B. Which was the better fund?
The answer may depend on our willingness to take on risk. Risk is the
ļ¬‚ip side of investment return. The higher the expected return, the higher
the expected risk. Thatā™s a truismā”and pretty true (although not always).
It doesnā™t necessarily work the other way, however. The higher the risk
does not necessarily mean the higher the return. Casinos, for example, can
be high risk, but for the gambler they all have a negative expected return.
What is risk?
Most fundamentally, risk is the probability of losing moneyā”or that
the value of our investment will go down. Most investments other than
U.S. Treasury bills and insured bank accounts have some reasonable prob-
ability of losing money. Other risks are outlined on the following page.
The most widely used deļ¬nition of risk is volatilityā”how much market
values go up and down over time. Volatility is most widely used because it
is the most measurable of all risks. Also, over long intervals of time, the
volatility of a portfolio encompasses most of the above risks. Volatility
measures the uncertainty surrounding an investment, or a portfolio of in-
vestments. Because it is measurable, it is more controllable.
How do we measure volatility? The simplest measure is annual stan-
dard deviation from the assetā™s (or portfolioā™s) mean rate of return, the
same standard deviation measure we may have learned to calculate in high
28 RISK, RETURN, AND CORRELATION
EXAMPLES OF SPECIFIC RISKS
Loss of Buying Power. We could go many years without losing
money and yet have suffered very real risk. A passbook savings
account, for example, would not have lost money, but its buying
power at the end of a long interval would be lower than when it
started if its rate of return failed to keep up with inļ¬‚ation.
Theft. The risk of dealing with someone, perhaps several times
removed from the person weā™re dealing with, who turns out to
be a thief. Some mighty sophisticated investors have at times
put large amounts of money into a company only to ļ¬nd out
that the inventory the auditor signed off on simply wasnā™t
there, and the company was heading for bankruptcy. There are
countless ways for dishonest people to separate us from our
money. We canā™t afford to compromise on the character and
trustworthiness of the people with whom we do business. Trust
is a sine qua non.
Complexity. Many a person has gotten into investments too com-
plex for him to understand. The press has reported numerous dis-
asters involving derivatives, some of which can have complexities
that are very difļ¬cult for mere mortals to fathom.
Loss of Control. A portfolio of investments can become so large
and diverse that it gets beyond our ability to understand or be-
yond what we (or our organization) are prepared to manage.
Illiquidity. When we have our money tied up in some nonmar-
ketable investment, we may suddenly need to use the money or
would like to sell the investment, and canā™t.
Maverick Risk. Making investments that none of our peers is
making. Because the investments are offbeat, we might fear being
viewed as imprudent for straying from the pack if one of the in-
vestments goes sour.
Benchmark Risk. Varying too much from a benchmark. If an in-
vestment managerā™s returns have too much variance from his
benchmark, how do we know whether or not he is doing a good
job? If our overall portfolio strategy strays too far from its bench-
mark, are we still really in control?
EXAMPLES OF SPECIFIC RISKS (Continued)
Putting Too Many Eggs in One Basket. No matter how conļ¬dent
we are about an investment, there is always some possibility that
it will go sour. The ļ¬‚ip side is that many of the wealthiest people
did just thatā”focused most of their wealth and energies on a sin-
gle investment that proved very successful. But we donā™t hear
about the large number who followed the same approach, then
went down the tubes. Bankruptcy courts are full of them.
school or college algebra. A low standard deviation of investment returns
over time means we had pretty high certainty of investment results. A high
standard deviation means we had a high degree of uncertainty. Low
volatility is good, high is bad.
The term āstandard deviationā can be pictured in the context of a curve
of probabilities, as in Figure 2.1. The higher the standard deviation, the
wider the curve. The lower the standard deviation, the narrower the curve.
Standard deviation works well in computer models that help us decide
the Policy Asset Allocation of our fundā”how much of our fund should be
0% Standard Deviations +1
ā“2 ā“1 +2
ā“20% ā“5% 10% 25% 40%
Expected Rate of Return
FIGURE 2.1 Bell Curve of Expected Return Probabilities, with a Mean Expected
Return of 10% and a Standard Deviation of 15%
30 RISK, RETURN, AND CORRELATION
allocated to various kinds of stocks and bonds, for example. (That decision
is the most important decision our committee will have to make. Weā™ll dis-
cuss that in Chapter 4.)6
Systematic Risk and Diversifiable Risk
Most individual U.S. stocks bounce up and down more than the overall
U.S. stock market. We can ease that roller-coaster rideā”reduce that volatil-
ityā”by adding more U.S. stocks, especially ones in different industries that
march to a somewhat different drummer. We can strive to eliminate this di-
versiļ¬able risk. But after a point, we will still be left with the āsystematic
riskā of the overall U.S. stock market.
Through statistical methods known as regressions, we can divide the
volatility of each U.S. stock into portions that are:
1. Systematic with the overall U.S. stock market.
2. Systematic with its own industry.
3. Systematic with stocks that have similar price/earnings ratios.
4. Systematic with stocks that have certain other common characteristics.
5. Not systematic with any of those characteristics. This is residual risk.
There are multiple ways to calculate annual volatility, and different ways can give
different results (as by annualizing daily or quarterly volatility). Moreover, stan-
dard deviations assume that every investment has a normal bell curve distribution
of returns. Some investments, however, have highly skewed distributions of returns.
In short, standard deviations have a lot of fuzz around them. But they may be the
best measure we have.
Other measures of risk are semivariance, shortfall risk, and betas. We neednā™t
worry about them, but letā™s deļ¬ne betas in case we hear the term used. Betas com-
pare the price movements of any stock (or portfolio) with those of the overall stock
market (commonly but not necessarily measured by the S&P 500). Does Stock A
go up more than the market when the market goes up, and down more than the
market when the market does down? Or does Stock A tend to move less than the
market? Beta is an effort to provide that measure.
A beta of 1.0 means that Stock A has tended to move up and down with the
market. A beta of 1.2 means that when the market was up 10%, Stock A tended to
be up 1.2 times 10%, which is 12%, and when the market was down 10%, Stock A
tended to be down 12%. (Conversely, a beta of 0.8 means that, when the market
moved 10%, Stock A tended to be up or down only 8%). Beta is part of a regres-
sion equation that relates the historical performance of a stock (or of a portfolio of
stocks) to the market.
We can diversify away these risks by adding more and different kinds
of U.S. stocks. But we canā™t diversify away volatility that is systematic with
the U.S. stock market simply by adding more U.S. stocks. We can reduce
this volatility only by adding other assetsā”nonā“U.S. stocks, bonds, real es-
tateā”assets whose volatility has a relatively low correlation with that of
U.S. stocks; the lower the correlation the better.
Diversiļ¬able risk is a critically important concept that we can put to
great advantage, as we shall see later in this book.
What To Do About Risk
All of the risks weā™ve mentioned are important. We must understand them
all and treat them with due respect. But we must place each into proper
perspective and not allow ourselves to become traumatized by risk. If we
have a good understanding of the risks, then we should be looking for
ways to use risk to our advantage.
We began this chapter with a truism: the higher the expected return,
the higher the expected risk. The job of running an investment fund is not
to see how little risk we can take, but to see how much risk we can takeā”
diversiļ¬able risk, of course. That is, intelligent diversiļ¬able risk.
This has powerful implications for an investment portfolio. The aver-
age individual stock in a large portfolio of stocks might have an annual
volatility of 30 percentage points per year, while the volatility of the over-
all stock portfolio might be closer to 15. We can reduce risk most produc-
tively by investing in multiple asset classes that have a low correlation
with one anotherā”domestic stocks, foreign stocks, real estate, bonds.
What is correlation?
āCorrelationā is a term of investment jargon whose great importance is of-
ten underappreciated. Correlation compares the historical relationship of
the returns of Stock A (or Portfolio A) with those of a market index or of
any other asset with which we want a comparison. Do returns on the two
move together? Or do they march to different drummers?
A correlation of 1.0 between Stocks A and B means they have al-
ways moved exactly together. A correlation of ā“1.0 means they have
always moved exactly opposite to one another. A correlation of 0 means
32 RISK, RETURN, AND CORRELATION
there has been no relationship whatsoever between the returns of Stocks
A and B.
The concept of correlation is the foundation for the concept of system-
atic risk and diversiļ¬able risk. By assembling a portfolio of assets whose
volatilities have a low correlation with one another, we can have a portfo-
lio of relatively risky assets that has a materially higher expected return,
but no more volatility than a portfolio of much less risky assets.
The Sharpe Ratio
We have now talked extensively about investment return and risk. There
are multiple ways to bring them together as ārisk-adjusted returns.ā
Perhaps the best-known way is the Sharpe Ratio, named for Dr. William
F. Sharpe, a Nobel Prize winner, who devised it. Itā™s not crucial that
we understand the Sharpe Ratio, but if we hear it referred to, hereā™s
what it is.
Conceptually, the Sharpe Ratio is a simple measureā”excess return per
unit of risk. Speciļ¬cally, itā™s an investmentā™s rate of return in excess of the
riskfree (Treasury-bill7) rate, divided by the investmentā™s standard devia-
tion. The Sharpe Ratio answers the question: How much incremental re-
turn do we get for the volatility we take on?
We can apply this ratio to a single investment or to an entire portfo-
lio. The higher the Sharpe Ratio, the more efļ¬cient an investment it is.
That does not necessarily mean that if Investment A has a higher Sharpe
Ratio than Investment B, then A is always a preferable addition to our
portfolio than B. The correlations of A and B with everything else in our
portfolio are also very important. Because of the beneļ¬t of diversiļ¬cation,
our overall portfolio would almost always have a materially higher Sharpe
Ratio than the weighted average Sharpe Ratio of our individual invest-
A Treasury bill, known as a āT-bill,ā is a very short-term loan to the U.S. govern-
ment, which is considered to have zero risk.
Conceptually, the Sharpe Ratio āleveragesā or āde-leveragesā actual
returns by saying, in effect: What would be the return if we added T-
bills to a volatile investment (de-leveraging the investment) until we
have reduced its annual standard deviation to our target volatility? Or
what would be the return on a low-volatility investment if we bor-
rowed at T-bill interest rates (leveraging the investment) until we have
increased its annual standard deviation to that of our target volatility?
Thatā™s a tough concept. Letā™s tackle it with a simplistic example.
Letā™s say, with T-bill rates at 6%, we have two investments, A and B,
with the following characteristics:
Return Volatility Sharpe Ratio Calculation
A 12% 15% .4 (12 ā“ 6)/15 = .4
B 9 5 .6 (9 ā“ 6)/ 5 = .6
B has a higher Sharpe ratio, .6 to .4. Thatā™s preferable. But why
should we prefer B when the return on A is 3 points higher? Implic-
itly, if we wanted to get the volatility of B up to the same 15% volatil-
ity of A, we would have to leverageā”buy three times as much B and
borrow two-thirds of the money. The return on our money would be
15%, or 3% more than that of A.
Risk-adjusted returns are viewed by many as the true measure of an in-
vestment manager. In the sense that less volatility is almost always better
than more, it is intuitively appealing to reward the lower-volatility man-
Personally, I have not placed a great deal of value on risk-adjusted re-
turns, for two basic reasons:
We canā™t spend risk-adjusted returnsā”only actual returns.
Our critical measure is not the absolute volatility of a single invest-
ment (or a single asset class) but the impact of that investment (or asset
class) on the volatility of our overall portfolio. Its impact depends on
(a) the correlation of that investment (or asset class) with our other as-
sets and (b) the percentage of our overall portfolio we devote to that
investment (or asset class).
34 RISK, RETURN, AND CORRELATION
Those two basic reasons lead to four corollary reasons:
1. Risk-adjusted returns tend to be theoretical and not real-world, in the
sense that, because of unrelated business income tax (UBIT) and other
reasons, it is often not feasible to borrow in order to leverage up a low-
volatility portfolio. Likewise, we would almost never choose to offset a
high-volatility manager by adding cash equivalents.
2. While we can afford to have only so many high-volatility managers in
our portfolio, the most productive way to deal with a high-volatility
high-return manager is to ļ¬nd another high-return manager in another
asset class who has a low correlation with him.
3. While the inclusion of a low-volatility manager in our portfolio does
make room for the inclusion of a high-volatility manager, we can gain
the proper beneļ¬t from that low-volatility manager only if we do in-
deed hire a high-volatility, high-return manager.
4. Of course, we should make sure the high-volatility high-return man-
ager doesnā™t push us beyond the volatility constraint for our overall
portfolio. But many endowment funds donā™t take on as much volatility
as they should. We donā™t deserve accolades for reducing overall portfo-
lio volatility below our target at the cost of lowering our overall port-
Perhaps the best argument against reducing portfolio risk in tradi-
tional ways is one articulated by Keith Ambachtsheer and Don Ezra, who
have said we should āconsider the opportunity cost of undertaking risk in
a different, perhaps more rewarding way.ā8
DERIVATIVESā”A BOON OR A DIFFERENT
Derivatives are so often associated with risk in many peopleā™s minds that we
should deal with them here. Common examples of derivatives are shown
in the box on the following page. Derivative securities are extremely
Keith P. Ambachtsheer and D. Don Ezra, Pension Fund Excellence, (New York:
John Wiley & Sons, Inc., 1998), p. 54.
Derivativesā”A Boon or a Different Four-Letter Word?
EXAMPLES OF DERIVATIVES
Futures. Agreements, usually exchange-traded, to pay or receive,
until some future date, the change in price of a particular security
or index (such as: S&P 500 index futures9).
Forwards (forward contracts). Agreements between two parties
to buy (or sell) a security at some future date at a price agreed
upon today (such as foreign exchange forwards).
Swaps. Agreements between two parties to pay or receive, until
some future date, the difference in return between our portfolio
(or an index) and a counterpartyā™s portfolio (or an index). For ex-
ample: āWeā™ll pay you the T-bill rate plus 50 basis points,10 and
you pay us the total return on the Financial Times index on U.K.
Call options. The holder of a call option has the right (but not the
obligation) to buy a particular security from the seller of the call
option at a particular price by a particular date. The holder can
ācallā the shares from the option seller. For example, a call op-
tion to buy S&P 500 index futures at an index of 1300 by Sep-
Put options. The holder of a put option has the right (but not
the obligation) to sell a particular security to the seller of the
put option at a particular price by a particular date. The holder
can āputā the shares to the option seller. For example, a put
option to sell S&P 500 index futures at an index of 1200 by
September 15. Options are often traded on a stock or commod-
Structured notes. Agreements between two parties, the nature of
which is limited only by the creative imagination of investment
An S&P 500 index future is an agreement to pay or receive, until some fu-
ture date, the change in the S&P 500 index. Cash equivalents equal in value
to the money we want to invest in the stock markets plus S&P futures would