# Chapter 4: A Nibble from the Free Lunch

### By: Investor Solutions

Spend a little time wandering around the University of Chicago and you are likely to spot joggers with some unusual T-shirts. The shirts appear to have handwriting and scribbles all over them. If you inquire, you will be told that those are the signatures of all the faculty that have won Nobel Prizes! The university is a world-class institution in many areas of study, but in finance and economics it totally dominates. No other institution is even close.

You may also spot T-shirts emblazoned with TANSTAAFL (“there ain’t no such thing as a free lunch”). TANSTAAFL is more than a religion at Chicago. Free lunches are identified and rooted out with the passion and conviction of the Inquisition. At Chicago, it is great sport to debate the implications of tax-deductible lunches, or tax-subsidized school lunches; a true Chicago graduate will deny to his death that there ever has been, or ever can be, a free lunch. Investors everywhere would be well advised to adopt TANSTAAFL as their personal credo. Beware of the salesman offering free lunches!

Harry Markowitz is a very bright star in Chicago’s galaxy of superstars. His Ph.D. thesis laid the groundwork for Modern Portfolio Theory (MPT) and revolutionized finance. Legend has it that Markowitz wrote the paper in a single afternoon in the University of Chicago Library in 1952. The paper was later edited, expanded and published as *Portfolio Selection*, and the contribution earned Markowitz a Nobel prize in economics in 1990.

Ironically, Markowitz’s paper almost didn’t earn him his Ph.D. The review committee had grave doubts about whether it was pure enough economics! That story, and many more about the founders of modern finance and their contributions, is told in the book *Capital Ideas*.

What follows is a simplified description of Modern Portfolio Theory. My aim is not to turn you into an economist, but to demonstrate how investors can use MPT to control risk. If you have an interest in finance and want a further explanation of MPT, I recommend you go to the source and read Markowitz’s *Portfolio Selection*. The book is very readable, even for those of us who are mathematically challenged. Markowitz does us all a great favor by alternating the chapters of text with mathematical calculations.

Markowitz starts out by assuming that we are all risk-averse. He defines “risk” as a standard deviation of expected returns. However, instead of measuring risk at the individual security level, he believed it should be measured at the portfolio level: Each individual investment should be examined not on the basis of its individual risk, but on the contribution it makes to the entire portfolio.

Now comes the great leap forward: In addition to the two dimensions of investment, risk and return, Markowitz considers the degree to which investments can be expected to move together. The third dimension is the correlation of investments to one another (or co-variation).

While Markowitz considered the impact of individual securities in a portfolio, today many advisors use MPT techniques with asset classes in lieu of individual stocks to construct globally diversified portfolios.

Correlation is a very simple concept. If investments always move together in lock step, they have perfect correlation, and that is assigned a value of +1. If they always move in opposite directions, they have perfect negative correlation, and that value is -1. If you can tell nothing about the movement of one investment by observing another, they have no correlation, and that relationship is assigned a value of 0. Of course, two investments can fall anywhere on the spectrum between +1 to -1 in relation to one another.

For instance, many factors will affect all airlines at once. Interest rates, cost of labor, the confidence of flyers, landing fees, regulation costs, and the cost of fuel are very much the same for American, Delta, and United. We would expect that the price of their stocks would tend to move together throughout the market cycle. In fact, the price of the stocks often move together. They are strongly correlated.

Often factors that are good for one industry are bad for another. Let’s look at oil companies and airlines. Fuel is a large expense for airlines. If the price of fuel goes up, we would expect that oil companies will profit, and airlines will suffer. As a result, the price of their stocks should move in opposite directions. They often do. They have a low, or negative, correlation.

So, how can we use this knowledge?

Imagine that somewhere in the world we can find one high-risk, high-return investment. As it goes through the market cycle, it might look like this:

Let’s also imagine another high-risk, high-return investment somewhere else. This second investment has perfect negative correlation with the first. Every time the first goes up, the second goes down, and vice versa.

If we put them together in a portfolio, the combined portfolio will have high return and zero risk! Short-term gains in one holding are exactly offset by losses in the other, but because the underlying trend in both investments is a high return, the combination has a high return.

Time for a little reality check. In the real world, we never find two holdings with perfect negative correlation. But the good news is that we don’t need to. Any correlation less than a perfect positive correlation will reduce the risk in the portfolio! Risk has not been removed: There ain’t no such thing as a free lunch! But perhaps Modern Portfolio Theory offers investors a discounted lunch. Or maybe it’s a free nibble!

The implications of this are staggering. For the first time, investors are able to construct portfolios free of the old risk-reward line. In mathematical terms, the portfolio has a rate of return equal to the weighted average rate of return of the holdings, but the risk may fall below the weighted average of the portfolio!

We have come to the point where we must conclude that where most diversification is good, some is better than others. We get a better diversification benefit by including an airline and an oil company in our portfolio than holding two airlines. Classic diversification reduces business risk. But diversification, in the sense that MPT uses it, can actually serve to reduce market risk. Ideally, we will want investments that combine attractive risk-reward characteristics with low correlation to our other investments.

I must be clear here. I am not looking for an opportunity that simply offers the chance to lose money while everything else is making money. To me that’s just another dumb investment. I think that each investment in my client portfolios must contribute to expected return.

There is another (perhaps even rational and reasonable) point of view. Many practitioners will include an asset like gold purely for its low correlation with other asset classes. This may be a purer point of view. And perhaps this approach leads to a lower portfolio risk. I look at gold’s 20-year low rate of return combined with its high fluctuation (risk), and decide not to waste a percentage of my portfolio on that asset.

The math is very heavy-duty, because for each investment we must factor in an expected rate of return, a risk, and the correlation to every other investment we are considering. The required data grows exponentially as we increase the number of possible holdings. Even worse, for just two assets, we must consider an infinite number of possible portfolios. We all know that we cannot have more than an infinite number of portfolios. So, I will leave it to the mathematicians to decide what happens when the potential number of assets in our portfolio grows over two. Those types of puzzles always made my head hurt. The answer may be closer to Zen than math. In any event, the math cannot be done without some heavy-duty computer power.

Markowitz laid out the math in his paper in 1952, and most people thought he had it nailed. But Markowitz had to wait more than 20 years — until the mid-1970s — to get his hands on a mainframe computer to prove that he had it right. Markowitz confessed that that was the happiest day of his life, not the day he won the Nobel Prize! At the time, a single run of the optimization problem on a mainframe cost as much as a brand-new car. Today, the definition of heavy-duty computer power has changed. You can do the same example on an old 8088 PC in a heartbeat.

In a portfolio of a certain number of holdings, only one possible combination will result in the maximum possible return for each amount of risk we might assume. Markowitz called this optimum combination of holdings “efficient.” Any other combination of holdings will result in a lower return at that same level of risk. These inferior combinations are less efficient. If we graph the efficient portfolios against the various levels of risk, the resulting line of best possible combinations is called the “efficient frontier.” Happily, the efficient frontier falls above the old risk-reward line.

Every point on the efficient frontier offers the investor the highest return for a particular level of risk. But the investor is still faced with an infinite number of efficient portfolios, and must decide how much risk to take. The theoretical answer is this: Select the portfolio on the efficient frontier that is tangent to his indifference curve! I personally think that answers like this give economists a bad name. No wonder we are considered rather boring and a little weird sometimes! Later, I will outline some ways investors might reach a more real-world conclusion to this question. In the meantime, if you should meet an investor who knows where his indifference curve touches the efficient frontier, please have him contact me. I would like to meet him – I think!

The MPT optimization process allows the investor to approach the investment decision from two perspectives. He can start by deciding how much risk he feels comfortable bearing, and then seek the optimum level of return at that point. He might frame the problem like this: I want to be 95% certain (two standard deviations) that I endure no more than a 10% decline in value during any one year. An advisor can then construct a portfolio that has the highest possible expected return within that risk criteria. Or the investor can frame the problem like this: I need to achieve a 12% rate of return, and want a portfolio to do that at the least possible risk.

Is MPT a free lunch? No. But MPT is an incredibly powerful tool to manage risk and construct portfolios to meet various constraints. More than any other person, Markowitz has dragged portfolio management out of the Dark Ages. As we shall see, MPT has substantial limitations, and isn’t a cure for risk. Today, financial management is still somewhere between art and science. But we have come a long way from alchemy. Investors who wish to achieve anything close to an optimum performance must not ignore MPT. The investment problem is multi-dimensional. The days when you could solve the investment problem by wandering into your nearest brokerage and letting the friendly salesman select a few good stocks are long gone. If your advisor isn’t using MPT, get another advisor.

In the next chapter [online May 9], we will examine just how far the MPT revolution has spread, look at some of its practical limitations, and consider two examples that demonstrate concrete benefits for investors.