The Harsh Realities of Bond Math
By Mark Oelschlager
May 22, 2012
Shortly after I graduated from college my father sat me down and tried to teach me about bonds. He proceeded to explain that prices and yields move in opposite directions, which made no sense to me. (“Wouldn’t you pay more for a higher yield?”) He tried to explain the difference between a bond’s yield and its coupon as well as the effect that time to maturity has on the sensitivity of a bond’s price to changes in interest rates. (“Wait, if the coupon is fixed, why would interest rates change?”) It all sounded so complex, and there were intertwining effects. This, combined with its counter-intuitive nature, made the concept of bond pricing difficult to grasp in a short lesson.
Over the past few years the American public has poured money into bond funds at an unprecedented rate. According to Wall Street firm ISI, as of last week, inflows into US bond funds so far in 2012 averaged a staggering $31 billion per month and were on pace to set a record for the first five months of any year. Conversely, US equity outflows are on pace to set a record for the first five months of any year. But it hasn’t been just this year. Empirical Research Partners tells us that from 2008-2011, a mind-boggling total of nearly $900 billion was redeemed from actively managed US equity funds. Much of this money ended up in bond funds.
As staggering as these numbers are, the trend is not all that surprising given human nature. When it comes to investing, people gravitate toward what has worked recently. Not only have bonds performed well in recent years, they have been in a bull market that has lasted for over 30 years. In addition, bonds did a much better job of protecting investors’ capital than did stocks during the financial crisis of 2008. So, bonds have offered, in recent years, better return with lower volatility. Given all this, and the fact that it still feels like we are in uncertain times, investors have pulled their money from stock funds and put it where it feels “safer” – bond funds.
But is it really safer there? And does the public, having flooded bond funds with their savings, truly understand the risks?
(At this point, if you would like to skip the basics of bond math, you may want to skip ahead to the table showing the change in bond prices associated with various interest rates.)
The yield to maturity on a 10-year US Treasury bond is currently about 1.7%. This means that if an investor buys that bond today and holds it until it matures, and the issuer (the US Treasury) makes all the scheduled payments, the investor will realize an annual return of 1.7%. Throughout this holding period, however, there will undoubtedly be fluctuation in prevailing interest rates, which will drive the price of that bond higher or lower, even though the coupon payments on the bond are fixed. If interest rates fall to, say, 1.4%, the price (value) of the bond will rise by about 3%. It is this effect of declining rates that has driven bond prices steadily upward in recent decades.
But it is important to remember that in the above example, even as the bond appreciates in value, if the investor holds until maturity, his realized return is still only 1.7%, which is not even enough to keep up with the current rate of inflation. Alternatively, if he does cash out after yields fall to 1.4%, takes his 3% gain, and wants to reinvest the proceeds in a new bond, the bond he will have the opportunity to purchase will offer a lower return (yield to maturity) of 1.4%.
And that’s the positive case! What if rates rise?
Let’s say prevailing market rates move from 1.7% to 2.5%. In this case, the value of the bond declines by about 7%. If rates were to rise to 3.5%, the price would decline about 15% from the original purchase price. Please note that this relationship between interest rates and price is set; it’s not speculation. We don’t know where interest rates are headed, but we do know what the price of a bond will be for a given yield.
Again, even if rates rise to 3.5%, if the bond is held to maturity, the realized return will still be 1.7%, but the holder of the bond will have earned a far lower return than what was prevailing in the market. Over a ten year period, the cumulative return, with compounding, for the bond yielding 1.7% is 18%, while that for the bond yielding 3.5% is 41%. It will do no good to sell the bond midstream in order to upgrade to a higher yield, as the total return from that point forward will be identical regardless of whether he holds his original bond or sells and reinvests in a new bond.
That may be confusing, but the key point is that once the investor purchases that bond at 1.7%, his return is locked into that number for the life of that bond, or ten years in our example. (This assumes no risk of not being paid back).
If rates rise, the opportunity cost can be large. The concept of opportunity cost may not strike fear in people’s hearts, but it is very important. One reason for this is that it is intertwined with the effect of inflation on one’s real return. If inflation were to rise to 4%, and one is still earning 1.7% on his bond, his real return is even more negative than it was before. Furthermore, if the investor decides midstream that he needs to sell the bond to finance a home renovation, college tuition, the purchase of a house or boat, or anything else, and rates have risen, suddenly it will become about more than opportunity cost, and he will get back less than what he invested because the value of the bond declined. One of the tenets of investing is that a loss is the same regardless of whether it has been realized (sold) or unrealized.
So, bonds can decline in value, and when they do it is painful to the investor, regardless of the fact that his original expected return is unaffected. To summarize our example, if rates decline to 1.4%, we have a gain in the price of the bond of 3%, whereas a rise in rates to 3.5% results in a loss of about 15%. Not very appealing. But let’s broaden our scope a bit and look at what the gain or loss would be for various interest rates scenarios. Again, this assumes purchase of a 10-year Treasury at 1.7%, followed by a move in rates to…
So, if rates fall to 0.5%, our bond rises in value by 11.5%. This type of a decline in rates seems very unlikely, but I suppose anything is possible. We do know that rates won’t go any lower than 0%, as investors would simply put their money under a mattress rather than invest in something with a negative return.
A move in rates to 1%, which is a major move from 1.7%, would generate a gain of less than 7%.
Of course the losses start when we get above 1.7%. A move to 2% rates results in a 2.7% loss, etc. As you can see in the table, the numbers get really interesting, and scary, as we get up into the mid-single digits for yields. A rise in rates to 5%, a number that for much of the past half-century looked low, would lead to a loss of over a quarter of the original investment, and a move to 9% would destroy almost half the value of the bond. It is easy to forget, but long-term interest rates were well into the double-digits just over 30 years ago. Of course, at that time, the beginning of a 30-year bull market in bonds, nobody wanted to touch bonds. But even in recent years interest rates were generally in the 2%-5% range.
Whether one is investing in stocks or bonds, the goal is to skew the odds in your favor. In looking at the table above, it is difficult to come to any conclusion other than bonds are a poor investment choice currently. The upside is limited, while the downside is large.
Furthermore, while it is extremely difficult to predict interest rates, and we aren’t going to try to do it here, there are some factors at play currently that seem to make a bet against higher rates (which is essentially what one is betting on when buying bonds) even riskier than usual. In the midst of the financial crisis and in its aftermath, the Fed has carried out an enormous expansion of the monetary base in order to try to support the economy. The definition of inflation is too much money chasing too few goods. The expansion in the monetary base has not yet led to high inflation because the flood of new dollars has not yet made it into the money supply through the traditional banking channels. The Fed of course has vowed that it will offset such a surge when it comes, but there is no guarantee it will succeed in this mission. If it doesn’t, there could be a spike in inflation, which would send interest rates sharply higher. So that is one risk.
A second risk is the faith of the public in the credit-worthiness of the US. We have seen what can happen in other countries (specifically, Europe) when investors lose faith in the state’s ability to pay its creditors and start demanding higher yields to compensate for what they see as increased credit risk. These higher yields make it even costlier for a nation to borrow money, which makes balancing their budget even more difficult and causes their debt to increase even more, which makes the public even more reluctant to lend (buy the bonds), which forces the nation to offer even higher rates, and so on. It’s a death spiral that requires outside assistance to arrest. The US has a tremendous advantage in that the dollar is the de facto global reserve currency, and that China is willing to lend to us because it doesn’t want our currency to collapse. However, there is no guarantee these factors will always be in place and be enough to outweigh the continued growth in the national debt. Our debt/GDP ratio isn’t much different from many of the European states that have seen their interest rates spike. It’s just that, at least so far, investors have decided they don’t care. It’s easy to forget that when one buys a US Treasury bond, one is lending money to the government. The US currently has a worrisome level of debt and a large federal deficit with little prospect for improvement (meaning the debt will continue to rise). Yet if you buy a 10-year Treasury bond today you are lending the government money for ten years at a measly rate of 1.7%. Does that rate adequately compensate someone for the risk that the value of the bond might decline significantly?
The aforementioned issues – potential inflation and deteriorating ability to pay – are actually related, and, arguably, the same thing. It is extremely unlikely that the US would default on its debt, so the ability-to-pay issue would likely be corrected through a depreciation of the currency (inflation). In other words, if the US has trouble paying off its debt, it can simply have the Treasury print money. This of course would lead to inflation and a spike in interest rates - and a dramatic loss in the value of any bonds held by the public.
One of the reasons investors have flocked to bonds recently is that people believe they are “safe.” The irony is that if some of these scenarios were to play out, bonds would be a disastrous place to be. But there are other ways bonds could perform poorly. If the economy continues to progress and GDP growth accelerates, bonds are likely to decline in value (yields rise) as the market demands a higher return. We wonder how many investors that have poured their money into bonds understand the potential for capital loss; our suspicion is that most do not.
Even if he has a hard time buying into the likelihood of any of the above scenarios coming to fruition, a bond investor should be extremely nervous about the recent stampede into bonds, given the history of the subsequent performance of asset classes that have drawn extreme levels of investor interest (money). In other words, the public has had an amazing propensity to plow into an asset class right at its peak in performance, resulting in disappointing returns. It is astonishing how consistently this has happened throughout history. With bond funds experiencing record inflows, why would we expect this time to be any different, particularly when the relationship between stock and bond valuations is so out of whack? Bonds have moved in one direction for so long that people have been conditioned to think that they can’t lose money with them. They had been similarly conditioned about residential real estate (“housing never goes down”) before the bottom fell out of that market.
So what should a person do if he is interested in preserving capital and doesn’t want to risk losing it? A far safer alternative to bonds is a savings account at a bank. True, his “yield” will be less – perhaps 0.2% currently – but he will have far more flexibility to take advantage of higher yields when they present themselves, and he will be far less exposed to loss. If bond yields were to rise from 1.7% to 3.5%, the bond investor must sell his bond at a 15% loss before taking advantage of that higher return, whereas the person who had kept his money in a savings account can shift into the 3.5% bond without taking any loss. Also, with this rise in long-term interest rates, it is likely that short-term rates (such as the rate paid by the savings account) will have risen as well, so, even if the money is left in the savings account, the return on that money will be higher than it was before, because the interest rate the bank pays will have risen. In sum, the person who stashes his money in a savings account is sacrificing only about 1.5% (the difference between 1.7% and 0.2%) of return, but has much less downside. Essentially in the bond market right now there are millions of people who are reaching for an extra 1.5% return, and in so doing are opening up themselves to the potential loss of 15%, 25%, or more, which is bonkers.
One footnote. The changes in yields and bond prices in this piece assume no change in the remaining time to maturity of the bond. In other words, the yield change and price change are assumed to occur instantaneously, rather than over a period of time. This is done for simplicity. If the changes were to take place over the course of years, the effect on prices would be muted somewhat, in both directions.
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