Fischer Black
on
MARKETS
Vol. 1, No. 5
April 12, 1976
WHY AND HOW DOES AN INVESTOR DIVERSIFY?
You diversify to recuce risk; to reduce your exposure to large losses.
With many stocks, you hope that when some go down, others will go up,
or will go down less, so your overall loss will not be too great. With
only a small fraction of your portfolio in anyone stock, you know that
if a company goes out of business, your loss will be limited. All of
that is clear.
What's not so clear is that you also diversify to increase the amount you
expect to gain from your portfolio; to increase the portfolio's expected
return, inciuding dividends, interest, and capital gains. At first, this
may seem odd, because diversification limits the possible upward moves in
a portfolio to about the same extent that it limits the possible downward
moves. It works, though, because you can hold more of a well diversified
portfolio than you can hold of a badly diversified portfolio. If the bad
things that can happen to a portfolio are limited, you can hold more of
it.
The total amount of money that you have to invest is, of course, limited.
When I say you can hold more of a portfolio, I mean that you can hold less
in bonds and more in stocks, or that you can borrow to buy more stocks, or
perhaps that you can hold riskier stocks in a well diversified portfolio
than you can hold in a badly diversified portfolio. And investors can generally
expect more from risky stocks than from safe stocks.
Since every stock has to be held by someone, every stock must be priced
so that it fits into at least some portfolios. This means that a portfolio
containing all the stocks there are will be quite attractive, if
the costs of putting together such a portfolio are low. Since all the
outstanding shares of every stock have to be held by someone, such a portfolio
would contain more of a large company's stock than it would contain
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of a small company's stock. I t would be a "market portfolio."
You don't really have to hold a piece of every stock to be holding
something like the market portfolio, though. Because almost all stocks
tend to go up and down together, smaller portfolios can be built that
will behave very much like the whole market. We can imagine everyone
holding a different portfolio, but the different portfolios acting so
much alike that each has behavior very similar to that of all portfolios
taken together.
While it is possible to build portfolios that will behave very much like
the market, it is also easy to build portfolios that will have returns
that differ greatly from the market's return from time to time, even though
the portfolios contain lots of stocks. Just concentrate the portfolio
in stocks with a history of growing earnings; or in high technology stocks;
or in stocks that seem less sensitive to the cost of energy than other
stocks. Almost any systematic rule for picking stocks will give a portfolio
that will act rather unlike the market at times.
It's also hard to know when you have a portfolio that acts like the market.
·The market contains not only listed stocks, but also unlisted stocks, stocks
that trade very infrequently, corporate bonds, assets of businesses that
aren't incorporated, and personal assets such as real estate. It even includes,
to some extent, human capital, government bonds, and foreign assets.
Its very hard to guess what many of these assets are worth at anyone time,
and it's even harder to know how much they have gone up or down.
There is reason to believe, though, that a diversified portfolio of listed
stocks (like the Standard & Poor's 500) will act very much like the market
portfolio we can't see.. The very largest companies in the U. S. make up a
very significant part of the whole U.S. economy; and the factors that influence
their values also influence the values of small companies and personal
assets. Similarly, the U.S. economy makes up a very significant part
of the world's economy, and the factors that influence it also influence the
rest of the world.
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It is the individual who is interested in diversification more than anyone
else. A corporation's assets need not be diversified if its shareholders
have diversified portfolios. Even a mutual fund need not be diversified
if it makes up only a small part of any individual investor's risks. It
is the individual, in the end, who wants to balance one risk against another.
There are some risks, though, that an individual has little control over.
Once he has trained for an occupation, and spent years developing the skills
and experience that make him good at it, he can shift to another occupation
only at great cost. While he can make many small shifts within his occupation,
he must normally take the risk of his occupation as given. He may
also take as given the risks of changes in the value of the home he owns,
and certain general risks such as the risk that the earth will be destroyed
by a comet.
Some of these risks are rather significant for an individual. If he takes
them as given, he may be relatively unconcerned about the precise extent
to which his portfolio of common stocks is diversified. A substantial reduction
in the risk of his common stock portfolio may mean only a small
reduction in the risk of his overall portfolio.
An individual will care about specific risks as well as about some measure
of the overall risk of his portfolio. He may be especially concerned about
inflation, or about the cost of food, or about the cost of housing. If so,
he may want to have positions that will payoff when things go badly along
one of these dimensions. He may want an asset that goes up in value when
the cost of the kind of housing he likes goes up, for example. If any asset
like that is available.
An individual may even care about doing well when his neighbors or friends
or coworkers do w~11, and he may not mind so much doing badly when they do
badly. If so, he may want to have the same kinds of risks they have. If
they have investments in rural land, he may want investments in rural land.
even though that may mepn a poorly diversified portfolio by the usual measures
of diversification.
Fischer Black on MARKETS Page 4
Even if an individnal decides he wants a very well diversified overall
portfolio, he still has a big decision to make. He has to decide how
much of that portfolio to hold: how much risk he wants to take. And he
must make this decision both now and in the future. He must decide
over and over again how much risk he wants to take, in the light of what
has happened and what might hl.ppen in the future.
In other words, he needs a strategy for changing his position over time.
One of the elements of this strategy is likely to be that he will want
diversification across time a, well as diverisification across assets.
"Time diversification" is oftEn just as important as diversification
across stocks. It helps because what happens to the market in one period
is largely independent of what happens to the market in some other
period. In fact, adding a stock to a portfolio may not help to diversify
the portfolio much, if there are other stocks like it already in
the portfolio. But adding investment in a different time period always
helps, because with tne market, every time period is different from
every other.
To illustrate, suppose you have a choice of the following strategies:
A. Invest $1000 in the market at the start of
year 1. Whatever happens in year 1, bring
your investment to $1000 again at the start
of year 2. Evaluate your position at the
end of year 2.
B. Keep all your money in short term bills during
year 1. Invest $1400 in the market at the
start of year 2. Evaluate your position at the
end of year 2.
It turns out that the uncertainty in what you will have at the end of year
2 is about the same for these strategies. With strategy A, you have $1000
at risk for each of tHO years, but large losses are unlikely because a loss
Fischer Black on MARKETS Page 5
in one year may be offset by a gain in the other. With strategy B, you
have $1400 at risk for only one year. If year 2 is a bad year, you're
out of luck.
So the two strategies have sbout the same risk. But strategy A has a
higher expected return. If the market is expected to return 6 percentage
points more than short term bills, the expected gain from strategy A is
$120 more than the gain on short term bills. But the expected gain from
strategy B is only $B4 more than the gain on short term bills.
Assuming a basic $1000 investment, the loss from using strategy B is $36
over two years, or $lB a year. This is equivalent to a loss of 1.B percentage
points on your basic investment every year. We can think of this
as the cost of poor time diverSification. A consistent cost of 1.B% per
year is a serious matter. My example is extreme, but it illustrates the
potential importance of diversification through time.
This doesn't mean, though, that an individual will want to keep a constant
number of dollars at risk all the time. In fact, he will want to change
his exposure for all sorts of reasons, ranging from unexpected medical
expenses to a gain due to a phenomenal rise in the market in a short time.
If the individual puts money into the market, and never adds anything,
but spends say 5% of the value of his holdings each year, then he will
have an amount of money at risk that depends on what the market does. If
the market suddenly drops 50%, the value of his holdings will drop 50%,
so he will have 50% fewer dollars at risk. If the market suddenly doubles,
he will have twice as many dollars at risk. This is a perfectly sensible
strategy for some people.
Suppose, - though, that you want to limit your losses. If you have all your
money in the market all the time, then you can lose all your money. If
you sell off some of your holdings as the market goes down, and buy them
back as the market goes up, shifting the money you get into and out of
short term bills, then you will limit your ~osses. But this method takes
Fischer Black on MARKETS Page 6
lots of trades, and means that you have to keep a close watch on the market.
no o m t your losses is to buy call options. Instead of putting
all your money in the market, you can put some in options and some in bills.
That can give the same effect when the market goes down as if you had all your
money in the market and sold gradually as the market declines.
Options have a habit of expiring from time to time, so a strategy involving
options also takes some attention and involves some trading costs. For
some investors, though, a strategy with options may cost less than any strategy
involving stocks alone. Espeeially if there's a bonus in the form of
tax gains from options trading.
For every buyer of options there must be a seller. The seller does not limit
his losses as much as he would with other strategies. So he must have some
other reason for selling. He may have tax reasons; he may be taking a naked
short position as a substitute for shorting the stock; or he may think the
option is overpriced. But it may simply fit the way he likes to adjust his
position over time.
When things go badly, some people react by doubling their bets. They increase
their exposure to lisk in hopes of recouping their losses. On the other hand,
when things go well they may reduce their exposure to risk so they can't lose
what they have won. It's a very common gambling strategy and it's a very
common philosophy of life.
The person who writes c.overed options may be doing just that. He starts out
with a fairly conservative position. Some of what he loses on his stock
position he will make on his options position, and vice versa. But if his
stocks go down, the protection he gets from his options is cut back. And
if his stocks go up, his position may become almost perfectly safe, because
his gains and losses on his stocks may be offset almost one-far-one by his
losses and gains on his options. Or his stocks may be called away.
Again, he can use a sim~lar strategy with stocks alone. He can buy more stock
Fischer Black on MARKETS Page 7
as the market declines, and sell off stock as the market goes up. Whether
options fit into the best strategy will depend on factors like convenience.
trading costs, the pricing of options, and taxes. Strategies involving
options, though, illustrate the variety of strategies that can be consistent
with good diversification over time.
If you have any questions or comments, please call me at 617-253-6691. or
write me at 50 Memorial Drive, Cambridge, MA 02139.