The Fed for the
fifth time this year lowered interest rates by 0.5 percentage points. This
brings the target nominal interest rate down to from 4.5% to 4%.
the labor department announced that for April (4.01) the consumer price
index rose by a seasonally adjusted 0.3%. This brought the rate of inflation
over the past 12 months to 3.3%.
slightly up, and nominal interest rates down, I though it might be interesting
to take a fresh look at the patter of real interest rates over time. But
first a quick description of what a “real interest rate” means.
the real interest rate is the real value of loan repayments. The nominal
interest rate is usually quoted in newspapers, and describes the amount
of money that must be repaid on a loan, but does not take into account
that the value of the repayment may be less due to inflation. The real
interest rate makes this inflation adjustment.
The Fisher equation
shows how one calculates the real interest rate (r) given the nominal interest
rate (i) and the inflation rate:
r = i – inflation
running at over 3% per year, this means that current real rate of interest
is getting close to zero.
Here’s an example.
Suppose that you put $100 in the bank and earned a (nominal) interest rate
of equal to i. After 1 year you would have 100 * (1 + i).
So if i is 10%,
you would have $110. However, if there is some amount of inflation in the
economy, then this $110 would be worth a bit less. In particular, it would
be worth $110 (1 – inflation). So if inflation were 5%, then it would be
worth slightly less than $105.
$100 –> 1 year –> $100 (1 + i)
which is worth –>
$100 (1 + i ) (1 – inflation) = $100 ( 1 + i – inflation – i*inflation).
If both the interest
rate and the inflation rate are both small, then we can ignore i*inflation
and then we can write
$100 –> is next year worth –> $100 (1 + i – inflation) = $100 (1 + r),
where r = i –
This again is
the Fisher equation.
Note that the
above is only true ex post – that is only after inflation has been
determined. The real interest rate for the coming year must take into account
expected inflation, since we are not exactly sure what inflation will be
in the future.
interest rates are often set in advance, if the inflation rate turns out
to be higher than expected, then the real interest rate will turn out to
be lower than expected. Since what people care about is the real exchange
rate, any unexpected inflation will benefit borrowers since the real rate
will turn out to be lower than anticipated – this is because the real value
of the payment, if not the actual number of dollars, will be less. For
the same reason, unexpected inflation will hurt lenders.
The graph below
shows the pattern of real interest rates over the past 50 years to so.
With real interest rates currently at about 1%, we will be dipping to levels
not seen since the last recession in the early ’90’s.
This would suggest
that the Fed has been taking a very aggressive stance towards what it feels
is a weakening economy. Will the recent interest rate changes do the trick?
Check back in about 6-15 months to find out.