Constructing a new model

Randall Lert, US-based chief portfolio strategist at the Russell Investment Group, has a worldwide network of portfolio managers and manager researchers at his fingertips. At the recent PortfolioConstruction Conference, he was asked to overview the new and emerging global trends in portfolio construction.

Lert’s message was this: the traditional portfolio construction model — mean variance optimisation — is starting to fray at the edges, and new methods are emerging.

“There’s an entire class of problems for which the traditional mean-variance portfolio construction model is completely ill-suited to provide a solution. We’re at an inflexion point at the moment in terms of the development of investment technology with respect to these issues,” he said.

Lert identified what he called “three interesting implementation issues” that the traditional mean-variance model does not cope well with in today’s environment:

n active versus passive investing;

n alternative asset classes, and regional versus global portfolio structures; and

n an emerging new portfolio objective for the retiree demographic.

He said the latter is one “the current model fails to address in any meaningful way whatsoever”. Here, in an excerpt from his address, Lert outlines these three implementation problems in detail.

Problem 1: active versus passive investing

The Markowitz theory of portfolio construction boils down to an optimisation problem. We seek the correct weighting of the assets we are contemplating putting in a portfolio, given Lambda, a risk aversion parameter. Most of us have seen this in the form of the traditional efficient frontier (see figure 1, page 28, MM, Oct 20, 2005).

You solve the equation for different levels of risk aversion to produce portfolios, and then you draw a curve between the different points. The best portfolio for a particular investor is the point at which their risk indifference curve hits the efficient frontier.

When I first got out of business school, I found it extremely annoying that my clients did not know the slope of their risk indifference curve because that was always provided as part of a study problem.

But the key problem when investment managers were adopting this in the late 1970s was that computer time was prohibitively expensive. My boss was extremely disinterested in letting me run multiple Monte-Carlo simulations to solve a client’s problem. And therein lies some of the origins of how this model has come to be used in the real world.

Until very recently, computers haven’t been powerful enough to solve real world investment equations. If I want to build a global equity covariance matrix, let’s just say roughly speaking to cover the big names of the world, I’d need information on about 6,000 securities, and hence a 6,000 by 6,000 covariance matrix. There hasn’t been a computer built that can solve that problem, and it’s not really easy to do by hand.

So what happened was we started grouping the problem down to an asset allocation level — we took a group of assets that more or less behaved alike with an expected return and volatility and covariance. We made the problem computationally tractable. But it’s not required by the theory. Yet it persists as the primary application of this particular optimisation tool, with the exception of a handful of what we often refer to as ‘quantitatively-oriented asset managers’.

Another interesting thing about this model is that it is a single period model — its only concept of time is now and then. It takes no account of the milestones we hit in our financial life as we manoeuvre through markets. There’s no multiple periodicity in this particular structure, and that’s a very significant flaw.

Third, by definition, this model is completely incapable of handling assets with non-symmetric return distributions. The mean variance model is predicated on the fact that everything you need to know about a potential investment is encapsulated in its mean, its expected return, and its standard deviation of return. The model is not equipped to deal with assets with non-symmetric return distributions such as options and absolute-return oriented strategies.

And finally, the mean variance model is focused exclusively on the accumulation of wealth. It has absolutely nothing interesting to say about the problem that more and more of us are going to face, which is the optimal depletion of our wealth at retirement.

The arithmetic of how markets operate

Markets can reasonably be modelled as finite entities — that means we can count the participants in a market conceptually. There are only so many people at any one time investing within a market, and if we assume they all want to buy low and sell high, we can come up with a lot of understanding.

But it’s a fact that there are markets where not all investors have the same objectives. The currency market comes immediately to mind, central banks are another example.

Think of this room as a market — all of us are the participants. We’re going to set up a stock market, we’re going to start trading, and we’re all going to have the same objective, being that we all want to make a lot of money. But we’re all going to deploy different strategies to do that. We have homogeneous objectives, but heterogeneous strategies.

The result is that the market will be a zero sum game — it is ‘predatory’. There will be winners and losers, with the winners taking money out of the pockets of the losers. Some participants will under perform in the market while others will outperform.

We’ll also have some people who equal the market return — those are the passive investors. The average return of the room is absolutely going to be the market return — there is no way around that. It is not a matter of market efficiency, it is simple arithmetic. Active management is a zero sum game.

Of course, index fund managers require the existence of active managers, because it is the process of active management that creates both price discovery and relatively efficient pricing for securities.

The conceptual case for active management

For the passive investor, the only way to increase your required rate of return is to increase your exposure to the higher return, higher risk asset. Generally speaking, that’s equities.

For example (see figure 2, page 28, MM, Oct 20, 2005), if I’m a 65/35 investor in active space, and assuming there’s a 4 per cent risk premium for equities and I want to add 100 basis points of return, I need to add 25 per cent equities to my portfolio — that is, I need to jump from 65 per cent equities to 90 per cent equities.

There is a huge increase in systematic volatility from going from 65 per cent to 90 per cent equities — that is, 90 per cent stock portfolios are hugely volatile, particularly compared to 65 per cent stock portfolios. If you believe, however, you could earn that 100 basis points actively, you’d be able to achieve that at much lower systematic risk. The risk you accept instead is the risk of year-to-year under performance — the so-called tracking error.

The argument simply becomes: if we want to increase returns, doing so in the active space is much more risk efficient than by increasing our stock exposure by 25 per cent.

But, you have to believe that either you can pick superior money managers or find somebody who can. If you don’t believe that, you should absolutely invest passively.

Problem 2: Alternative assets

Moving on, when we’re talking in the traditional model, we try to improve the efficient frontier by adding asset classes. We try to keep pushing the efficient frontier further and further up into the northwest quadrant — that is, increase the return for a given level of risk.

But these days, the things we’re adding are very, very, very difficult to model in terms of their impact on the efficient frontier.

Let’s start with hedge funds. In my view, they are not an asset class, but rather a broad term used to encompass an incredibly large group of eclectic investment strategies. Most operate within existing liquid marketplaces, so they’re not an asset class — they’re a different way to deploy active management strategies.

In some ways, they are the purest form of active management currently available. Many hedge fund strategies seek to cut off the left tail of the return distribution — that is, they’re focusing on a non-symmetrical distribution. They’re willing to earn less in very strong markets in order to limit the downside in sideways to weak markets. It’s completely impossible to model that correctly in a mean variance framework.

Private equity funds are another example. Private equity runs in cycles — sadly, most investors choose to buy private equity after everything already looks good in it. It’s not really a good idea to market time asset classes that take 10 to 12 years to realise returns. Like wine, you want to focus on good vintages or have a diversified group of vintages in your cellar — if you’re going to invest in private equity, I recommend you do the same thing.

That said, there are certainly logical reasons to think about adding private equity to a portfolio. But it’s nearly impossible to model private equity in mean variance space. If anyone could tell me what the volatility of a start-up firm is that never goes public, I’d be interested in knowing. Statisticians call this problem with private equity the problem of asynchronous trading, which means the asset is not being sold at a continuous auction. With a continuous auction, we can measure relatively well the volatility of an asset.

Handling these assets within the current mean variance framework is at best an art, and not a science.

Problem 3: Global investing rather than multi-country investing

There’s an emerging idea of creating global portfolios. You may recall that around 25 years ago the early cases were being made for multi-country investing. The rationale was based on the low correlations of returns between equity markets — we could reduce systematic volatility of equities for example, by investing globally. The focus of the research is “how much should I put outside of my home market?”

We had some very primitive international funds developed by the asset management community; inflows occur, and this increased the sophistication of the products developed by the asset management community. So then of course what happens is equity market correlations increase — and asset managers start saying that multi-country investing is not just about diversification, it’s about an expanded opportunity set.

But what we’re seeing now is an important shift in the investor paradigm, from “how much money do I put outside my home market”, which is a multi-country perspective, to “how do I get the best stock portfolio irrespective of company domicile”. That is what global investing is coming to mean.

I really like global investing as a concept. The prevailing equity portfolio structure in the US first splits the universe into US versus non-US assets, and then splits each of those into three different styles, value, core and growth. The prevailing structure in the rest of the world is to create a series of regional equity portfolios, for example, Japan, Pacific Basin, North America, and Europe.

But the emerging paradigm is a series of global managers stock picking across the world. Bernstein has done some analysis on the issue. It has a US strategic value fund that holds 60 stocks and which it claims earns alpha of 3 per cent. It also has an international strategic value that holds 50 stocks, and which returns an alpha of 4 per cent. A combination of the two would hold 110 stocks, and earn 3.5 per cent.

But, it claims, a global strategic value fund can return 4 per cent alpha. How? When you build an efficient US equity portfolio, you’re going to have to own some stocks you don’t like much, just for diversification reasons. But if you build it globally, you can avoid that.

Part of the reason you can’t sell this in the US is that people ask “how do I model that in my asset allocation structure?” It’s another example of a good product that is emerging in the industry that the current mean variance model handles poorly. There’s no reason the model couldn’t handle this — it’s just that nobody wants to modify the model to handle this in an effective manner.

Problem 4: An emerging new portfolio construction objective

In about 10 years, baby boomers are going to be at a completely different stage of the investment life cycle. They’re going to start to ‘decumulate’ rather than accumulate wealth.

But the ‘decumulation’ phase has been completely ignored in a true systematic way by the traditional portfolio construction paradigm. And there’s an additional component to this problem now.

Figure 3 (see page 28, MM, Oct 20, 2005) shows a very simple version of the investment life cycle problem:

n Y equals income (as it always does in economics);

n C equals consumption (and we’re assuming we have a rational person who has kept consumption below income for their entire life, so clearly not from the US);

n R equals retirement; and

n D equals death.

We try to build up our wealth, W, until we get W to the present value of all known consumption, until death. It’s an easy calculation to make. Then we start to run the portfolio down.

In this rather simplistic example, income (Y) stops at retirement — this is why we invest to begin with, so that we have income replacement when we’re no longer capable or willing to earn it any more.

Most significantly, we now have two parameters of risk tolerance — the risk of W, or the variability in ending wealth, and the risk of C, or the variability in required cash flow.

Of course, there’s a point at which if cash flow gets hit hard enough, we drop below minimum consumption standards. This tends to really annoy clients.

So this is a complicated problem with an additional parameter.

Furthermore, it is absolutely not a single period problem — because wealth at time T (that would be today) is a function of wealth at time T — 1 (for example, a year ago), multiplied by what you earned on the wealth then, less what you spent over that period. That means this is what’s called a path dependent problem — we’re going to get a different answer every time we look at this problem.

When you start breaking it down, what this problem looks the most like is a dynamic hedging problem (what we used to call portfolio insurance).

What that means is that at every time period, we would want to reset and re-look at how we would engage in this problem.

When markets have been going well and our wealth is up, we might increase our risk exposure a little bit. When markets are doing poorly, and our wealth is down, we’re going to reduce our risk exposure.

We end up with a non-continuous asset allocation as the actual optimal solution. The traditional mean-variance model cannot do this.

There’s another component to this problem as well. Some risk may be able to be insured — with for example, an immediate annuity. The cost of a lifetime annuity could be modelled as the ‘fail safe’ wealth level that has to be maintained. But then the problem becomes optimising across the annuity.

In my view, over the next 10 years, this is going to be a big issue as the demographics of the developed nations continue to unfold.

The future

The traditional mean variance portfolio construction model continues to be stretched — by issues such as which asset classes to use, and whether to use passive or active investment styles. These will remain ongoing topics of debate in the industry.

The traditional model is heavily challenged by new investment strategies — for example, absolute return styles — that do not fit neatly into mean variance optimisation.

New active investment strategies — for example, true global equity funds — will force us to re-examine asset allocation issues.

And finally, the traditional mean variance model is totally silent on the emerging wave of retiree demographics and how to best build portfolios for them. The emerging wave of ‘decumulation’ is forcing us to rethink portfolio construction entirely.

Deirdre Keown is managing editor of PortfolioConstruction Forum. Full proceedings from the conference are available on www.PortfolioConstruction.com.au.