Against the Gods: The Remarkable Story of Risk (51 page)

Markowitz himself was concerned about obstacles to the practical
use of his ideas. In cooperation with William Sharpe-a graduate student who later shared the Nobel Prize with him-Markowitz made it
possible to skip over the whole problem of calculating covariances
among the individual securities. His solution was to estimate how each
security varies in relation to the market as a whole, a far simpler matter. This technique subsequently led to Sharpe's development of what
has come to be known as the Capital Asset Pricing Model, which analyzes how financial assets would be valued if all investors religiously fol lowed Markowitz's recommendations for building portfolios. CAPM,
as it is known, uses the term "beta" to describe the average volatility of
individual stocks or other assets relative to the market as a whole over
some specific period of time. The AIM Constellation Fund that we
looked at in Chapter 12, for example, had a beta of 1.36 during the
years 1983 to 1995, which means that AIM tended to move up or
down 1.36% every time the S&P 500 moved up or down 1%; it tended
to fall 13.6% every time the market dropped 10%, and so on. The more
stodgy American Mutual Fund had a beta of only 0.80%, indicating that
it was significantly less volatile than the S&P 500.

Another mathematical problem stems from the idea that a portfolio, or the security markets themselves, can be described with only
two numbers: expected return and variance. Dependence on just
those two numbers is appropriate if, and only if, security returns are
normally distributed on a bell curve like Gauss's. No outliers are permitted, and the array of results on either side of the mean must be
symmetrically distributed.

When the data are not normally distributed, the variance may fail to
reflect 100% of the uncertainties in the portfolio. Nothing is perfect in
the real world, so this is indeed a problem. But it is more of a problem
to some investors than to others. For many, the data fit the normal distribution closely enough to be a useful guide to portfolio decisions and
calculations of risk. For others, such imperfections have become a source
of developing new kinds of strategies that will be described later on.

The matter of defining risk in terms of a number is crucial. How
can investors decide how much risk to take unless they can ascribe
some order of magnitude to the risks they face?

The portfolio managers at BZW Global Investors (formerly Wells
Fargo-Nikko Investment Advisors) once built this dilemma into an
interesting story. A group of hikers in the wilderness came upon a
bridge that would greatly shorten their return to their home base.
Noting that the bridge was high, narrow, and rickety, they fitted
themselves out with ropes, harnesses, and other safeguards before starting across. When they reached the other side, they found a hungry
mountain lion patiently awaiting their arrival.'

I have a hunch that Markowitz, with his focus on volatility, would
have been taken by surprise by that mountain lion. Kenneth Arrow, a
man who thinks about risks in many different dimensions and who
understands the difference between the quantifiable and the messy,
would be more likely to worry that the mountain lion, or some other
peril, might be waiting at the other side of the bridge.

Nevertheless, volatility, or variance, has an intuitive appeal as a
proxy for risk. Statistical analysis confirms what intuition suggests: most
of the time, an increase in volatility is associated with a decline in the
price of the asset.10 Moreover, our gut tells us that uncertainty should
be associated with something whose value jumps around a lot over a
wide range. Most assets whose value is given to springing up violently
tend to collapse with equal violence. If you were asked to rank the riskiness of shares of the Brazil Fund, shares of General Electric, a U.S.
Treasury bond due in thirty years, and a U.S. Treasury bill due in
ninety days, the ranking would be obvious. So would the relative
volatility of these four securities. The overwhelming importance of
volatility is evident in the role it plays in fashioning the risk-hedging
instruments known as derivatives: options, swaps, and other instruments
tailored to specific investor requirements.

Morningstar, the Chicago-based service that analyzes the performance of mutual funds, has provided an interesting example of how
well volatility serves as a proxy for risk." In May 1995, Morningstar
reported that mutual funds that invest in bonds and that charge fees
(known as 12b-1 fees) to cover their promotional expenses-fees that
come out of the shareholders' pockets-had standard deviations that
averaged about 10% higher than bond funds that do not charge such
fees. Morningstar came to this conclusion: "The true cost of 12b-1 fees,
then, at least for bond funds, is not a slightly lower return, but a higher
risk investment.... [I]t is the logical consequence of moving marketing costs into the investment equation."

Yet there is no strong agreement on what causes volatility to fluctuate or even on what causes it in the first place. We can say that
volatility sets in when the unexpected happens. But that is of no help,
because, by definition, nobody knows how to predict the unexpected.

On the other hand, not everyone worries about volatility. Even
though risk means that more things can happen than will happen-a
definition that captures the idea of volatility-that statement specifies no time dimension. Once we introduce the element of time, the linkage between risk and volatility begins to diminish. Time changes risk in
many ways, not just in its relation to volatility.

My wife's late aunt, a jolly lady, used to boast that she was my only
in-law who never asked me what I thought the market was going to
do. The reason, she explained, was this: "I didn't buy in order to sell."
If you are not going to sell a stock, what happens to its price is a matter of indifference. For true long-term investors-that small group of
people like Warren Buffett who can shut their eyes to short-term fluctuations and who have no doubt that what goes down will come back
up-volatility represents opportunity rather than risk, at least to the extent that volatile securities tend to provide higher returns than more
placid securities.

Robert Jeffrey, a former manufacturing executive who now manages a substantial family trust, has expressed the same idea in a more formal manner: Volatility fails as a proxy for risk because "volatility per se,
be it related to weather, portfolio returns, or the timing of one's morning newspaper delivery, is simply a benign statistical probability factor
that tells us nothing about risk until coupled with a consequence."12
The consequence of volatility to my wife's aunt was nil; the consequence of volatility to an investor who will need to invade capital
tomorrow is paramount. Jeffrey sums the matter up in these words:
"[T]he real risk in holding a portfolio is that it might not provide its
owner, either during the interim or at some terminal date or both, with
the cash he requires to make essential outlays." (The italics are mine.)

Jeffrey recognized that the risk inherent in different assets has
meaning only when it is related to the investor's liabilities. This definition of risk reappears in many different guises, all of them useful. The
central idea is that variability should be studied in reference to some
benchmark or some minimum rate of return that the investor has to
exceed.

In the simplest version of this approach, risk is just the chance of
losing money. In that view, a zero nominal return becomes the benchmark as investors try to build portfolios that minimize the probability of
negative returns over some time period.

That view is a long way from Markowitz's, as we can see from the
following illustration. Consider two investors. One of them invested
100% in the S&P 500 at the beginning of 1955 and held on for forty years. The other invested in a 30-year Treasury bond. In order to maintain the 30-year maturity, this investor sells his original bond (now a 29-year bond) at the end of each year and buys a new 30-year bond.

According to the Markowitz method of measuring risk, the second investor's bond, with an annual standard deviation of 10.4%, was a lot less risky than the first investor's stock portfolio, whose standard deviation worked out to 15.3%. On the other hand, the total return on the stock portfolio (capital appreciation plus income) was much higher than the bond's total return-an annual average of 12.2% as against only 6.1%. The stock portfolio's high return more than compensated for its greater volatility. The probability of a year with a zero return on the stock portfolio was 22%; the bondholder faced a 28% probability of a down year. The stock portfolio returned more than the bond's average return in two-thirds of the years in the time period. Which investor took the greater risk?

Or consider those 13 emerging markets I mentioned earlier. From the end of 1989 to February 1994, they were three times as volatile as the S&P 500, but an investor in the package of emerging markets had fewer losing months, was consistently wealthier, and, even after the sharp drop at the end of 1994, ended up three times richer than the investor in the S&P 500. Which was riskier, the S&P 500 or the emerging markets index?

The degree to which a volatile portfolio is risky, in other words, depends on what we are comparing it with. Some investors, and many portfolio managers, do not consider a volatile portfolio risky if its returns have little probability of ending up below a specified benchmark.*
That benchmark need not be zero. It can be a moving target, such as the minimum required return for a corporation to keep its pension fund solvent, or the rate of return on some index or model portfolio (like the S&P 500), or the 5% of assets that charitable foundations are mandated to spend each year. Morningstar ranks mutual funds by riskiness in terms of how frequently their returns fall below the return on 90-day Treasury bills.

Yet measuring risk as the probability of falling short of a benchmark in no way invalidates Markowitz's prescription for portfolio manage ment. Return is still desirable and risk is still undesirable; expected return
is to be maximized at the same time that risk is to be minimized; volatility still suggests the probability of falling short. Optimization under these
conditions differs little from what Markowitz had in mind. The process
holds up even when risk is seen as a multi-dimensional concept that
incorporates an asset's sensitivity to unexpected changes in such major
economic variables as business activity, inflation, and interest rates, as
well as its sensitivity to fluctuations in the market in which it trades.

Risk can be measured in yet another probability-based fashion, this
one based exclusively on past experience. Suppose an investor acts as a
market-timer, trying to buy before prices rise and sell before prices fall.
How much margin of error can a market-timer sustain and still come
out ahead of a simple buy-and-hold strategy?

One of the risks of market timing is being out of the market when
it has a big upward move. Consider the period from May 26, 1970, to
April 29, 1994. Suppose our market-timer was in cash instead of stocks
for only the five best days in the market out of that 14-year period of
3,500 trading days. He might feel pretty good at having just about doubled his opening investment (before taxes), until he reckoned how he
would have done if he had merely bought in at the beginning and held
on without trying anything tricky. Buy-and-hold would have tripled his
investment. Market timing is a risky strategy!

Risk measurement becomes even more complicated when the
parameters are fluid rather than stationary. Volatility itself does not
stand still over time. The annual standard deviation of monthly returns
on the S&P 500 amounted to 17.7% from the end of 1984 to the end
of 1990; over the next four years the standard deviation was only 10.6%
a year. Similar abrupt changes have occurred in bond-market volatility.
If such variation can develop in broadly diversified indexes, the likelihood is much greater that it will appear in the case of individual stocks
and bonds.

The problem does not end there. Few people feel the same about
risk every day of their lives. As we grow older, wiser, richer, or poorer,
our perception of what risk is and our aversion to taking risk will shift,
sometimes in one direction, sometimes in the other. Investors as a
group also alter their views about risk, causing significant changes in
how they value the future streams of earnings that they expect stocks
and long-term bonds to provide.

An ingenious approach to this possibility was developed by
Markowitz's student, associate, and fellow Nobel Laureate, William
Sharpe. In 1990, Sharpe published a paper that analyzed the relationship
between changes in wealth and the willingness of investors to own
risky assets." Although, in accordance with the view of Bernoulli and
of Jevons, wealthy people are probably more risk-averse than other
people, Sharpe hypothesized that changes in wealth also influence an
investor's aversion to risk. Increases in wealth give people a thicker
cushion to absorb losses; losses make the cushion thinner. The consequence is that increases in wealth tend to strengthen the appetite for
risk while losses tend to weaken it. Sharpe suggests that these variations
in risk aversion explain why bull markets or bear markets tend to run
to extremes, but ultimately regression to the mean takes over as contrary investors recognize the overreaction that has occurred and correct
the valuation errors that have accumulated.