The (Amazing) Power of
Zero Interest Rates
Interest Rates are one of the
most powerful forces in the financial world.
Warren Buffett described it
this way:
At all times, in all markets, in all parts of the
world, the tiniest change in (interest) rates changes the value of every
financial asset. You see that clearly with the fluctuating prices of
bonds. But the rule applies as well to farmland, oil reserves, stocks, and
every other financial asset. And the effects can be huge on values. If
interest rates are, say, 13%, the present value of a dollar that you're
going to receive in the future from an investment is not nearly as high as
the present value of a dollar if rates are 4%.1 (emphasis
added)
For many financial assets
including bonds, stocks and houses, it is longer term interest rates which
have the most impact on value.
North America is currently
experiencing record low interest rates. This is especially the case for
short-term interest rates but is also the case for long-term interest rates.
Where will interest rates head next?
Many financial analysts expect that interest rates will rise significantly
in the next few years due to excessive government borrowing. It may be
logical to expect interest rates to rise back to more normal levels given
that they are currently at record low levels.
But many other financial analysts
predict that interest rates will
stay low or even decline. They predict that higher taxes to pay for
government borrowing will lead to
recession or even depression and lower interest rates. They point out
the fact that long-term interest rates in Japan (which is one of the largest
and most modern economies in the world) are dramatically lower than in North
America. As of July 10, 2010, the 10-year government bond yield (interest
rate) in the United States is a near-record-low 3.05%. Meanwhile in
Japan, the 10-year Government bond yield or interest rates is 1.155% which
is a staggering 62% lower than the near-record-low U.S. interest rates.
In this article, I will not
attempt to predict whether long-term interest rates will rise or will fall.
This article will focus on what will happen to the value of government bonds
if interest rates rise or fall. As Warren Buffett says, the value of all
financial assets including stocks, houses, oil reserves and farmland are
also affected by changes in interest rates. However, except in the case of
government bonds, those values are also impacted by many other variables that can affect the expected cash
flows from such assets. Understanding the impact of interest rates on the
value of government bond investments is useful in itself and it also goes a long
way to understanding the impact of interest rates (as one isolated factor)
on the value of all other financial assets.
Given their importance, all
investors could benefit from a better understanding of interest rates and
their impacts on the fair value of all investments.
The impact of changes in
interest rates becomes more dramatic, the longer the time-frame that is used. We
will use the example of 30-year government bonds which is the longest
maturity bond that the United States (and Canadian) government issues.
As of July 10, 2010, United
States Government 30-year bonds will pay an investor who purchases them an
interest rate of 4.0%.
If an investor purchases a
$1000 30-year government bond, then it will pay an interest rate or coupon
of $40 per year to the investor and at the end of 30 years, the government
will also return the original $1000.
Now imagine that if immediately
after the purchase of this bond something changes in the economy and
investors perceive more risk and demand higher interest rates. This
could easily happen if for example the United States government announced
that it was going to enter into yet another costly war, let's say with
Iran. Now, the government would find that it needs to pay say 5.0%
interest on new 30-year bonds in order to entice investors to buy. So now
when it issues bonds they will pay 5.0% or $50 per year and will return the original
$1000 after 30 years.
So what happens to the market
value of our 4.0% bond, the one that is identical to the new 5.0% bond but
pays only $40 per year instead of the $50 per year available on the new bonds?
Well, the new bonds are
selling for $1000 and deliver $50 per year. So clearly the
"old" bond (though it is is actually only say 1 day older in this
example) that only pays $40 is not worth as much as the $50-paying bond. Its value is
clearly something less than $1000. It only takes a bit of financial math in a
spreadsheet to calculate the new value of the 4.0% bond. I'll show you
the figure in a moment. The important thing to understand is that the value
of an existing long-term bond paying a fixed interest rate automatically
goes down when interest rates rise in the market.
Conversely, the market
interest rate on 30-year United States bonds could fall even lower than the
current near-record-low 4.0% level. (Remember that interest rates are dramatically
lower in Japan). Imagine that it
was announced tomorrow that Japan and Europe were both going to renege on
their bonds. They were simply not going to pay back the money that they had borrowed
since their deficits were too high and they were running out of
ability to raise income taxes. And imagine at the same time that the Unites
States deeply condemned this action and pledged that it would never even
consider defaulting on its bonds. In this admittedly extremely unlikely
scenario we would see a "flight to quality". International
investors would rush to sell any Japanese and European assets they had and
would rush to buy United States Government bonds. This surge in demand for
Unites States Government bonds which would allow them to be sold at even lower
interest rates. Say, for sake of example, 3.0%.
So now we would have new
bonds in the market that cost a $1000 and paid only $30 per year as well as
the return of the $1000 after 30 years. So now, what would be the value of
our identical day-old bonds that paid $40 per year? Clearly it would be
higher than $1000.
To expand the analysis and to
give the precise value changes of the "old bond" as market interest rates
change, I have provided the following table.
It shows the percentage increase or decrease in the value of our 4.0%
30-year bonds if interest rates were to suddenly jump to a new level, a
higher level or a lower level.
|
Value of a 4.0% 30-year Government Bond at
Various Interest Rates
|
| Market Interest Rate |
0.0% |
0.5% |
1.0% |
2.0% |
3.0% |
4.0% |
5.0% |
6.0% |
8.0% |
10.0% |
15.0% |
| Bond
Value |
$2,200 |
$1,973 |
$1,774 |
$1,448 |
$1,196 |
$1,000 |
$846 |
$725 |
$550 |
$434 |
$278 |
| Gain
or Loss |
120% |
97% |
77% |
45% |
20% |
0% |
-15% |
-28% |
-45% |
-57% |
-72% |
The Table shows that the original
value of the 4% bond is $1000 when the market rate of interest is 4%. If interest rates suddenly drop to 3.0% then
a 4.0% bond (with a full 30-year life remaining) is suddenly worth 20% more or
$1196. In an extreme and unrealistic case, if interest rates were to drop all
the way to zero then the value of the bond tops out at $2,200 which is the
value of 30 years times $40 per year ($1200) plus the original $1000.
The Table also shows that if
interest rates were to rise, then the value of an existing 4.0% 30-year bond would
drop quite dramatically. If interest rates were to rise 1.0% to 5.0% such a bond
would lose 15% of its value. And if 30-year government interest rates were
to double to 8.0% then this bond would lose 45% of its market value.
It can also be shown that at
lower interest rates there is not as much room for a 30-year bond to
increase in value as rates drop. The following table shows what happens to a
30-year bond of various starting interest rates if interest rates suddenly
fall in half or (as an extreme example) fall all the way to zero.
| Staring
Interest Rate for 30 Year Bond |
Market Value % Gain if
rates immediately fall by half |
Market Value % Gain if
rates immediately fall to 0% |
| 20% |
94% |
600% |
| 10% |
77% |
300% |
| 6% |
59% |
180% |
| 4% |
45% |
120% |
| 2% |
26% |
60% |
| 1% |
14% |
30% |
The Table illustrates that if
30-year rates start out high like 20% then there are tremendous gains as
interest fall. But if rates are already low, then obviously they don't have
as far to fall. But even at today's 4% 30-year rate, there would be a 45%
gain if 30-year rates were to quickly fall in half to 2%. That seems
unlikely but not impossible.
I mentioned above that 10-year
interest rates in Japan are at just over 1%. That leaves very little room
for gains if interest rates drop even further.
Even if 10-year rates in Japan suddenly fell to zero, the maximum that 1%
bonds could rise to is $1100 (1000 plus 10 years times the $10 coupon).
As I (and perhaps somewhat more
convincingly,
Warren Buffett) mentioned above, the changing level of interest rates also affects
the value of stocks and all other financial assets. Due to all the factors
that can affect the expected cash flows from stocks (whereas the cash flows
on a U.S. government bond are know with certainty) it's not as easy to
determine what will happen to stock prices if interest rates drop. The value
of cash flows go up as interest rates drop, but lower interest rates may also
affect the outlook for corporations and so the analysis becomes much more
complex for stocks as opposed to bonds.
Perpetual Bonds and Fun
with Numbers
To really illustrate the
absolutely amazing power of zero interest rates, I have to move now into the
realm of the theoretical.
There is a class of
investments called perpetuities which promise to pay out a given coupon
forever. The problem is that most of them are not really perpetual in that
the issuer has some right to buy them back at a fixed price. I am not sure
if there any government perpetuities that exist and where the government has
no right to buy them back at any set price. British consol bonds which were
issued in the 1700's and which I understand still trade and pay 2.5%, may be a rare
real-life example, but even there I understand the British Government has
the right to buy them back at par, although it would take an Act of Parliament.
Given their low interest rate, I would expect them to trade well below par.
Now imagine a perpetual
bond issued by a government that pays $100 per year. And imagine market interest
rates applicable to perpetuities are at 10.0%.
The value of this $100 per
year to be received in perpetuity can be easily calculated by the simple
formula of $100 divided by the interest rate. In this case $100/0.10
results in a value of $1000.00 for this perpetual bond.
Now what is the value of this
perpetual bond if the market interest rate falls in half to 5%? The answer
is $100 / 0.05 or $2000. Notice that the value of the perpetual bond
precisely doubles as the interest rate drops in half.
If interest rates drop in
half again to 2.5% the perpetual bond is then worth $100/0.025 or $4000.
At a 1.0% interest rate the
bonds value has increased 10 fold to $100/0.01 or $10,000
Now, remember that we are in
the realm of the theoretical here. It is hard to imagine that the market
interest rate for a perpetuity would ever fall as low as 1.0%.
But, if rates could keep
falling, how many times, in theory, could the rate fall in half and how many times could
the value of our perpetual bond double? The answer is - an infinite number of
times.
If the interest rate on a
perpetual bond somehow fell to 0.1% then its value is calculated as $100 /
0.001 or $100,000. Notice that this is a 1000 year payback which seems rather
long! (It would take 1000 years to earn back what you paid for the bond -
after that though it would all be "gravy" as they say.) In the limit at a 0% interest rate the value of a perpetuity is
theoretically infinite.
And, that really illustrates
the truly amazing power of zero interest rates!
Sadly, the value of your
30-year government bond will not rise to infinity as interest rates drop
towards zero. The reason is that it only pays out for 30 years which,
although a long time, is seriously less than infinity. The maximum value
that a 30-year bond can reach is simply the sum of the coupons to be
received
plus the value of the principal.
END
Shawn Allen, CFA, CMA, MBA, P.
Eng.
President
InvestorsFriend Inc.
July 10, 2010
1. See Warren Buffett in Fortune Magazine
article
of December 10, 2001