Liguidity Premiums
Fischer Black
Graduate School of Business
University of Chicago
February, 1970
Many writers seem to think that long term bonds ought to return more
than short term bonds because the individual who liquidates them before
maturity may get less than he paid for them; in other words, that long
term bonds ought to have "risk premiums". The capital asset pricing
model, however, tells us that a long term bond is no different from
any other asset: the risk premium on a long term bond should depend
on the amount of market risk in the bond. As a first approximation,
a bond probably has no market risk at all; all of its risk can be
diversified away, so it should not bear any risk premium.
Other writers feel that long term bonds and other risky assets are
less liquid than cash and short term debt securities because the
transactions costs are greater. Other things equal, the argument
goes, people would rather hold assets with small transactions costs than
assets with large transactions costs, so they will accept lower returns
on assets with small transactions costs.
This argument centers on the dealer spread as the irreducible portion
of the transactions cost. If an investor liquidates an asset bec~use
he needs the cash, then presumably he sells the asset immediately at
the current bid price. (And if an investor buys an asset because he
has cash available, then presumably he buys the asset immediately at
the current asked price.) If he buys and then sells immediately, he
pays the dealer spread.
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Some have argued that the dealer spread compensates the dealer for
the risk of changes in the value of his inventory (or the value of his
short position). But we know that the expected return on his inventory
automatically compensates him for his inventory risk. To the extent
that the inventory risk is market risk, the expected return on his
inventory will compensate him directly. To the extent that the
inventory risk is specific risk, he can eliminate it by diversifying.
In fact, on the New York Stock Exchange we find dealers banded
together into specialist firms, where each firm handles a diversified
portfolio of stocks from a number of different industries.
, L TreynorJargues that the dealer spread compensates the dealer for the
fact that he loses money at a certain rate to people who have more
information about a company than he has. The dealer is unable to tell
whether a trader is acting on special information or out of a need to
shift into or out of cash. As a result, he must charge all traders
his spread.
Treynor's argument seems valid in the following sense: a person without
special information, buying or selling a specific risky security, can
expect to lose an amount related to the dealer spread to other traders
who do have special information. This can be true even if there is
no actual dealer, and all trading is done by matching orders.
However, his argument seems to have little relevance to the person
who is trying to deal with uncertain cash flows, since such a person
does not need to make transactions in risky securities at all. A person
can handle uncertain cash flows by buying and selling sure assets: cash,
savings deposits, Treasury Bills, commercial paper, and other short term
debt securities. In addition, he can add to or reduce his short term
liabilities such as bank loans. Treynor's argument does not apply to
these assets at all: since they are short term assets, they do not
need to be traded, and since they are virtually riskless, no special
information is involved in setting prices on these assets. So there
certainly will be no dealer spread of the type Treynor describes,
and we will have to look elsewhere for an explanation of the
transactions costs on these assets.
An individual generally does not have any reason to hold particular
assets. He can earn risk premiums by holding some amount of the
market portfolio, and the amount he wants to hold will not ordinarily
be affected by his cash flows. When large unexpected cash flows change
his wealth, or when he receives information that changes his wealth,
he may want to adjust his holdings of the market portfolio. But
Treynor argues convincingly that dealer spreads on the market portfolio
will be virtually zerm, so this is not a factor. Note also that the
individual adjusts his holdings of the market portfolio when he receives
new information, and this information will rarely come in the form of
an unexpected cash flow.
The individual certainly does not have to hold long term bonds, and
he does not have to hold individual securities. He will hold long
term bonds (other than as part of the market portfolio) only if he
believes he has special information on the future course of interest
rates. He will hold individual common stocks (long or short) only
if he believes he has special information on the companies involved.
Thus we can view all trading in risky securities as information
motivated. This means that the liquidity supposedly provided by
dealers and specialists who stand ready to buy and sell from their
inventories is of dubious value. If a person is anxious to buy or
sell because he has a valuable piece of information, it hardly seems
to hurt society to make him wait until a matching order comes in
from someone else who believes he has valuable information of the
opposite kind. Immediate execution of market orders seems to be
very unimportant if all orders are information motivated.
Actually, in a full equilibrium model, there will be no trading in
individual risky securities at all. If there is no liquidity motivated
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trading, then information motivated traders on average will not
make money. Those with better information will make money at t.he
expense of those with worse information. But this will cause
those with worse information to drop out of the game. Since there
will always be some people with better information and others with
worse information, more and more people will drop out, until there
are no more people left. Prices will adjust instantaneously on
the arrival of new information, but the force that causes the
adjustment will be potential trading rather than actual trading.
Ignoring the differences between the various short term securities,
we can classify people as net lenders of short term securities or
net borrowers of short term securities. When a lender receives an
unexpected cash payment, he simply adds to his holdings of short term
securities; when he is forced to make an unexpected cash payment, he
simply reduces his holdings of short term securities. When a borrower
receives an unexpected cash payment, he reduces his loan; and when he
is forced to make an unexpected cash payment, he increases his loan.
In the extreme, we can suppose that checking accounts pay interest
at the going rate and that negative balances are allowed that are
charged interest at the going rate. In this case, it is clear that
cash flows, whether expected or unexpected, will automatically change
a person's holdings of short term interest bearing assets.
I am arguing that long term bonds, like other specific risky assets,
will be held or sold short only for speculation on interest rates. They
will not be held as liquid assets or as substitutes for short term
borrowing and lending.
One objection that some will make to this view is that it costs the
borrower too much in transactions costs to be continually issuing short
term notes. It is cheaper for both borrower and lender to issue one long
term' bond than a whole series of short term notes. This argument
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disappears, however, once we separate the transactions cost of issuing
or transferring a note from the pure interest rate on the note. The
transactions cost can be paid Once when the lender buys a short term
note, and again when he refuses to accept a replacement for a maturing
note. So long as he holds a continuous series of short term notes,
the cost to him or the borrower should be no greater than the cost
of issuing a single long term bond. Thus if transactions charges
are separated from interest payments on short term notes, and if
they are applied only when the lender refuses to renew the note, the
cost of issuing a series of short term notes should be no greater
than the cost of issuing and transferring a long term bond.
Another objection that might be raised is that some individuals have
real assets with fixed future cash flows, and they want to reduce their
risk by selling long term bonds that mature on the dates of these
cash flows. First of all, it is hard to imagine a real asset with
fixed future cash flows. And second, who will want to buy the long
term bonds that these individuals want to sell?
Finally, some claim that an individual has a specific horizon that
he uses for his investment decisions, and that he maximizes the expected
utility of his wealth at that time. It is claimed that these people
will want to buy or sell long term bonds that mature at their horizons.
It is hard for me to believe that individuals have such horizons. The
most general approach to individual decision making is to assume that
an individual maximizes the expected utility of his total consumption
stream over time. It is only because this problem is hard to handle
analytically that horizons were invented.
Even if individuals have distant horizons, the usual argument is
incorrect. The usual argument is that a long term bond is riskless,
and a series of short term notes is risky for such an individual, so
he will demand a higher rate of interest on the short term notes. This
argument assumes that there are no other assets in the world. In fact,
we should be looking at the market risk in a~ asset, not the total
risk. If the market risk (from a one period point of view) of a long
term bond is positive, then the market risk (from a horizon point
of view) of a series of short term notes will be negative. Thus
the horizon argument gives the same conclusion as the one period
argument: short term notes should have a lower expected return than
long term bonds. If the market risk in long term bonds is negative,
then the two arguments still give the same conclusion: short term
notes should have a higher expected return than long term bonds.
And if the market risk is zero, they should both have the same
expected return.