Bond duration is one of the biggest and most important things to understand when managing a portfolio that includes bonds or other fixed income assets. Managed well, bond duration can give the chance for huge capital gains profits. Managed poorly, bond duration can wipe out a supposedly conservative bond portfolio in no time, leaving nothing but a capital losses. This is precisely the sort of topic that is important but can’t be discussed because it will scare away most new investors.
The heart of bond duration is the idea that interest rates matter when you value things. In fact, interest rates matter a lot. The value of all assets are influenced by interest rates. All else being equal, there are two rules you need to memorize:
- When interest rates fall, the value of all assets increases.
- When interest rates rise, the value of all assets decline.
The reason behind these two facts is that a shift in interest rate changes your “opportunity cost” – that is, the amount you could earn on your money by doing other things with it such as put it in the bank or pay off debt. This leads to another rule:
- The further in the future you expect to part with or receive cash, the more powerful the effect of the first two rules will be.
That is, if you are set to receive $1,000 for a bond 30 years from now and interest rates increase, the value of your bond is going to plummet compared to a bond that matures 1 year from now. This has to do with discounting cash flows in the time value of money.
The further in the future your bond (or other asset) is expected to generate cash flow for you, the higher its duration is said to be. That is why experienced investors are obsessed with bond duration and making sure it doesn’t get out of control in their portfolios. Property and casualty insurance companies, and other firms with large bond portfolios, practice a risk management technique known as “asset / liability matching” whereby they attempt to match the duration of bonds with the time period when the cash needs for those funds is expected, while keeping an eye on protecting shareholders from potential interest rate shocks.
A Look at Bond Duration for Two Hypothetical Investors
Consider two bond investors, Brandon and Charles. Both have exactly $1,000,000 in their bond portfolio.
- Brandon owns $1,000,000 worth of McDonald’s bonds that pay 5% annually and mature in 30 years.
- Charles owns $1,000,000 worth of McDonald’s bonds that pay 5% annually and mature in 1 year.
The moment these bonds were issued, they had the following present values (note: I’m not going to teach you how to calculate and discount cash flows; that is what I’m working on for my second book and it is almost 3:30 in the morning – it’s too late to go into it):
- Brandon’s bond has a present value of $772,716 for the interest income he will receive over the next 30 years and $227,284 for the principal he will receive when the bond matures for a total present value of $1,000,000.
- Charles’ bond has a present value of $48,185 for the interest income he will receive over the next year and $951,815 for the principal he will receive when the bond matures for a total present value of $1,000,000.
Now, let’s consider two scenarios: A sudden rise in interest rates and a sudden fall in interest rates. How will both of these investors be affected?
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The Effect of Bond Duration In a Rising Interest Rate Environment
If interest rates for similar bonds immediately and overnight rose to 10%, the bond duration will result in drastically different outcomes for our two investors.
- Brandon’s bond will have a present value of only $473,232 for the interest income he will receive over the next 30 years and $53,536 for the principal value he will receive at maturity for a total of $526,768. That means that he is sitting on an unrealized loss of $473,232 or 47.32% of his money! If interest rates remained constant, it would take him 30 years to get all of his money back and experience no loss. That is a long time to wait and the hit to his balance sheet will be immediate. He wouldn’t be able to sell out of the bonds without taking the loss.
- Charles’ bond would have a present value of $46,485 for the interest income he will receive over the next year and $907,030 for the principal value he will get back upon maturity for a total of $953,515. That is an unrealized loss of $46,485 or 4.65%! Of course, is Charles just waits the entire year, he will collect his entire $1,000,000 in full but if he needs to sell his bond early, he will be forced to take the loss.
The only difference between these two investors is the bond duration of their investment. Brandon has a loss of more than 10x the loss experienced by Charles simply due to the fact that his 30 year bond has a higher duration.
The Effect of Bond Duration In a Falling Interest Rate Environment
If interest rates for similar bonds immediately and overnight fell to 2% the bond duration will result in drastically different outcomes for our two investors. Only this time, they would experience capital gains.
- Brandon’s bond would have a present value of interest payments of $1,123,876 and a present value for the face value of principal on the bond he will receive back at maturity of $550,450 for a total of $1,674,326. Due to the high bond duration, a drop of 3% in interest rates resulted in a $674,326 profit, or 67.43% on his money!
- Charles’ bond would have a present value of $49,260 for the interest payments he will receive and $980,296 for the principal value of the bond he will get back at maturity in 1 year for a total of $1,029,556. That is a capital gain of $29,556 or 2.96% on principal if he sold the bond today.
Using Bond Duration As a Portfolio Management Strategy
You can probably see how bond duration could be used to make speculations on the direction of interest rates and how, if you were correct, the gains could be huge by choosing high duration bonds. Likewise, the losses could be massive if you turn out to be wrong and there is no way to predict the direction of short-term interest rates.
As I wrote on September 24th, I think we are living in the midst of one of the greatest bond bubbles in history. Money is effectively free and the yield on 2-year Treasury notes reached an ALL TIME low of 0.36% on Thursday, October 7th. Got that? All time. We can’t get any cheaper short of entering deflation, which I just don’t think is probable in the long-term for the United States based on the current evidence. (I was actually kind of pleased to see that Warren Buffett just came out and said almost the same thing, arguing that equities are far cheaper than bonds right now and that he can’t “imagine” someone wanting to put their money into long-term bonds under these conditions.)
That means that when the Federal Reserves determines inflation threatens to rear its ugly head, they will respond by raising rates. The faster the recovery, the quicker the rate increase will likely be. So a strong recovery would ultimately lead to rapid increases in bond rates. That would result in huge losses to long-term bonds with high bond durations. It’s just a function of mathematics and discounting cash flows.
In Response To Your Question About Bond Duration
James, you asked:
Do you have any thoughts on the Vanguard High Yield fund (VWEHX)? Just started putting money into it but it’s money I’m not looking to use for 20 years. The average maturity of the bond portfolio is about 6.5 years and they seem more conservative than most high yield funds. I’m 39 now and I’m hoping by the time I’m 60 it’ll be a resource for income since I won’t have a pension. Do you think the fund is going to get killed as interest rates rise or do you think their average maturity will allow them to adjust?
First, let me be abundantly clear about something. I do not make buy, sell or hold recommendations about specific investments. I have no opinion about this security or any security. I am a private investor who is managing his own money. I am not a financial adviser. I am not a broker. All I do is explain to people how I think about specific investments and value investing in particular. I could be completely wrong. Anything I say is pure speculation on my part. If you listen to it, you very well could end up down by the river, homeless, with no home and no savings. I vehemently and passionately disavow any responsibility for any statement on this site or in response to this question. You proceed at your own risk.
Specifically, you asked about the bond duration of a fund with a 6.5 year horizon (which is considered intermediate) so I’ll talk about that and ignore credit quality concerns (if you own a bond portfolio and the underlying credit quality is bad or the particular type of bond suffers a liquidity crisis, that would cause a fall in value that would have nothing to do with interest rates).
- If the bond interest rate increases came over a period of several quarters or years, which is likely, the effect would be more muted because each quarter that passed would bring you closer to your maturity date and thus dampen the influence of interest rate swings on net present value.
- If you plan on holding a bond fund for the same length of time as the underlying bond duration value and there is no risk you may need to liquidate early, these fluctuations became more of an academic abstraction rather than a practical problem. That is, if interest rates did skyrocket suddenly and a 6.5 year bond duration fund dropped in value, but you were able to hold on for another 6.5 years, the unrealized losses you saw on your account statement during that time period should be recovered.
To put that in practical terms, if it took 2.5 years from now for rates to be back to where they were a few years ago, you’d only be the equivalent of 4 years out from the original duration at the time of your purchase.
If it were me, I planned on holding the bond fund for at least 5 years, there was absolutely no way, under any condition, that I would have to sell the fund prematurely, and I was insistent upon having some fixed income portion in my portfolio, a 6.5 year duration wouldn’t panic me at this point. I’d be fine with it. You said you plan on investing in this fund for 20 years, which reduces much of the duration risk.
The specific fund you asked about, though, is a junk bond fund. It is a junk bond fund in the honest-to-goodness definition of the word. It buys high risk junk. According to the description:
It invests at least 80% of assets in corporate bonds that are rated below Baa by Moody’s and have an equivalent rating by any other independent bond-rating agency; or, if unrated, are determined to be of comparable quality by the advisor. The fund may not invest more than 20% of assets in bonds with credit ratings lower than B or the equivalent, convertible securities, and preferred stocks.
That means, if the world went off a cliff again and the economy turned south, bond duration is not the biggest problem a fund like that would be facing. More likely, it would be the underlying default of the bonds held in the portfolio, which could cause significant and substantial losses.
[mainbodyad]My preference, but this is entirely me, would be to find a high quality real estate investment in a town I knew and get a 10% or greater cap rate (return) and that didn’t require much, if any, debt against it. Heaven knows I would never have more than a nominal portion of my portfolio in a junk bond fund! The words of the father of value investing, Benjamin Graham, ring out in my ears, “More money has been lost reaching for a little extra yield” than almost any other mistake in investing. You’re reaching for yield right now. Unless you’ve done a detailed study of the underlying securities held by that fund and have a reason to think they will perform better than the market expects, and even then you could be wrong.
That is, to say, the 6.5 year duration wouldn’t bother me alone. The 6.5 year duration, coupled with a junk bond fund? I know that given my own opportunity costs I could generate higher returns with far less risk so I wouldn’t touch it with a 10 foot pole. But that is me. I have no idea what is appropriate for you and, frankly, given that I am not a financial advisor, I wouldn’t tell you even if I did.
A Way to Get Around Bond Duration Problems
One way to get around bond duration problems on a decent sized portfolio for an average American is to invest in United States savings bonds such as I Bonds. The reason? In most cases, savings bonds have no effective duration (that is, a bond duration of zero) because they can be sold back to the government at any time at their intrinsic value.
How to Calculate Bond Duration
Seriously? No. I might include this in my new book but there is absolutely no practical reason for the average investor to have to manually calculate the duration of a potential fixed income investment. Most online resources can now tell you the average bond duration for a specific security or a bond fund. It would be a waste of time and energy to calculate it yourself unless it were vital to your risk management procedures, such as an insurance investment officer. Even then, I’d guess most just take the figures off the Bloomberg terminal on faith.
Reader Comments (10)
Comments are presented chronologically, with replies indented beneath the comments to which they respond.
timmerjames
October 8, 2010
Joshua,
Thank you for your thoughtful analysis; especially at 3:30 in the morning. What you wrote is pretty much what I expected. And you are exactly right about reaching for yield. That is exactly what I'm doing. Helicopter Ben is forcing us into taking more risk as the 1% savings rate just won't cut it. Of all the money my wife and I have, this junk bond fund is about 5%. Stocks are about 15% and the rest is in cash.
I can't tell you how extremely frustrated I am by our current investing climate. Savers are getting punished in this environment. I've tried valuing some local businesses for sale but can't seem to get to the valuation the local sellers want. By the way, when is your book coming out so I can use it to value a business?
In your post you wrote, "My preference, but this is entirely me, would be to find a high quality real estate investment in a town I knew and get a 10% or greater cap rate (return) and that didn’t require much, if any, debt against it". Did you mean by that statement that you would pay cash for the building and have no mortgage?
I don't know if I'm an outlier on your blog or not but again I am extremely frustrated because finding yield in this environment is tough. If interest rates do rise sharply maybe I'm better off being in cash right now anyway so in 5 years maybe I can get 6% CDs. Because of the investing climate we really haven't expanded our net worth the past couple of years which is frustrating and now it seems I'm paralyzed because of all the uncertainty which is why we are mostly in cash.
Thanks for your post and this blog.
James
Joshua Kennon
October 22, 2010
Replying to timmerjames
Timmerjames,
Sorry for the delay; I'm just now responding to all of the comments from the past few weeks. It's really hard for me to keep up with writing this time of year.
I know what you mean about yield. There were some really exciting convertible preferred stocks a la Benjamin Graham quality back during the crisis that were yielding 12%, 15% or more plus had attached conversion privileges. I remember one Wells Fargo issue falling from a par value $1,000 to $500 and it had most of the upside due to a common conversion right ... I don't remember the specifics now, but most people don't even know stuff like that exists. We lived through a crazy time.
The statement I made: Yes, I meant I wouldn't have used debt. Or, at the very least, I'd have to have a very good reason to use debt. You know, if I could issue bonds or borrow at 4% fixed rate for 30 years, I might consider it but only if there were virtually no chance of missing a payment. I just don't like to worry about my finances. If I had used more leverage in certain situations, I'd be far richer now. But I don't want that kind of pressure in my life. I like what I do and want to keep doing it as long as possible.
You aren't an outlier in your frustration for yield. An older family friend of mine has a seven-figure portfolio and is almost 80 years old. He was complaining that he can't earn more than $10,000 for every $1,000,000 he has amassed over his lifetime without taking on risk. He knew it was stupid to reach for yield but he couldn't stand that his money wasn't earning anything. I think he ended up buying some office buildings and a bunch of rental houses, paying all cash, and parking the rest in high-quality short-term municipal bonds just to bide his time.
There is a reason that I began selling off a lot of our equity positions once the market had recovered a great deal. The opportunity was better to earn a return in our operating businesses. I figured I'd just put the money to work by expanding our core sporting goods company, then take the profit and park it in cash equivalents earning almost nothing. There were reportedly 5-6 year periods where Charlie Munger sat on nothing but Treasury bonds. Sometimes there are droughts. If you avoid losing money, you get to take advantage of situations others can't even imagine.
As for your problem valuing local businesses: A lot of business owners are DELUSIONAL when it comes to valuing their company. Think about this: If you were going to buy a cigarette store (that is on my mind due to the tobacco reports I've been reading, even though I don't smoke) why would you pay a multiple of earnings for a business that did less than, say, $500,000 or $1,000,000 in sales? Unless they are a destination due to their position in the community, you'd be better off opening another cigarette store next door because you would be able to buy the inventory, fixtures, real estate, etc. at book value with no multiple. If you can reproduce a business by buying the fixed assets only, it is often cheaper to do it that way. Where it is worth it to pay a multiple is when you have a business that is a draw in town; e.g., a local jeweler that everyone has used for generations and has a strong customer base that won't be likely to go anywhere else.
I'm hoping to get the book out by late December. It has just been put on hold due to the businesses. In a few years, once we have everything in place, I can't wait to reveal what we've been working on this whole time.
Austin H
October 8, 2010
Joshua-
One of my favorite posts thus far. I've generally avoided bonds until reading "The Intelligent Investor" and added some to my portfolio. Actually, I converted my Roth IRA to bonds to avoid the capital gains taxes. I got that idea from your blog as well. Your words have had a positive impact on my bottom line. -Thanks. I'll pre-order your book if possible. Signed front cover?
timmerjames- If you are worried about inflation, holding cash to wait for a better CD rate might not be the best decision. A good blue chip stalwart with a decent yield would probably work out as a better hedge against inflation. If you wait 5 years with a high inflation rate, your money (buying power) is going to be significantly less than it is now. You will also forgo 5 years of 'gains' as the stock prices adjust to reflect valuation adjusted for inflation.
I too am guilty of having junk bonds and falling trap to chasing a % or 2 of yield. I've love HYG and its monthly dividend. I have the security on auto sell order if the value drops to prevent Armageddon on my portfolio when the day of reckoning comes for bonds.
Thanks again Joshua
Joshua Kennon
October 22, 2010
Replying to Austin H
Austin, I'll be happy to sign a book as soon as I get it published. I'd like just one day to actually write! This time of year, it's hard to get anything done. Aaron is taking care of some changes at our sporting goods business and he is working from 9 in the morning until midnight. I said in another comment a few minutes ago, I can't wait to tell everyone what we are working on but it may be a few years because it would be stupid for the competition to know.
al
December 31, 2013
Joshua,
"My preference, but this is entirely me, would be to find a high quality real estate investment in a town I knew and get a 10% or greater cap rate (return) and that didn’t require much, if any, debt against it."
Getting a 10+% cap rate around certain areas, like SF bay area, is very unlikely. So where would one start the process of finding a town (possibly outside of the state) and "a high quality real estate investment" in that town? What would be the things you would look for and think about if you were looking for rental property investment?
Joshua Kennon
April 11, 2015
Replying to al
There are plenty of research firms that produce regular reports on cap rates for various property types in specific geographic areas.
galacticduck
April 11, 2015
This is a very educational article, and I'm glad I read it without noticing the date. I thought it had been written this year, but when I saw "2010" I smiled. I bought my first my long-term bonds that year and they are currently up 36%. Perhaps it's time to exit long bonds.
Joshua Kennon
April 11, 2015
Replying to galacticduck
I can't offer an opinion on what to do about your long-term bonds (my goal is to get people to make informed decisions based on their own, personal opportunity costs, risk tolerance, etc. since I have no proverbial dog in the fight other than, I hope, to help others live a better life by enjoying financial independence). That said, here is how I generally think about risk management.
When I look at an investment, I'm trying to figure out the odds of permanent, long-term loss of purchasing power after taxes and inflation. Fluctuations in asset values of less than 5 years mean nothing to me since I generally hate debt, don't utility derivatives for speculative purposes, and otherwise behave like an old man living through the Great Depression: Pay cash, hold outright, sit tight on the best assets you can find and generally things work out. Historically, that recipe has led to the greatest wealth accumulation if one has the emotional temperament to stick to it.
Five years ago, you accepted a promise of fixed future dollars, which means you effectively went short the currency and bet that interest rates wouldn't rise. That was the economic reality of the risk you had taken onto your books. Let's assume you are an ordinary, taxable investor. For those two very substantial risks, you made 36% before taxes. Meanwhile, your interest income was taxed at personal income tax rates, which can be high for most affluent households; sometimes 40%+ or more by the time state and local taxes are considered. (Hence the reason it is almost always a mistake for an individual earning a decent amount of money to buy anything other than tax-free municipal bonds in a fully taxable account; you run the taxable equivalent yield formula and it's rarely even close to being a hard decision.)
Now, you are sitting on a 36% unrealized gain, which represents a deferred tax interest-free "loan" from the U.S. Treasury (and potentially your state) of as much as 7% or 8% of the total investment position (we'll assume a worst-case scenario of a rich family living in California). That is capital lost if the position needs to be sold and switched into something else. Even if you are lower income, in a lower tax state, it's still quite a few percentage points - several years' worth of interest income, in any event.
On top of this, in the subsequent 5 years, you've lost 7% to 8% in purchasing power due to inflation.
All things considered, on a risk-adjusted basis, for the exposures you took onto your family's books, a 36% gain in 5 years on an after-tax, inflation-adjusted basis was not at all appealing. You got, for a lack of a more polite term, screwed. You weren't compensated nearly highly enough.
(Side note: This isn't a new phenomenon. Wharton Business School's finance department has been studying the perpetual underperformance of bonds since the U.S. left the gold standard because it represents a total inefficiency of sorts in the market. Investors do not demand a high enough yield for the risks they accept. Thus, bonds haven't managed to actually beat equities, for example, in any rolling 17 year period for something like 150+ years. Going to a fiat fundamentally changed the nature of a bond but investors don't, quite, realize it.)
Meanwhile, at the same time 5 years ago, you could have bought America, Inc. by purchasing the S&P 500. Everything from the biggest oil companies in the world to the biggest soft drink giants on the planet; widespread diversification, low individual firm risk. What did you get?
- Your passive income was taxed at rates sometimes approaching 1/2 or 1/3rd those applied to interest income from bonds
- You enjoyed nearly triple the unrealized gain on the appreciation in the underlying market value of the holdings (just shy of 100% to date excluding dividends)
- You aren't restricted to a single security so there is a much lower chance of engaging in switching costs for portfolio rebalancing, meaning you can enjoy that interest-free loan from the U.S. Treasury on the deferred tax bill you'll owe once you sell the holding for much longer, meaning more money working for you
- The equities represent business ownership and can, as a group, produce higher earnings over time due to new product launches, efficiencies, share repurchases, and a host of other value-added activities given the incentive systems of our capitalist-based economy.
Likewise, there are times when bonds offer far more attractive after-tax, after-inflation return probabilities than stocks based solely on valuation - witness the late 1990's, which I once wrote about here, using a real-world example of long-term Treasury bond yields vs. the earnings yield on Wal-Mart shares.
All of this is to say, I'd argue that you were severely underpaid for the risks you took on back in 2010. That 36% gain is not even remotely worth the downside you accepted. It was a terrible risk-adjusted return, which is what I harp on all the time. It's all about risk-adjustment. A much better deal would have been something like buying an apartment building with 100% cash in the Midwest at the time for 10% or 15% cap rates as the world fell apart. You'd not only have a far higher yield, you'd enjoy much lower effective tax rates on that yield due to things like depreciation allowances, and, at some point, the property itself was likely to recover in value. You'd have received many of the benefits of a bond with few of the drawbacks.
Please don't misunderstand me because I think bonds absolutely have their place in a portfolio (real estate, too, for that matter), but only after risks such as tax law differences and inflation have been evaluated relative to other opportunities at the moment of acquisition. In my own mother-in-law's taxable account, I have her weighted about 1/3rd high-grade corporate bonds with maturities ranging from 3 to 12 years. This had to do with the timing of her retirement; making sure some money was always available, in cash, at pre-determined withdrawal rates when she needs it so I wouldn't be forced to sell her wonderful business ownership stakes in everything from Diageo to Nestle at the worst possible time were we to go into a Great Depression.
galacticduck
April 11, 2015
Replying to Joshua Kennon
Very interesting, and I agree with everything you wrote above. I just want to add that the bond purchase was part of a Harry Browne style Permanent Portfolio. I don't know whether you've ever posted on that but in short it's 1 part cash, one part long bonds, 1 part S&P 500 or total market, and 1 part gold. It would be crazy to only buy the long bonds or gold.
Cheers, and looking forward to rereading your post & comment above when I get home tonight.
Joshua Kennon
April 12, 2015
Replying to galacticduck
Ah! Carry on then, haha! I haven't written about that particular approach but, well structured, it can make sense. I, personally, wouldn't be comfortable ever going past intermediate bonds (probably 8-12 years at most) unless I really had a good reason to do so but the overall portfolio could still work out nicely if it were part of an overall, comprehensive, basket of securities meant survive all seasons and conditions, no matter how remote.