LINEBURG

The answer may depend on our willingness to take on risk. Risk is the

¬‚ip side of investment return. The higher the expected return, the higher

the expected risk. That™s a truism”and pretty true (although not always).

It doesn™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 money”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.

Volatility

The most widely used de¬nition of risk is volatility”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 asset™s (or portfolio™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

I

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 in¬‚ation.

Theft. The risk of dealing with someone, perhaps several times

I

removed from the person we™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 ¬nd out

that the inventory the auditor signed off on simply wasn™t

there, and the company was heading for bankruptcy. There are

countless ways for dishonest people to separate us from our

money. We can™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-

I

plex for him to understand. The press has reported numerous dis-

asters involving derivatives, some of which can have complexities

that are very dif¬cult for mere mortals to fathom.

Loss of Control. A portfolio of investments can become so large

I

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-

I

ketable investment, we may suddenly need to use the money or

would like to sell the investment, and can™t.

Maverick Risk. Making investments that none of our peers is

I

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-

I

vestment manager™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?

29

Risk

EXAMPLES OF SPECIFIC RISKS (Continued)

Putting Too Many Eggs in One Basket. No matter how con¬dent

I

we are about an investment, there is always some possibility that

it will go sour. The ¬‚ip side is that many of the wealthiest people

did just that”focused most of their wealth and energies on a sin-

gle investment that proved very successful. But we don™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 “standard deviation” 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 fund”how much of our fund should be

Probability

25%

20%

15%

10%

5%

0% Standard Deviations +1

“2 “1 +2

“20% “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. We™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 ride”reduce that volatil-

ity”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-

versi¬able risk. But after a point, we will still be left with the “systematic

risk” 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.

6

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 needn™t

worry about them, but let™s de¬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.

31

Correlation

We can diversify away these risks by adding more and different kinds

of U.S. stocks. But we can™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 assets”non“U.S. stocks, bonds, real es-

tate”assets whose volatility has a relatively low correlation with that of

U.S. stocks; the lower the correlation the better.

Diversi¬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 we™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 take”

diversi¬able risk, of course. That is, intelligent diversi¬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 another”domestic stocks, foreign stocks, real estate, bonds.

What is correlation?

CORRELATION

“Correlation” 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 “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 diversi¬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.

RISK-ADJUSTED RETURNS

The Sharpe Ratio

We have now talked extensively about investment return and risk. There

are multiple ways to bring them together as “risk-adjusted returns.”

Perhaps the best-known way is the Sharpe Ratio, named for Dr. William

F. Sharpe, a Nobel Prize winner, who devised it. It™s not crucial that

we understand the Sharpe Ratio, but if we hear it referred to, here™s

what it is.

Conceptually, the Sharpe Ratio is a simple measure”excess return per

unit of risk. Speci¬cally, it™s an investment™s rate of return in excess of the

riskfree (Treasury-bill7) rate, divided by the investment™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 ef¬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 bene¬t of diversi¬cation,

our overall portfolio would almost always have a materially higher Sharpe

Ratio than the weighted average Sharpe Ratio of our individual invest-

ment programs.

7

A Treasury bill, known as a “T-bill,” is a very short-term loan to the U.S. govern-

ment, which is considered to have zero risk.

33

Risk-Adjusted Returns

Conceptually, the Sharpe Ratio “leverages” or “de-leverages” 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?

That™s a tough concept. Let™s tackle it with a simplistic example.

Let™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 “ 6)/15 = .4

B 9 5 .6 (9 “ 6)/ 5 = .6

B has a higher Sharpe ratio, .6 to .4. That™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 leverage”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-

ager appropriately.

Personally, I have not placed a great deal of value on risk-adjusted re-

turns, for two basic reasons:

We can™t spend risk-adjusted returns”only actual returns.

I

Our critical measure is not the absolute volatility of a single invest-

I

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 ¬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 bene¬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 doesn™t push us beyond the volatility constraint for our overall

portfolio. But many endowment funds don™t take on as much volatility

as they should. We don™t deserve accolades for reducing overall portfo-

lio volatility below our target at the cost of lowering our overall port-

folio return.

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 “consider the opportunity cost of undertaking risk in

a different, perhaps more rewarding way.”8

DERIVATIVES”A BOON OR A DIFFERENT

FOUR-LETTER WORD?

Derivatives are so often associated with risk in many people™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

8

Keith P. Ambachtsheer and D. Don Ezra, Pension Fund Excellence, (New York:

John Wiley & Sons, Inc., 1998), p. 54.

35

Derivatives”A Boon or a Different Four-Letter Word?

EXAMPLES OF DERIVATIVES

Futures. Agreements, usually exchange-traded, to pay or receive,

I

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

I

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

I

some future date, the difference in return between our portfolio

(or an index) and a counterparty™s portfolio (or an index). For ex-

ample: “We™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.

stocks.

Call options. The holder of a call option has the right (but not the

I

obligation) to buy a particular security from the seller of the call

option at a particular price by a particular date. The holder can

“call” 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-

tember 15.

Put options. The holder of a put option has the right (but not

I

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 “put” 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-

ity exchange.

Structured notes. Agreements between two parties, the nature of

I

which is limited only by the creative imagination of investment

bankers.

9

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

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