This
interview was first published by the Global Association of Risk Professionals
on February 14, 2013

It
is an enormous challenge to gauge a developed market and an emerging market in
the same light. To start with, the way pensions have developed, they have
emerged as the core of the welfare system. Secondly, the defined benefit
pension plans have failed in the countries of the West. Thirdly, large
companies like General Motors and Ford are just pension-generating companies,
nothing else. Fourth, governments organize pensions based on an average
mortality.

No.
Look at the equity-based contribution schemes that are now very popular in the
developed nations. They often force people to liquidate everything at
retirement date and buy an annuity. If the market is down in a particular year,
and equities form 40% of the pension, then that is enormous risk. I would say
this has to be removed soon.

One
thing that should not be done is setting up a defined benefit scheme. Because
you can never guarantee payoffs at the end of 5, 10 or 30 years. But what one
can do is pool all the knowledge and best practices to create a mutual scheme
or a pension scheme. The scheme should be diversified in terms of age of the
participants, and it should have a large base of participants. Then keep
adjusting the payoffs from time to time, depending on changes in life
expectancy and economic conditions. So we aim to get the highest possible
payout in the least expensive way. The challenge is how to set up such a scheme
and make it fair so that, in principle, it is fully transparent to everyone.

There
are different contribution plans that give different choices at retirement.
This has to be put on the table. That is, if one contributes a certain amount
in cash, then something will be done with that cash. It will be invested using
certain strategies that target the highest possible payout. When you retire,
you will get a payoff stream, like that of a life annuity, in cash. There is an
agreement in principle that you get payments only until you die.;;

Yes,
certain countries have certain regulations, and one can operate only under
these regulations. I believe the policy in India is to very much keep pension
funds inside the country. It may be too early now, but there will come a time
when the authorities will realize the advantages of diversifying beyond the
country.

I
use the Benchmark Approach, a kind of more general framework that we have today
in finance. It does not take anything away from existing classical theory. John
Larry Kelly Jr., of Kelly criterion fame, published a paper, in 1956, founded
on maximizing expected portfolio growth based on logarithmic utility and
gambling contracts.

Yes.
Almost 90% of the literature. But I don't believe that the risk-neutral
probability measure exists. In fact, I know that this measure does not exist
when fitting long-term models. Parts of the industry see the problem too, and
that is why the largest reinsurance company in the world is interested in what
I found.

While
we don't take anything away from the classical theory, we go into a richer
modeling world by making a very simple assumption: that there exists a
numeraire portfolio. The numeraire portfolio, when used as a benchmark, makes
all benchmarked non-negative portfolios supermartingales -- their current
benchmarked value is greater than or equal to the expected future benchmarked
values. The greater-than-or-equal sign indicates the crucial supermartingale
property. Since this property holds for all non-negative benchmarked
portfolios, one can say that the numeraire portfolio is the best portfolio in
this sense. It performs so well that when used as a benchmark, it forces all
non-negative portfolios in expectation down, besides those that are
martingales. With the supermartingale property, and no extra assumptions, I can
prove that this portfolio in the long run outperforms any portfolio. It's a
dream portfolio.

If
I look with the Benchmark Approach beyond the classical theory, then there are
some classical arbitrage opportunities in this richer modeling world. However,
these are strategies and portfolios where I have to allow, for certain periods,
some probability to become negative. But I argue that it is not necessary to
exclude those strategies. We should look only at non-negative portfolios,
because, with a notion of reasonable economic sense, when the worth of market
participants becomes negative, then we have to remove them from the market
because they are bankrupt. We take limited liability into account, but there is
no need to look at the negative portfolios and exclude arbitrage for these.

The
numeraire portfolio is very diversified -- the best diversified portfolio you
can build. In principle, it is capturing the non-diversifiable risk of the
market that follows from a theorem that I have. Of course, this clings very
much to the classical theory. Harry Markowitz once told me that I should call
my theorem the Diversification Theorem, which brings all the finance theorems
and principles together.;;

The
strategy of an EWI is to buy low and sell high, and if a market is always
trending up, you get people only wanting to buy and not to sell. But this fund
will sell in such a scenario. On the other hand, if the market crashes, this
fund will buy. So it has a very stabilizing effect on the market. The systemic risk
in the market, with this kind of portfolio on a macroeconomic scale, is
reduced.

The
pension fund must invest in a proxy of the numeraire portfolio. Not just that,
but the numeraire portfolio also gives us a pricing rule. In the
supermartingale world, we call it the fair price process. Let's take a savings
account; and also a proxy of the numeraire portfolio, a benchmark; and let's
benchmark the savings account. Over the long term we get an on-average
downward-sloping fluctuating curve for the benchmarked savings account, because
the numeraire portfolio is going up more in the long run than the savings
account. So this is a self-financing portfolio. Financial planning tells you
that when you are young you should invest in the equity market (the benchmark),
and then in later years fixed income (the savings account).

People
like their pension payouts to be inflation-indexed. That is because the pension
contract is very long-term and much can happen over that period. In my
experience, interest rates are generally a percentage or two higher than
inflation in most economies. It is very difficult over long time periods to get
the interest modeled correctly. So why not take it out completely? What we do
is assume that one unit of payment is equal to one unit of the saving account.
All the payments that you contribute and get later on in your post-retirement
stream are in the form of savings account units. In particular, the targeted
payouts are units of the savings account. So when you purchase your life
annuity, you get rid of the risk or uncertainties from the modeling problems
coming from the short rate. My payout unit is the unit of the saving account;
my basic instruments are the benchmark and the savings account.

The
complexities of pension fund management and maximizing retiree returns are
compounded by "enormous risks," observes Eckhard Platen, professor of
quantitative finance at the University of Technology, Sydney. "There is a
need of a little bit of academic direction to do something about it. There is a
way to do it. Even developed countries need to wake up and say, 'now something
has to be done."Noting
that classical finance theory has not filled all the gaps, Platen brings to the
discussion a "Benchmark Approach" that, in a recent interview, he put
in the context of a numeraire portfolio and how it could be applied to the
practical issues and concerns surrounding pension schemes. At UTS Sydney since
1997 --as a joint appointment of its School of Finance and Economics and School
of Mathematical Sciences -- Platen has been contributing to efforts to improve
the pension system in Australia.

With
a Ph.D. in Mathematics from the Technical University in Dresden and a Dr.Sc.
from the Academy of Sciences in Berlin, where he headed the Sector of
Stochastics at the Weierstrass Institute, Platen has written more than 150
research papers in quantitative finance and applied mathematics, and his books
include "A Benchmark Approach to Quantitative Finance" (Springer,
2006).
This
interview conducted by Nupur Pavan Bang, senior researcher, Centre for
Investment at the Indian
School of Business in Hyderabad, covers the evolution
of Dr. Platen's views on diversification principles and risk neutrality, the
numeraire portfolio and practical approaches to pension investing.

**You do not believe in the classical principle of no-arbitrage. That is the most fundamental principle of asset pricing theories in financial literature.**
In
the early 1990s, when I started working with leading investment banks in
Australia, I was confronted, in practice, with the classical paradigm called
the no-arbitrage pricing theory. Over time, it became clear to me that this
theory is too narrow; the assumptions made are too constraining, and we must
have an alternative that is more appropriate, especially in the case of longer-term
contracts. It just occurred to me that something is wrong. The classical notion
of no-arbitrage restricts too much the modeling world. There is a less
restrictive and economically very reasonable notion of arbitrage that one
should use. In principle, we should be able to create financial contracts and
hedge them in a way that is less expensive than what classical theory
propounds. Over the years, I was able to demonstrate how this is indeed
possible.

**Are pension schemes, therefore, very long-term contracts where you think your theory can be applied?**
Think
of it this way: Governments, companies and individuals contribute to pension
funds. The amount is very big for most of us. As soon as we start earning, we
are told that this contribution is mandatory. The cumulative contribution over
the years is very significant, because if you start earning at the age of 20,
you will end up contributing for 40 to 45 years. Lots can be done with this
money from the time when the contribution is made and the payoffs are really
paid off.

**What are the concerns with the traditional pension schemes? What went wrong?**

The
aging population is a concern in a lot of countries. Let's say people live
longer -- say, 15 years longer on an average. The calculations completely go
wrong. Also, some major industries of some countries or some economies, they
may just decay or vanish. We have seen this many times. For example, if a
pension scheme invests a big chunk of the money in, say, a mining group in
Australia. It could happen that after 15 or 20 years, the mining action shifts to
Africa. What do you do then? So it would be very good if a scheme is widely
diversified, so that its performance does not depend on a single industry or
nation.

**There are many different types of contribution schemes nowadays. Doesn't that solve the problem?**

**What can be done?**

**How can such a scheme be set up?**

This
pension has to be fully sustainable, fair and, of course, globally diversified.
Since the level of payouts cannot be fully guaranteed, it should be a targeted
life annuity. The entitlement depends on how much one paid in -- how many units
of the life annuity one has purchased over time by contributions to the scheme.
The assets and liabilities are matched regularly over time, using what I call
real-world pricing. They are adjusted periodically, based on the latest
mortality figures and model adjustments available.

**In some countries -- for example, India -- the regulations do not allow for global diversification of the pension pool.**

**Can you explain your approach in more detail?**

In
July 1990, theJournal of Financial Economics,a mainstream finance journal,
published "Numeraire Portfolio," a paper by John Long Jr. This is a
portfolio which, when taken as a "numeraire" or a benchmark, and some
given portfolio is denominated in units of this benchmark, then the current
benchmarked value of the portfolio is greater than or equal to its expected
future benchmarked values. Using this insight, we can potentially get a fair
benchmarked portfolio process, forming a so-called martingale, where the
current benchmarked value is equal to the expected future benchmarked values. I
am suggesting to search always for this least expensive portfolio to hedge
future payoffs. When doing this, use the real-world pricing formula, assuming
that there exists a numeraire portfolio -- the benchmark -- and the
expectations are taken under the real-world probability measure that models
future change.

**Doesn't most of the financial literature use a risk-neutral probability measure?**

I
can tell you that I am a non-equity premium puzzle person, because the modeling
world that the Benchmark Approach provides is so rich that a high equity
premium is not a puzzle at all. It's like you want to force a classical
risk-neutral model [to calculate a risk premium] onto something where, in
principle, you should accept and use the observed risk premium, which is higher
than the classical theory allows. It is just another indication that the
classical theory is too narrow.

**How does your theory compare with the classical theory?**

It
is also the portfolio that maximizes the expected logarithmic utility. It is
growth-optimal. It's a portfolio that in the shortest time reaches a certain
level. It is the portfolio that cannot be systematically outperformed in any
time period by any other portfolio. All these properties are model-independent
and, thus, very robust. In fact, even the Indian market, if you take a close
look at it as an investment universe, has its own numeraire portfolio
somewhere, extremely well-performing. The question is just to find and
construct it.

**How do you account for the down side?**

This
supermartingale property is also in this respect very elegant and powerful. It
provides the simple mathematical conclusion that any non-negative
supermartingale that reaches zero will never get out of zero. In this sense,
one cannot create out of zero capital some positive wealth with a non-negative
portfolio. This type of arbitrage, called strong arbitrage, is then
automatically excluded in the wider modeling world of the benchmark approach.

**How do you construct the numeraire portfolio?**

Using
this diversification theorem, I create, in its simplest application, an equally
weighted index (EWI), equi-weighted over companies, industries and countries.
This index has a higher growth rate and higher Sharpe ratio (as well as lower
volatility) when compared to the index weighted by market capitalization. It is
a better proxy for the numeraire portfolio than the market-cap-weighted index.
It can be used directly in portfolio management, as a best performing
portfolio, as a benchmark.

The
larger the number of companies, the closer we get, in principle, to the numeraire
portfolio. The fundamental Law of Large Numbers is at work here. The market
needs to be well securitized, which is a very simple and easy condition. In a
well-securitized market, with an increasing number of securities, the sequence
of equally weighted indices is a sequence of approximate numeraire portfolios.
This is something that is covered by the Naïve Diversification Theorem.

**How does the numeraire portfolio work as an investment strategy?**

Then
there are people who might say, "All this is good, but what about
transaction costs?" At 40 or 80 or even 200 basis points, the performance,
of course, goes down but this portfolio still performs better than the
market-capitalization-weighted portfolio. The Sharpe ratio is still better for
the proxy of the numeraire portfolio. It is a very robust, stable kind of
situation.

**How can the pension fund industry use the numeraire portfolio?**

Using
the numeraire portfolio and the savings account, about which I just spoke, we
can construct a self-financing hedging strategy, where according to some model,
you invest almost everything into the numeraire portfolio when you are young
and then slide over, in a precisely defined manner, to the savings account over
time.

**Does this portfolio take care of inflation? In a country like India, where inflation is on the higher side, people are worried about the time value of their money.**

Current
actuarial methodologies focus primarily on modeling the interest rate evolution
to value pension funds and life annuities. Several developed countries have
moved to a zero-interest-rate regime. This creates problems for the growth of
wealth when using classical actuarial methods. Using the benchmark approach and
the proposed targeted pension, one can avoid several of the currently burning
problems. In the design of new pension schemes, one can benefit in several
ways.