the
merchant was trading with China So not all your eggs in that one boat.
Dr. Markowitz. In my first economics class I learned about Adam
Smith and the famous invisible hand theory. Toward that end, do you believe that theory
has played a part in how the morality of the securities industry has gone? In addition,
how do you think that economists should assess risk in light of that morality?
I think markets need regulation. To a certain extent businessmen
rely on each other’s word, but also they rely on laws which are appropriate. So subject to
the constraint that there be reasonable laws and somebody there to enforce it, I do believe
in the invisible hand, I do believe in Adam Smith, the division of labor and so on.
Now you didn’t ask, but I will volunteer how portfolio theory fits into this, and
then we’ll get back to your question about uncertainty. People are competing to serve the
same market, or to find a market niche. However once somebody finds a market niche
other people will come in and try to outdo them. That has two consequences. One is that
everybody has to try very hard. As Adam Smith explained, the butcher, the baker and the
candlestick maker all do good jobs so that you will come back to them. The other thing
is that if you want to invest in one of those people, you do not know who is going to win.
So the flip side of the invisible hand is the uncertainty that competition causes, and that is
why we diversify our portfolios.
I think that uncertainty has always existed and continues to exist. From the
middle 1950s on there are new uncertainties that have to do with the possibility that the
human race will wipe itself out, and that civilization as we know it will disappear. But
ignoring that scenario I think the same uncertainty persists today as it did in Antonio’s
time. So don’t trust all your goods in one bottom.
With that, Dr. Markowitz, we thank you very much and wish you a
good evening.
Second Interview taped at the Office of Dr. Markowitz
Your work has had a remarkable impact on practice. What are
your reactions to changes in the industry that have taken place?
I seem to have specialized in theoretical things which then became
practical. One way to measure whether theoretical things in operations research in fact
contribute to the theory of rational behavior under uncertainty is to see if they are used in
Where did you get your interest in practice? You probably didn’t
get that from your academic training in economics.
No, that is interesting. It was somehow an axiom in my system. I
mean I don’t know where it came from, but all my life if nobody used a discovery, I
wondered why it wasn’t used. It is sort of like in physics. If you have a hypothesis you
test whether the hypothesis predicts something that the other theories can’t predict. In the
case of operations research the goal is the development of a technique which somebody
can actually use.
Were you trained in operations research or just in economics?
No, I picked up OR. I was trained in economics, and I got a degree
in economics. I think operations research was already in existence in England someplace
at the same time I was getting a degree in economics. But when I went to The Rand
Corporation for my first job they were doing theoretical things which were supposed to
actually help the Air Force. So maybe that is where it came from.
For years I thought of you as an applied micro economist, but I did
not understand the extent. Now I am picturing you going to a grocery store looking for
bananas and actually calculating marginal utilities as micro theory assumes. But if you
do that, you are the only one I know who does.
Right. No, no. There’s a disutility to keeping records or doing
calculations. I never charge my clients for my small travel expenses like taxis, because
they pay me enough anyway and besides keeping track of taxis is a great disutility to me.
Okay, fair enough. So you have a cost perspective on this.
But the field of portfolio selection has in fact become very applied.
Did you ever anticipate in your wildest dreams that your work would have this kind of
impact on the way people manage their investments?
Strangely yes and no. I guess now that I think about it, when I was
sitting there in the library at the University of Chicago, where these ideas first arrived, I
thought that people could actually use this. But to think that billions of dollars would be
managed using this method, that really didn’t strike me.
At the time you did your work I think the custom was to buy
individual stocks and perhaps hold five or ten if you wanted to diversify.
That was one of the things I read. As I said last night I got a
reading list from Marshall Ketchum. Graham and Dodd was on the list as was John Burr
Williams’ Theory of Investment Value. One of the other things on the reading list was
Weisenberger’s Investment Companies. There were scores, if not hundreds, although not
thousands of companies.
Not thousands? There weren’t more investment companies than
there were securities as there are today?
Not as there are today, right. But there were lots. And they held
lots of securities, and they subdivided their holdings. They had a sense of covariance.
Did you interpret existing investment companies as primarily
diversification intermediaries?
Yeah, that’s what I thought. The practice was there, but the theory
wasn’t. In other words, if you take John Burr Williams, it doesn’t imply the kind of
behavior that these investment companies were following.
Part of your computational effort focused on linear constraints on
portfolio choice and nonnegativity constraints. What is your reaction to the change in
institutional structures, for instance securities lending programs, that make it easier to
short sell securities, or options and futures contracts that make negative positions easier
to execute today.
Even if the computer program is set up so that variables have to be
nonnegative, you can still represent short sales. You just have two variables. One
variable represents a long position, and the other variable represents a short position.
That way short positions can be included as is assumed in CAPM, or in the more realistic
way that shorts are constrained in the real world by virtue of Reg T. For example, the
paper “Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions” by
Jacobs, Levy, and Markowitz in Operations Research, July/August 2005, addresses
optimizing portfolios that are subject to Reg T and contain both long and short positions.
There are actually a couple of versions of CAPM. One is the Sharpe-Lintner
CAPM which assumes that securities holdings are nonnegative but you can borrow or
lend all you want at the risk free rate. The other CAPM probably dates back to Bill
Sharpe. It is hard to track down exactly where this comes from, but this CAPM assumes
your only constraint is the sum of the holdings equals one. Actually, that goes back to
Roy. He was the one that made that assumption. He was a little apologetic about it.
Now they don’t apologize. They just make the assumption. That assumes, for example,
that if you have a weight of minus 5,000 and a weight of plus 5,001 that is feasible
because the weights add up to 1. If you think that is realistic, call your broker and say, “I
am sending you a thousand dollars. Would you please short a million dollars worth of
…” and so on. Reg T says that if you think of a short as the negative of a long, then the
sum of the longs plus the absolute value of the shorts must be less than or equal to 2.
There are two choices when you are dealing with nonnegative variables. I don’t
want to get into technical details, but if you want to see the technical details get my 1987
book on Mean Variance Analysis and look in Chapter 2. It explains how to represent
both of those kinds of shorts with nonnegative variables.
The bottom line, I guess, is that you think this can be implemented.
Yes. In other words, you can make a portfolio of any of those
kinds of securities, and the method of using linear constraints with linear equalities and
nonnegative variables turns out to be very flexible as the linear programming folks have
shown. We have a linear programming type constraint set, but we have different
You mentioned the CAPM. What is your reaction to using the
market portfolio as a dominant portfolio strategy in combination with risk free borrowing
or lending?
First let me say two things. The CAPM is a thing of beauty. With
a little poetic license it turns out some very neat results. That is thing one. Thing two,
you will be talking with Bill Sharpe pretty soon, and Bill Sharpe and I have had a long
and lasting friendship. One of the fun things about this long and lasting friendship has
been a long lasting argument about the CAPM.
I may be the only one in the profession who still has reservations about the
market portfolio. Let me illustrate on the blackboard. Suppose you make all the other
assumptions of CAPM, like everybody’s a mean variance optimizer, everybody acts
rationally and everybody has the same beliefs, but you give up the assumption that
anybody can borrow all they want at the risk free rate, or can short sell without limit and
use the proceeds, not just for collateral and collect a bit of the interest on it, but can
actually take the proceeds from the short and buy long. If you cannot give your broker a
thousand bucks, short a million dollars and take the million plus a thousand and buy long,
if you don’t make either of those two assumptions, then it turns out that the market
portfolio is not necessarily an efficient portfolio, and in fact is typically not.
I’ll give you an example of why that’s not true. I’ll use an example in which
there’s no shorting and no borrowing, that’s the easiest to draw a picture of. But it also
works if you allow shorting but the Reg T kind of constraint on shorting. It has to do
with whether or not you hit a boundary as you move along the efficient frontier.
[The following example is from the Markowitz article on “Market Efficiency: A
Theoretical Distinction and So What?” Financial Analysts Journal 2005. September 2005
pp.1-14. Dr. Markowitz recommends that you read the article and skip to the next
Let me show you a simple example of that. Let X1 denote the fraction invested in
the first security. I’ll plot that on the horizontal axis. Let X2 denote the fraction invested
in security two and plot that on the vertical axis. This will be a three security example
but you just have to remember that X3 is equal to 1 minus X1 minus X2. Add the
constraint that X1 is nonnegative, X2 is nonnegative, and X3 is nonnegative. That means
that you have to be in this triangle which has these points as their vertices. If you are
below the line, X2 is negative, if you are left of the axis, X1 is negative, and if you are
above here, X3 is negative. So you got to be on or in the triangle.
Somewhere on this page is a portfolio with minimum variance. It might be here,
or it might be there. You get the same conclusions but I have to draw it someplace, so
I’ll put it here for example.
From CAPM theory we know that if this were the only constraint the set of
portfolios which minimize variance for various levels of expected return would all lie in a
straight line. So somewhere in this plane there is a straight line that represents the set of
all portfolios with minimum variance for a given level of expected return. In one of these
directions expected return decreases, and in one of these directions expected return
increases. It could be either, but we’ll say expected return increases in this direction. So
the set of efficient portfolios goes from the minimum variance point out forever along
that line. This is the way the set of efficient portfolios looks if this is the only constraint.
Now suppose you can’t let X2 be negative. At the X2 boundary you can no longer
continue on this line.
In general, for any system of linear constraints, the set of mean variance efficient
portfolios is piecewise linear. It goes in one straight line until it hits a boundary, and then
it goes in another straight line, and so on. Each corner point corresponds to a new set of
active variables. Lines connecting corner points are called efficient segments and
represent mean variance efficient portfolios that share a common set of active variables.
CAPM is a special case with just one corner portfolio, and it has just one efficient
segment that keeps going forever. In the more general case the efficient frontier looks
like this. [Indicating a piecewise linear figure.]
Suppose there are some old guys, like us, who want a fairly conservative
portfolio, and there are some younger guys who want a fairly aggressive portfolio. The
market will be on a straight line between their portfolios. The market will just be an
average weighted by our respective wealths. So the market will be somewhere like that.
[Indicating an intermediate point.] But the market is not an efficient portfolio for the
CAPM guy or for us. If you look in my 1987 book, Chapters 11 and 12, you will see
examples where the market has roughly maximum variance for its expected return rather
than minimum variance for its expected return.
It is also not true that expected returns are linearly related to beta, as measured
against the market. To see that suppose you ask if the expected return for these three
securities are linearly related to the covariance between the return for the security and the
return for a given portfolio. The only time the answer is yes is for a portfolio that is
efficient in the CAPM sense. So it is not true that expected returns are linearly related to
beta as measured against the market. So CAPM is a lovely theory, but it takes a little
poetic license to get neat conclusions. One should remember that if you don’t take those
particular poetic licenses you don’t get the same conclusions.
Is there a role then for institutional fund managers to attempt to
solve this constraint problem for individuals through specialized mutual fund?
The big problem is how to estimate return distributions. But if we
all had the same means, variances and covariances then in this example there should be
three mutual funds. There should be one here, one here, and one here. [Indicating one
for each corner portfolio.] These guys will mix between these two funds. These guys
will mix between those two funds, and the guy who offers the market portfolio won’t
make any money in this world with nonnegativity constraints.
But if an institution could solve the constraint problem, and get
them in effect a negative value for X2…
[The following answer is also from the Market Efficiency: A Theoretical Distinction and
So What? article. Dr. Markowitz again recommends moving on to the next question.]
Let me change the question a bit. Suppose there was one guy who
could make X2 negative. Suppose he has access to a warehouse where they keep
securities. He goes in the middle of the night and he “borrows” the securities and he sells
them. And as long as he covers before the auditors come in 30 days, it’s okay. So as we
move out this direction, we have higher expected return and higher volatility, and he’s
obviously a risk taking kind of guy. So he can choose a portfolio here. He could have
that portfolio if he wanted it.
Now one question you surely want to ask is the following. Since this is inefficient
and this is efficient, shouldn’t he go short the market and long the efficient portfolio, and
won’t he drive away the inefficiencies that way. Well if in fact he goes short this and
long that, then he will be on a straight line between the market and this portfolio. And
because he is short this and long that, he will actually be out further. So that is not an
efficient portfolio for him. He should just forget about the market. He is not going to
short the market. Now if we add him to the mix, what happens to the equilibrium? Well
it’s going to be somewhere between here and here. If it is down here that can’t be an
equilibrium because it has a negative amount. In this economic equilibrium the supply
and demand market solution is going to happen somewhere up here, and it’s not going to
be efficient. It could get close, but it won’t be mean variance efficient. It won’t be
CAPM efficient in any case. You could maybe get a little closer to this particular
efficient portfolio but…Anyway, so approximately a hundred percent of equilibrium
theory is built on the assumption that you can short and use the proceeds, and I think
there is a great field of daisies to be picked if you drop that assumption.
Okay, if we do drop that assumption, what would be your advice
for someone just starting out with, say, $100,000 to invest?
There are two versions of that question. The straightforward one is
if you just have 100,000 and nobody is offering you any special services like are now
being offered the 401(k) participants, what should you do? In that case, I would put some
in a broadly diversified investment company. That has been my routine answer for the
last 50 years. But maybe now I would switch to an ETF or an index fund.
Maybe? Or do you prefer the index fund?
I think so. I would look at the costs, but I would go passive.
And how broad is broad? S&P 500? Dow Jones Wilshire 5000?
I would go with the more the merrier, but the S&P 500, or the
spiders, are good enough.
Are you thinking of the market model idea, or is there something
Now that’s a good point. Here I am advising the market portfolio,
and I say the market portfolio is not efficient.
Do you want to change your answer?
Right…No… That’s my answer, and I stick with it. Let’s go
back. I want to make sure I said that you put part of your money into the spiders or index
fund and part of your money into something less volatile. To determine the mix you
should look at a picture of the S&P 500 since 1926, or something like that. And, if push
comes to shove, I’d say maybe you ought to a have a little small cap, so maybe the 3,000
or the 5,000.
One of the broader indices?
Yeah, one of the broader indices. As a practical matter, if it is just
the person by themselves without an advisor, then this is better than they are likely to do
otherwise. It’s certainly better than having them listen to the television set, or having
them invest in whatever did really well last month or last year.
Or whatever did really poorly?
Yeah, maybe, or even having them invest in whatever did poorly,
Over the years, a lot of strategies have been associated with your
name. I recently came across one rule for determining the allocation between risk-free
and risky assets. I am virtually certain this strategy should not be attributed to you
because I believe you have always claimed that that is a subjective matter. The rule
states that you are supposed to take your age and subtract that number from 120 to
determine the percentage investment in risky assets.
Yeah, that is not my rule.
You do not subscribe to any particular guidance as to how much
money you should keep in relatively safe assets versus risky assets.
No. I do not have a set number. I think there is methodology
around which will help you choose a number, but that will vary from person to person.
And not necessarily be indexed by age or circumstance?
And not necessarily be indexed by age or by circumstance. There
are studies that show that if you end up at retirement time, at age 65, and you put all your
money into bonds or cash, you’re going to have a lot of trouble if you live to 85 or
something like that. So these 401(k) advisory services now do Monte Carlo simulations
to see how well you would do if you followed various strategies, both up to retirement
time and beyond retirement time. I think that can contribute to good decisions.
Are you talking about a tax advantage? Or, is there something
beyond tax advantage?
It’s not only tax advantage. Let’s go back to an earlier question
where I said I would give you two answers to the question of what somebody should do
with 100,000 bucks. One answer was with advisor, and one was without advisor. I said
that without an advisor an investor should look at a chart of the long term performance of
a broad index and decide how much to put in the broad index and how much to put in
cash. I lean toward spiders because they are more liquid than some of the others, but a
broad index would be good. But maybe an investor can do even better with an advisor. I
want to say Gary Brinson, okay?
So what does that mean? What is it code for? Well it is code for thinking in
terms of asset classes. For example, we have found that on the average over the long run,
small caps tend to have higher return than big caps. And emerging markets have
somehow managed to have very high returns on average, but they also are tremendously
volatile, and so on. So if you ask what combinations of asset classes, subject to realistic
constraints, are efficient for the plunger, and which are efficient for the widow and
orphan, you get a frontier.
But we don’t necessarily use historical means and variances. When I helped
advise people I noticed that if you plot historical means against historical standard
deviations they fall on a fairly straight line. CAPM says that if you plot expected returns
against betas they will fall on a straight line. However when we plotted expected returns
against standard deviations, they fell on a fairly straight line except that emerging market
return was higher than the line. We said that bothers us, and we just moved it back down
to the line and said, “Okay that’s our estimate”. We’ll put in some constraints, we don’t
want to stick our neck out too much. That is what I am saying when I think an advisor
can come up with asset class mixes some of which more suitable to one kind of investor
and some are more suitable to another kind of investor.
One thing that is exciting to me has to do with the history of using mean-variance
analysis in an asset class context. That started out being used primarily by institutional
investors. They would invest in asset classes, either passively, or by trying to find
managers that could outperform the benchmarks. Then in about 1990 Randy Moore
founded something called Frontier Analytics which computed asset class frontiers. They
peddled the software to financial advisors, and they tell me there are 25 to 30 thousand of
these little subscriptions out there for financial advisors who are generating frontiers for
Then of course there is the business which Bill Sharpe created. Bill Sharpe has
made many contributions, most of which I don’t argue with him about. Fortunately we
have this one thing we can argue about. That’s very pleasant. But one of his great
contributions was Financial Engines for providing 401(k) advice. In addition I happen to
consult for a firm called Guided Choice, which is a rival. We conduct mean-variance
analysis, subject to realistic constraints, and we come up with the asset class portfolios. I
think that is how Bill does it. That is certainly how we do it. We then implement the
model for some combination of the actual investment companies permitted by the
particular pension plan. So I think that those applications are useful.
Now if you had someone who could tell you what the world
market portfolio really was in terms of all these asset classes, is that information an
individual investor should be aware of?
Well it certainly wouldn’t be bad to know about it, but I think there
are better alternatives. If you have the widow and orphan, the guy getting close to
retirement, and the businessman that doesn’t need the money anyway but would like to
make as much as possible, then I don’t think the proper solution for all three is to just
combine the world portfolio with either borrowing or lending. I think there is a better
efficient frontier for them.
So you are not a believer in a super separation theorem.
No I’m not. The super separation theorem happens under special
Moving on to your background, while I haven’t talked to him yet, I
have read where Professor Sharpe credits you with pointing him in the particular
direction that led to his share of the Nobel Prize. Is your recollection similar to his?
Well, I was working at The Rand Corporation, we figure about
1960, so it was after the 1959 book was out. A young man presented himself at my door,
at Rand and said, “I also work at Rand Corporation. My name is Bill Sharpe and I am
trying to get a PhD at UCLMARKOWITZ: My Professor, Fred Westin, said why don’t
you ask Harry? They had read my 1952 article, and Fred Westin suggested that Bill
come over and ask me for a suggestion about a dissertation topic.
One of the problems that bothered me in the book was that there were so many
covariances. With even 500 securities it would mean 500 squared divided by two
covariances. That is too many to have a team estimate them one at a time. I suggested
essentially the one factor model on pages 97 to 100, roughly, in my 1959 book. So Bill
and I talked about the problem of too many covariances and the one factor model. That
led to his 1963 article about the simplified model of portfolio analysis, something like
that. But I had no input to his ground breaking, earth shaking, 1964 article about CAPM.
You didn’t suggest that he look at the market implications?
No. That was his ideMarkowitz: One of many of his ideas.
All right. Well if a new PhD want-to-be were to show up at your
office and have similar interests and similar enthusiasm. What direction would you
Well, first I’d find out whether he wants -
- to win the Nobel Prize? Did I add that part of the question?
Oh, well, then you have to do something new. I can start him in
some direction, but he will have to find a whole new dimension. The right one will find a
whole new dimension that will get him the Nobel Prize. But what gets published these
days is work on continuous-time models. Bob Merton is wonderful with this kind of
model. So if he is going to get published in the best journals, like the Journal of Finance,
he should learn continuous-time mathematics at a rigorous level.
On the other hand, in terms of something new that is fun, I was showing you
earlier today the output of this asynchronous market model where we could have
thousands of investors of different types, and maybe some day when we go to super
computers we could have hundreds of thousands or millions of investors, and they could
be following different kinds of decision rules. As I showed you, depending on the
balance between those who are essentially following price sensitive and price nonsensitive strategies, you can get very wild markets, or very tame markets, or markets that
look like real markets with no news or anything like that. I think that is an exciting
direction which I hope to persuade people to follow.
I was fascinated.
Well thank you.
You have made a number of phenomenal contributions and won all
kinds of awards including the Nobel Prize. Of all the papers you have read that other
people wrote - so excluding your own contributions - are there any papers that you
secretly wish you had written and could tack onto your vita?
Well, yeah, that’s interesting. Are we talking about finance
Finance if there’s one that comes to mind, but if another one comes
to mind in a different area, feel free to mention that.
If somebody asked me what they should read from any field, I
would say, Descartes’’ first Meditation, and Hume’s Essay on Human Understanding.
But getting a little closer to home, I think Leonard J. Savage’s Foundations of Statistics is
one of the great pieces of all times. Of course George Dantzig’s, simplex algorithm or
the solution to the traveling salesman problem. There are all sorts of things. Lots of
great works.
As a twist on the last question, looking forward are there any
particular unsolved problems or puzzles that you wish you had solved or hope that you
can solve in the future. Again, it doesn’t have to be finance, finance is one that comes to
mind, but any field.
Well the big problem in finance is illiquidities. You know with
continuous time or no continuous time, if you have perfectly liquid markets then we can
somehow find optimum solutions, or approximations to optimum solutions. But when
there are illiquidities, and changing probability distributions, and so on, then problems
get really hard. I have this Financial Analyst Journal article on “Single-Period Mean
Variance Analysis in a Changing World” that offers a hypothesis about a heuristic that I
think would help out there. Maybe somebody else will get a great insight into the
problem. Going back to your original question about what do I wish I could do, I would
like to add to the great monumental works on programming by Ralph Gomory and others.
Perhaps somebody of that caliber would have some insight into the illiquidity problem
and advance our knowledge beyond just a next best heuristic.
You have had a phenomenal career in research, teaching and
consulting. If for some reason that hadn’t panned out, so your committee had absolutely
refused to give you a degree, and no one would hire you in that field, what would have
been your back up choice for a career?
Oh that’s interesting. That’s funny. I never was good at backup
choices. For example, I only applied to the University of Chicago. Usually people apply
to lots of places, but my family had always spoken as if I were going to go to the
University of Chicago, and I didn’t apply to anyplace else.
When I was in high school I read philosophers like Hume, and I read science like
physics and astronomy at a popular level, you know, the A-B-C of relativity kind of
thing. When I applied to the University of Chicago, they said my marks weren’t very
good. That was because I didn’t do some of the repetitive homework like the exercises in
algebrMarkowitz: Homework in algebra was very repetitive, and I just typically didn’t
do it, except for the last problem that the A students couldn’t get. They would come to
me and I would solve it for them. So I’d do well on the test, but I didn’t do very well on
the overall course.
I wrote to the University of Chicago and told them the kind of things I had read,
and they wrote back saying they usually didn’t take people who were that far down in the
standing in their high school. But they would allow me to take the entrance test. When I
took the entrance test not only did they let me into the University of Chicago, they said I
didn’t have to take the survey course for the physical sciences because I had already
learned as much as they would teach in that course.
At that time, the University of Chicago gave a bachelor of philosophy after
completing two years of survey courses. When I got to the end of the two years I had to
decide what department or division I wanted to go into. I had forgotten that I really liked
physics and astronomy. I had taken an economics course recently that seemed to titillate
me with both the math and the rigor.
So I went into economics.