**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 |
$1000 |
$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% |

94% | 600% | |

77% | 300% | |

59% | 180% | |

4% |
45% |
120% |

26% | 60% | |

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

articleof December 10, 2001