Interest rates primarily reflect the price that an investor is paid for
the use of his money over time. Hence the interest rate will affect the
price of assets, financial and real.
The Real Rate of interest versus the nominal rate
At a simple level of analysis, since money represents purchasing power,
the interest rate represents the equilibrium reward at which people are
willing to lend real resources from one period to another (machinery,
units of land, corn etc.). Thus, if at the margin, a saver is willing
to defer the use of one unit of resources this period, and instead transfer
it to an agent (who wishes to invest in a project), in return for 1.05
units next period, we would say that the real interest rate is 5%. The
rate is referred to as a real rate, since the payment next period is stipulated
in real resource units.
Determinants of the real interest rate
The Nominal Interest Rate
- The supply of funds from savers, primarily households; i.e. their
willingness to postpone consumption
- The demand for funds from business to be used to finance physical
investments in plant, equipment, and inventories
- The government's net supply and/or demand for real resources
The interaction of the demand for and
supply of real resources determines the real interest rate. However, we
do not normally borrow and lend in real consumption units, since this
is only an abstraction. We must borrow and lend in money, that is, dollars.
Now suppose the price level next period is expected to be 10% higher than
the price level this period; i.e. things costing $1 today are expected
to cost about $1.10 next period. Then, in order to receive this promised
real return of 5%, our saver must demand a return of (1.05)(1.1) or $1.155
per dollar lent today. If he does receive 1.155 in dollars next period,
then he can buy 1.155/1.10 or 1.05 times what he could have bought for
the dollar that he gave up this period.
The nominal interest rate (i.e. the rate denominated in dollars) that
would, on average, compensate an investor for expected inflation of p
% and give him a real rate of interest of r % can be computed (approximately)
by adding the inflation rate to the required real rate: p + r.
However, if an investor faces inflation risk, he might want more than
an average real return of r%. We may add a risk premium term as
well to obtain the following augmented model of interest rate determination:
i = r + E(p ) + inflation risk premium
Note that the inflation risk premium compensates not for the fact of
inflation (the E(p ) term does that), but for uncertainty regarding the
future inflation rate. However, the Fisher equation says that the
required inflation risk premium is zero; the more common used form of
the above equation is:
i = r + E(p )
The Inflation Rate
On a simple level, inflation is the change in the price level. The total
amount of money (not just currency) represents ownership of the totality
of goods and assets in the economy. Hence the price level is simply the
total money supply divided by the quantity of goods.
Price Level = Total Quantity of Money/Quantity of Goods
This is called the Quantity Theory of Money. Changes in the price level
therefore reflect changes in the supply of goods, as well as changes in
the supply of money. As we have shown above, the nominal interest rate
will be affected by the markets expectation of future inflation
Using the Fisher Equation:
Note that the Fisher Equation simply relates real interest rates, nominal
interest rates, and inflation rates. Hence, we could use it to predict
nominal interest rates, by using inflation rate estimates and real interest
rate estimates from outside the model. Alternatively, we could use it
to predict inflation, but using real rate estimates from outside the model.
Finally, we could use it to estimate real interest rates, by using nominal
interest rate and inflation rate estimates from outside the model.
Lets see how we would use this simple model to predict three-monthly
interest rates. First, we would look at peoples preferences for
immediate consumption versus delayed consumption. Even though these preferences
might and do vary across time and across space, they are unlikely to vary
much from one year to another in a given country. The average monthly
inflation rate over the 1968-1997 period (using the urban CPI) was 0.435%.
On an annualized basis, this works out to 5.35%. The average 3-monthly
T-bill rate over that same period was about 7.4546%, annualized. This
yields an ex-post real interest rate of about 2.1%. Assuming that peoples
expectations of interest rates and inflation were correct on average,
we can use this ex-post real rate average as an estimate of the ex-ante
short-term real interest rate. Let us assume that this real interest rate
does not change in the short run.
To predict the three month interest rate, we must predict average inflation
over the next three months, and add it to our real interest rate estimate
of 2.1%. The inflation rate over 1997 was about 1.7. Using the current
inflation rate as a predictor of near-term future inflation rates, an
analyst in early 1998 might come up with a 3-month T-bill rate estimate
of 2.1+ 1.7 or 3.8%. (Alternatively, we could use a structural model to
relate interest rates to variables such as monetary growth. This
structural model could then be used in conjunction with the current rate
of monetary growth to estimate the inflation rate for the near future.
If we compare it to the actual 3-month T-bill rate on January 25, 1998,
we see that it was 5.16%. These two numbers may be reconciled by positing
either a higher short-term inflation rate estimate for the market or a
higher short-term real rate.
Similarly, we can come up with a long-term T-bond rate estimate as well.
Our estimated inflation rate using data from the last 20 years was 5.35%.
The average 30-year T-bond rate over the same period was about 9.1%, giving
us an estimated long-term real rate of about 3.75%. Adding our inflation
rate estimate of 1.7%, we get an estimated nominal 30-year rate of 5.46%.
The Effect of the Feds Actions on Interest Rates:
An important point to keep in mind in analyzing the impact of changes
in the money supply on prices and interest rates is the following.
In one sense, money is passive and nominal money prices simply reflect
the relative valuation of different real goods and assets in the economy.
However, in addition to that, money has a real effect as well. Money
works like a lubricant; it facilitates transactions. Hence a change
in money supply can sometimes have real effects, as well as nominal effects.
Suppose the Federal Reserve increases the money supply, either by lowering
the interest rate at which it stands ready to lend to member banks, or
by buying back Treasury securities and releasing funds into the system.
The market may interpret this decision as an indication of freer availability
of future money. The pure nominal effect of this action would be
to increase the price level, since the output of goods has not changed,
while the supply of money has. This would lead, not just to a currently
higher price level, but also to a higher inflation estimate.
However, there could also be a real effect. Suppose there was not
enough money in circulation, originally, to accommodate the transactions
that people wish to undertake. Then the Fed's actions might have
the effect, not only of increasing the money supply, but also that of
increasing the amount of goods by facilitating transactions. The
net effect could therefore be a zero change in the price level, but a
higher level of the Gross Domestic Product.
However, this also depends upon the excess capacity in the real sector.
If there is sufficient excess capacity, then the additional liquidity
can provide the impetus for higher growth, thus restraining inflation.
However, when there is little excess capacity, providing additional liquidity
will lead to expectations of a heated economy and will lead to higher
expectations of inflation, without any substantial corresponding increase
in production. In general, since money is necessary as a lubricant for
the economy to function and to grow, the Federal Reserve through its actions,
can encourage growth as well as inhibit it. This, in turn, can affect
the real interest rate.
In summary, the Fed's actions could have two different kinds of effects:
one, increasing the money supply could lead to market expectations of
higher future inflation, causing nominal interest rates to rise, but not
necessarily affecting real rates; two, increasing the money supply could
cause real interest rates to drop by stimulating growth. This, in turn,
would decrease nominal interest rates. Decreasing the money supply would
have the opposite effects.
Why does the Treasury market sometimes move with the stock market
and sometimes not?
We will see first show that the simplest way of looking at the stock
and bond markets leads us to expect that bond markets and stock markets
will move in the same direction. We will then show that a consideration
of indirect effects allows for the possibility of the markets moving in
opposite directions as well.
Why stock and bond markets might be expected to move in the same direction:
Factors that directly affect stock market valuation
Let us first look at a simple model of equity valuation. Suppose we look
at a firm i, which pays constant dividends of $D per share per
year, its stock can be valued as D/ri, where ri
is the required rate of return on the stock of firm i. Clearly,
the stock price will go up if the market increases its estimate of D or
if it decreases its estimate of ri. What determines ri?
A useful model for this is the Capital Asset Pricing Model (CAPM), which
says that ri = rf + bi[rm
- rf]. The symbol rf refers to the risk-free rate
of return, which is essentially the same as the nominal interest rate,
r, of which we have been speaking, in this note. rm is the
required rate of return on the market portfolio, the portfolio of all
risky assets in the economy. bi is the beta risk factor of
the stock, which is a measure of the risk of a stock relative to all other
assets; the b of the market portfolio as a whole is unity (see webnotes
on CAPM). If we ignore movements in the rm for a second,
it is clear that if the stock market rises, there are two possible reasons:
either nominal interest rates have dropped and/or the market has increased
its estimate of corporate earnings.
Finally, it is possible that the market has also changed its estimate
of rm - rf, the market risk premium, or the excess
of the required rate of return on the market portfolio over the risk-free
rate. Again, we need a model of determination of the market risk premium.
A simple model for this can be found in Bodie, Kane and Marcus' chapter
on the CAPM, where we learn that, under appropriate assumptions, the market
risk premium, rm - rf, is directly proportional
to As2, where A stands for the average
risk aversion parameter of agents in the market, and s2
is the variance of returns on the market portfolio. Hence, the market
risk premium, rm - rf, will increase if investors
become more risk averse, or if market conditions become more uncertain.
Now, investors' risk aversion reflects their taste for risk, and is fairly
stable. Hence changes in the market risk premium are usually caused by
changes in market uncertainty.
In summary, the following factors can, ceteris paribus, cause stock prices
At this point, looking only at the effect of one factor at a time, it would
seem that bond markets and stock markets should move in the same direction,
i.e. an increase in riskfree rates decreases bond prices, and also decreases
stock prices through its impact on required rates of return on equities.
- an increase in the market's expectations of corporate cashflows
- a decrease in market uncertainty
- a decrease in the riskfree rate of return
- a decrease in investors' risk aversions.
A look at factors that affect interest rates directly and indirectly
An attempt to explain more complicated combinations of stock and bond
We have already seen above, the factors that directly affect nominal
interest rates - the market's estimate of the inflation rate, and the
relatively stable ex-ante real rate. However, there is also an indirect
effect of market uncertainty on interest rates, due to a substitution
effect. Because of this, if market uncertainty increases, it is most likely
that there will be two effects: one, investors try to switch more of their
wealth into risk-free assets, and end up lowering interest rates; two,
investors try to switch more of their wealth away from risky assets, and
end up increasing the market risk premium for risky assets. Supply adjustments
are unlikely to affect the situation much, since the supplies of risk-free
and risky assets are fairly constant in the short run. It is however,
most likely that the drop in interest rates will be insufficient to offset
the increase in the market risk premium. As a result, the required rates
of return on risky assets as a whole go up.
|Market uncertainy rises
- Interest rates drop
- The stock market drops
|Market uncertainty falls
- Interest rates rise
- The stock market rises
Now we have a simple way of classifying the four possible scenarios
-- the combination of the stock market's movement and the change in the
level of interest rates. The following table gives some of the explanations
for the four possible scenarios, assuming that investors' risk aversions
||Stock Market Rises
||Stock Market Drops
|Interest Rates Rise
- The market has increased its estimate of corporate earnings
more than enough to compensate for the increase in interest rates
due to an increased inflation estimate.
- Market uncertainty has decreased; in addition, the market may
have increased inflation estimates.
- The market has decreased its estimate of corporate earnings,
and has increased inflation estimates.
- If the market increases its estimate of corporate earnings,
the effect is insufficient to compensate for the rise in interest
rates due to an increased inflation estimate.
|Interest Rates Drop
- The market has either increased, or not changed its estimate
of corporate earnings, and has lowered inflation estimates.
- If it has decreased its estimate of corporate earnings, the
decrease is not sufficient to offset the positive effect of lower
interest rates, due to lowered inflation estimates.
- The market has decreased its estimate of corporate earnings
more than enough to compensate for the otherwise positive effect
of lower interest rates, caused by lower inflation estimates.
- Market uncertainty has increased
How to Interpret Current Events in the light of the Model:
Interpretation is valuable only if it reduces the content of the object
being analyzed to a few variables, whose relationship is already well
known. The fundamental variables in this sort of analysis based
on the discussion above are: expected rates of inflation, ex-ante real
rates, market uncertainty, market risk premium and expected future corporate
profits. A fruitful approach is to look at the facts of the situation
(as distinct from interpretations and opinions offered in news reports)
and see how they impact the fundamental variables. Opinions can
then be looked at in the light of this analysis.
Case 1: On October 1, 1998, the yield on the 30 year T-bond dropped
to a low of 4.95%, but the stock market also dropped. How do we explain
To begin with, let us consider that investors have three broadly defined
options: one, to consume today; two, to invest in riskfree bonds and three,
to invest in risky equity securities. If investors increase their preference
for the first alternative over the second and the third, interest rates
will increase and the bond and stock markets, confronted with higher required
rates of return will fall. On the other hand, if investors maintain their
current rate of preference for immediate consumption, but believe that
the risk of equity markets have increased, then stock markets will drop
with no concomitant movement in interest rates. Finally, it is possible
to have what is often described as a flight to safe havens. This would
correspond to the bond market rallying, with stock markets dropping. The
initial impetus for this might be increased uncertainty in equity markets
causing a fall in stock market values. The reduced wealth of investors
might lead them to reduce current consumption and seek to invest more
for the longer term. This then shows up in lower interest rates. This
seems to be what happened in the market on October 1.
Case 2: If we had looked at the 30-year rate on Friday, Jan. 25,
1997, we would have found it to be 5.97%, compared to a rate of 5.87%
as of late Thursday, Jan. 24, 1997. Using the augmented Fisher model,
and assuming a real rate estimate of 4.2%, we would have inferred that
the markets expectation of the long-run inflation rate has jumped
from 1.67% to 1.77%. What could have caused the market to spook? Was all
of the rate change due to a revised inflation estimate? Or should we infer
that the market was revising the real interest rate?
One, the White House scandal could lead to weaker leadership from the
White House; this, in turn, could lead to a lack of control over Congress,
potentially leading to inflationary legislation e.g. increased tax cuts,
leading to higher money supply without necessarily higher real growth.
This would point in the direction of a higher nominal domestic interest
rate in the future, leading to higher long-term interest rates currently.
Two, the Associated Press reported the Japanese government was considering
investing in top commercial banks. The actions of the Japanese government
could lead to increased optimism about Asian economies; this could generate
increased demand for funds in those economies, which would raise the level
of real interest rates everywhere (since the major world economies are
integrated). However, the increased demand for limited productive resources
could also lead to inflation.
Hence the domestic interest rate rise could be due to an increase in
worldwide real interest rates, or due to a higher expected domestic inflation
For Interpretations of market events on Feb. 10 and 11, 2000, look at
the relevant WSJ articles in the Media
Articles section under the heading "Interest Rates."