Bond Basics 1: Why Bond Prices Fall When Rates Rise

Bonds have a reputation for being conservative, even boring. But no one ever accused them of being easy to understand. I get a steady stream of emails and blog comments about bonds, and they reveal that many investors are very confused by how bond ETFs work, how they’re affected by changes in interest rates, whether investors can use alternatives to bonds, and even whether it’s OK to abandon them altogether. So my next podcast (which goes live on April 19) is devoted to answering common questions about bonds, with the hope of clearing up some of this confusion. As a companion to the podcast, I’ve also created a short series of blog posts addressing the same questions.

In this first installment, let’s dig into one of the most fundamental concepts for bond investors to understand: the inverse relationship between bond prices and interest rates: when one goes up, the other goes down. This is confusing for many people—after all, investors regularly complain that bond yields are low, so shouldn’t higher interest rates be a good thing? And why are we told to stay away from bonds because yields might rise? You never hear people say you should avoid stocks because their dividends might get higher. So what gives?

Yields up, prices down

I’m going to try to explain this important idea using a simplified example. Let’s say Darryl buys a newly issued five-year bond with a face value of $1,000 and an interest rate (or coupon, as it’s called) of 3%, which is the prevailing rate for five-year bonds with similar risk. That bond will pay Darryl $30 in interest each year for the next five years.

Let’s also assume that just hours after Darryl buys his bond, interest rates rise sharply. His brother Larry is now able to buy a five-year bond with the same risk but with a 4% coupon. Larry’s bond will pay him $40 in annual interest for every $1,000 in face value.

Darryl Larry
Face value $1,000 $1,000
Maturity 5 years 5 years
Coupon 3% 4%
Annual interest $30 $40

 

Enter Lisa, who is looking to buy a bond for her RRSP, so she approaches both Darryl and Larry about making a purchase. As you can guess, if both bonds had the same price, Lisa would obviously choose Larry’s bond because it pays more interest. But although Darryl’s bond pays less than the prevailing rate, it’s not worthless. That 3% coupon and its $30 in annual interest is still worth something, even if you can buy similar bonds yielding 4%.

This is where we turn to the elegant mathematics of bond pricing. The value of Darryl’s bond will fall just enough so that its total return will be the same as Larry’s. The calculations are complicated, but a financial calculator or online tool can do it for you easily, as long as you’re careful to use the right inputs. To keep things simple, here’s how the numbers work out in this example, assuming that the bond pays its interest once a year:

Characteristic Darryl’s bond
Face value $1,000
Coupon (annual interest rate) 3%
Annual interest payment $30
Prevailing rate on comparable bonds 4%
Number of years to maturity 5
Market price $955

 

Because of the rise in interest rates from 3% to 4%, Darryl’s bond has fallen in value from $1,000 to $955. That is the price at which Darryl’s bond would deliver the same return as Larry’s over the full five years to maturity.

This means Lisa could buy Larry’s bond for $1,000 and receive $40 in annual interest for five years, for a total of $200 in interest. Assuming she is able to reinvest those interest payments at the current rate of 4%, her total return on the investment would be 4.3% annually. (It’s a little higher than 4% because of compounding: that is, interest earned on the interest.)

On the other hand, Lisa could buy Darryl’s bond for $955. She would receive just $30 in annual interest for five years, for a total of $150, which is $50 less than Larry’s bond paid. But at maturity, Lisa would receive the full $1,000 face value, even though she only paid $955 for the bond. That’s an additional profit of $45. And assuming she is able to reinvest all the interest payments at the prevailing rate, her total return will also be 4.3% annualized over five years:

Darryl’s bond Larry’s bond
Initial investment $955 $1,000
Coupon 3% 4%
Interest received $150 $200
Face value returned at maturity $1,000 $1,000
Final value of investment (including compounding) $1,162 $1,217
Total return over five years 21.7% 21.7%
Annualized return 4.3% 4.3%

 

Even if you struggle a bit with the math, I hope you now understand the main idea: that is, why bond prices fall when interest rates rise. If the prevailing rate on five-year bonds is 4%, a bond like Darryl’s with a 3% coupon must be worth less than face value. To attract investors like Lisa, Darryl would have to lower the price of his bond just enough to make it equivalent to Larry’s bond with its higher coupon. At a price of $955, investors like Lisa now have no reason to prefer Larry’s bond over Darryl’s .

The other way around

Of course, the opposite is also true: if interest rates fall, older bonds with higher coupons become more valuable. To continue our example above, if rates had fallen from 3% to 2% immediately after Darryl bought his five-year bond, its value would have shot up from $1,000 to about $1,047. That is the price at which both bonds would deliver the same total return:

Darryl’s bond Larry’s bond
Initial investment $1,047 $1,000
Coupon 3% 2%
Interest received $150 $100
Face value returned at maturity $1,000 $1,000
Final value of investment (including compounding) $1,156 $1,104
Total return over five years 10.4% 10.4%
Annualized return 2.1% 2.1%

 

What about bond funds?

If you’re a Couch Potato investor you’re probably not buying individual bonds: you’re more likely to buy index funds or ETFs that hold hundreds of bonds. But the principle is still the same: when interest rates rise, the value of all these underlying bonds will fall in value, so the price of your fund will decline to reflect that.

Now here’s the silver lining in all of this. Because the coupons on existing bonds don’t change when rates move, the interest payments you receive every month likely won’t get any lower. Darryl bought a bond that pays $30 in interest, and he’s still going to get that as long as he owns his bond, whether rates fall to 2% or rise to 4%. Here’s where it pays to think like dividend investors, who seem much more willing to tolerate a decline in the price of their stocks so long as their income stays the same.

Indeed, if rates rise gradually, the interest payments on a bond fund will increase as older bonds mature and newer ones are purchased with higher coupons. That means every new dollar you put into your bond fund will have a higher expected return than in the past, because you’re paying less for every dollar of interest. That’s why investors who are still many years from retirement should welcome a modest increase in interest rates: it would cause some short-term pain, but it would also mean higher bond returns over the long term.

 

33 Responses to Bond Basics 1: Why Bond Prices Fall When Rates Rise

  1. BG April 13, 2017 at 12:05 pm #

    This is true for fixed rate bonds only.
    Floaters dont move all that much when interest rates move.

  2. Braj April 13, 2017 at 12:23 pm #

    Thank you for the excellent explanation. I often feel as bonds are unnecessarily convoluted by people. The confidence from understanding what you are holding helps a lot in the canadian couch potato journey!

    Is it even somewhat wise to divert slightly from the CPP, this case being to add in max 5% (of portfolio) ZPR or CPD (preferred shares index ETF)?

    I have recently been considering this but the simplicity of the CPP reigns supreme IMO, it can be hard to justify.

  3. Tim April 13, 2017 at 1:11 pm #

    @Braj Check out the series of posts Dan wrote on preferred shares and the comments at that page: http://canadiancouchpotato.com/2015/03/12/the-role-of-preferred-shares/

    Preferred shares have much more price volatility than bonds and definitely add risk to your portfolio compared to the same money in a bond fund. If you are looking for improved total returns, then owning preferred shares really becomes more of a gamble in the hope that interest rates will rise in the future and that the prices of rate-reset preferreds (which are the largest segment of the Canadian preferred market) will go up as well. Generally speaking, this is true and preferred prices have been going up since late 2016 as people have been anticipating future interest rate rises. But if improved total returns are really the goal, it is simpler in terms of portfolio construction, more clear in terms of risk and cheaper in terms of expense ratios to just adjust your asset allocation to have more in regular equities.

    If you don’t care about total returns and only want monthly income, then I think there is more of an argument for preferred shares. Their yield has dropped compared to last year as their prices have risen, but the CPD 12 month trailing yield is 4.44% right now, for example, so materially above bond yields. But an income-only oriented portfolio is quite different in terms of construction and goals than Dan’s couch potato reference portfolios, which are total return-oriented.

    Regards,
    Tim

  4. Jamie April 13, 2017 at 1:32 pm #

    a few years ago, there was a panic by my investment advisor to sell all my bonds because rates were going to continue changing in one direction for the forseeable future (I can`t recall which).
    I didn`t think this was logical, since selling would lock in $7000 loss.
    So i got a second opinion from a competitor company, who agreed with the first.
    Being stubborn, I sought the opinion of a 3rd company, who agreed with the first.
    Assuming I was clearly not understanding something (I was new to personal finance at the time) that investment gurus did, I sold my bonds and realized a loss.
    That loss hit me hard early in my investment years, when I would work weekends to make extra cash. Realizing I had now worked all those weekends, essentially, for free, was not fun.
    Of course, immediately after I sold the cost of the bonds started climbing, and were worth more than what I bought them for 2 years later.
    I accepted this as the cost of education and have since managed my own investments.

  5. Canadian Couch Potato April 13, 2017 at 3:50 pm #

    @Braj and Tim: Thanks for providing the link to the paper of preferred shares: it sums up my thoughts on this issue, which is that preferred shares are not a necessary asset class, and they certainly are not a replacement for bonds, as their risk profile is very different. Regarding the comment, “If you don’t care about total returns and only want monthly income, then I think there is more of an argument for preferred shares,” I think it’s important to point out that it makes no sense to be unconcerned about total return. Whether you need monthly cash flow or not, no investor can afford to focus on income without also being concerned about capital losses or gains.

    @Jamie: Sounds like the advisors you spoke to were all certain that interest rates would rise. Had they done so, your bond holding would have lost more than it already had. The problem is that no one can predict the direct of interest rates movements, though there is no shortage of commentators who think they can:
    http://canadiancouchpotato.com/2014/07/04/bond-bears-admit-you-were-wrong/

  6. Carl April 13, 2017 at 4:23 pm #

    Thanks Dan, very clear explanation..quick question how does credit rating affect these calculations? Based on your example it does not matter whether is a government or junk bond…thank you!

  7. John Cray April 13, 2017 at 6:46 pm #

    @Dan: Would it be fair to say that if @Jamie had an investment time horizon *longer* than the average duration of the bonds (he mentioned that he was early in his investment years anyway) it would not have made sense to sell at all but keep the bonds instead and not even bother speculating on the direction of the interest rate?

    Reason being – if you wait until your bond matures you get your principal back, so there is *no* way you could realize any net loss?

    Looking at the examples above – if you held the $1000 face-value bond for the full 5 years you would get your $1000 back regardless what the change in interest was. Sure, you might have made more or less on interest depending on the change of the dominant interest rate on new bonds but you would *not* lose _any_ of your nominal initial investment ($1000), so you wouldn’t have to work extra hours to compensate for that realized loss in the case of Jamie.

    The only way to lose all/some of your initial $1000 would be in the case of default – but this is the the credit risk parameter, not interest change.

    I am new to this so please correct my assumptions above if I am off.

    Thank you,
    JC

  8. RR April 13, 2017 at 7:06 pm #

    @ Carl – the credit rating in the example is implied when stating “prevailing rate for five-year bonds with similar risk” and the second bond has the “same risk.” Credit ratings are a guideline for risk and the example is saying that there is no difference in risk. I’m guessing there will be an “all bonds are not created equal” post in this series going into the effect of credit risk on interest rates and yields.

  9. Oldie April 13, 2017 at 7:49 pm #

    @CCP: Excellent explanation again.

    I think you have always been consistent in advising us investors that as long as we are clear on our long term investment horizon (15+ years) we should use bond index funds of approximately 10 year average maturity as our core bond holdings. For illustration, could you describe for us the relative outcomes of holding (not necessarily selling immediately) an ETF of Short maturity bonds under the same circumstances?

  10. Effie April 13, 2017 at 8:43 pm #

    so, if you believe interest rates are going up, and you’re retiring in 5 years, but investing for 20-35, is the reason you would hang on to VAB rather than switch to a short – term bond ETF that the higher yields of the medium term bonds make up for the losses in value you incur?

  11. Canadian Couch Potato April 14, 2017 at 7:59 am #

    @John Cray: If you’re a long-term investor with a properly designed portfolio, it never makes sense to sell your holdings based on your feeling about where interest rates are headed, because you have no idea where interest rates are headed. Your summary is correct: if you hold a bond to its maturity you will not lose money, except in the extremely rare case of default. With bond funds this is a little trickier, because bond funds do not mature, but as you point out, if your time horizon is at least as long as the fund’s duration, there is minimal risk of loss over that period.

    @Oldie: http://canadiancouchpotato.com/2015/05/18/how-changing-interest-rates-affect-fixed-income/

    @Effie: In general, longer-term bonds have higher yields, but are also more sensitive to changes in interest rates. A bond fund like VAB or ZAG has an average maturity of 10 years, so if you plan on drawing money out of the fund in five years it is not appropriate. It could still be appropriate in a retirement portfolio if you also hold, for example, a ladder of GICs to provide cash flow in the shorter term.

  12. JayRoc April 14, 2017 at 12:41 pm #

    Thanks for the read. Does a laddered bond fund provide any defence against rising interest rates/lower bond fund values?

  13. Claude April 14, 2017 at 3:35 pm #

    I must be missing something.
    Late last fall, I put a substantial amount of money in the XBB etf.
    During the months that followed, the value of the unit share of XBB went down.
    If I were to sell XBB now, I would be loosing.
    Furthermore, you are saying that if interest rates rise, the value of XBB will likely go down.

    Well, tell me why putting money in XBB is better that buying 10-year bonds at a fixed 2.55% interest rate per year, with absolutely no risk?

  14. mark April 14, 2017 at 3:38 pm #

    I think a reasonable person who is in touch with what is going on can make a strong case for the beaten down ZPR preferred shares market period, regardless if your looking for income or capital appreciation.
    And considering BOC will most likely follow the USA if they follow through with there projected rate hike cycle? Your getting yield and capital appreciation as preferreds grind higher 🙂
    2018 might set the stage for rising rates in canada if usa raises 3 times this year?

    http://www.theglobeandmail.com/globe-investor/markets/stocks/summary/?q=ZPR-T

    Time to get in was a year ago?

  15. Canadian Couch Potato April 14, 2017 at 3:48 pm #

    @Claude: You’re missing two things. First, XBB paid you monthly interest that would of partly (perhaps completely) offset the decline in the unit price. So you may not have suffered a negative total return. Second, if you bought a 10-year bond last fall then its value would have fallen, too, just like the share price of XBB. And if you sold that 10-year bond now you would have a capital loss, just as if you sold XBB.

    Many investors believe that individual bonds are less risky than bond ETFs, but this is not the case. They are merely more predictable:
    http://canadiancouchpotato.com/2010/03/29/bonds-v-bond-funds/

  16. Canadian Couch Potato April 14, 2017 at 3:52 pm #

    @JayRoc: A laddering strategy can reduce volatility by spreading out your interest rate risk: the shortest bonds in the ladder will be very stable, while the longest ones will be more sensitive to changes in rates. But remember that each individual bond in the ladder will behave the same way as in the example above: they will fall in value when rates go up and vice-versa.

  17. John Cray April 14, 2017 at 6:03 pm #

    @Claude, to @Dan’s point regarding the offset of the unit loss by accrued interest: I am in a similar situation as yourself. I purchased VAB (similar to XBB) on November 1st, 2016 for $26.15 per unit. Over the following months the fund did drop in price and I accumulated paper capital loss. Then it slowly recovered until last Thursday when the last trade price was $25.79 per unit. Still less than what I paid for it.

    If we look at the initial investment depreciation we would have: $25.79 – $26.15 = -0.36 loss per unit.
    Meanwhile though I received $0.284779 per unit. Therefore I have a total loss of only -0.075221 per unit so far. So about 8 cents instead of 36 cents.

    Part of the problem,I think, is that most portfolio tracking software that I’ve seen doesn’t seem to account well for distributions (dividends/interest) as part of the total return. Instead they only show you capital loss/gain. That is for example what google finance does. It keeps the distributions in a total cash section of your portfolio making it difficult to attribute those to individual securities.

    I’ve been on a quest for a good portfolio tracker for DIY investors which does a decent job in the above task as well as others but so far I’ve had partial success. I am curious to know what @Dan has to recommend for good, free, online portfolio tracker?

    On the other hand @Dan, I keep wondering why VAB fell in price over the last 5 months providing that Bank of Canada has been very stubborn to keep the rate untouched? Maybe I’ll find out in the following articles 😉

    Cheers,
    JC

  18. zwzlife April 15, 2017 at 11:17 am #

    Hi Dan,

    Is it now the time to give another consideration for US Total Market Bond (the CAD hedged one from Vanguard – VBU)?

    The YTM of BND/VBU is 2.5% vs ZAG’s 2.02% now.
    How about a 50/50 split of ZAG/VBU?

    Thanks,

  19. Canadian Couch Potato April 15, 2017 at 12:39 pm #

    @John Cray: More to come, but this should help for now:
    http://canadiancouchpotato.com/2013/08/07/is-your-bond-fund-really-losing-money/

    It’s also important to understand that there are many interest rates: short, medium and long term. The Bank of Canada only controls the shortest of short-term rates (the overnight rate) and this has very little effect on the bond market.

  20. mike jeffries April 16, 2017 at 12:09 pm #

    I’m for simple investing. I need equities for portfolio growth. But also, a portfolio diversifier as ballast during bear markets. What is the strongest negative correlator to large cap equities that I would want? Correct me if I’m wrong but it is high quality government long bonds. Therefore it makes sense that a Canadian Long federal government bond fund/etf would be the best diversifier. Corporate bonds behave like equities so I can’t see their usefulness in a portfolio?

  21. Canadian Couch Potato April 16, 2017 at 12:29 pm #

    @mike: Using only long-term bonds in a portfolio usually does not provide the ideal risk-reward trade-off: in general, investors are not usually rewarded significantly for taking that additional term risk. (Long-term bonds are very volatile and carry behavioural risk as well.) A broad-based bund fund with an average maturity of 10 years or so is likely to provide a smoother ride without giving up much in returns.

    Investment-grade corporate bonds don’t behave like equities: they can indeed lose value in a crisis (as they did in 2008-09) but high-quality corporates do still provide a diversification benefit in a balanced portfolio. That said, I don’t believe they’re essential. Using a government-only bond fund instead is a reasonable choice.

  22. Oldie April 16, 2017 at 3:42 pm #

    @CCP:

    “Using a government-only bond fund instead is a reasonable choice.”

    This is is still part of the answer to @mike jeffries’ question regarding the strongest negative correlator to large cap equites to use as “ballast”, right?

    I presume you mean in a practical sense to include funds like ZAG, VAB, XBB, etc., which are not “government-only”, but pretty close, and, more pragmatically, available for low MER.

  23. mike jeffries April 16, 2017 at 10:16 pm #

    @CCP

    I was initially attracted to long gov’t bonds after studying the merits of the permanent port. (PP). During deflationary periods the rationale of the PP as described made sense as the ideal diversifier. The low equity allocation and the unreasonable gold allocation however was not as appealing.
    I think you make perfect sense that high quality corporates should be as good a diversifier and that intermediate bonds offer less volatility and not that much less income benefit than long bonds. I will switch my ZPL and XLB to ZAG. I appreciate your reply.

  24. Manny April 18, 2017 at 8:58 pm #

    @CCP I am 47, have $80k in RRSPs that will move this week to my itrader account, and plan to live a modest retired with just $1000 monthly expenses (already own a house in a latin american country). Should this influence how much I should invest in bonds? or should I keep the 75% stocks and 25% bonds as suggested by a few experts? Others suggest to go for 85% stocks and 15% bonds, and some even 90% stocks! what would you suggest?

  25. Kyle April 26, 2017 at 10:14 pm #

    Hi Dan,

    When investing in a bond ETF like ZAG, does it matter how long you hold the fund, be it 6 months or 6 years, or 16 years?

    Doesn’t that all just get washed out in the purchase price, the sell price, and interest paid out over the term you hold it?

    Thanks

  26. Kyle April 26, 2017 at 10:28 pm #

    In making the move to a Couch Potato strategy away from traditional mutual funds, I am now sitting on about $300k cash in RRSP and TSFA accounts. Is there any timing strategy for transitioning a larger sum of monies in non-taxable accounts from cash into bond ETF’s like ZAG. Also, I haven’t seen any recommendations to look beyond Canadian bond ETF’s…any concern with it all being Canadian?

    Thanks.

  27. Canadian Couch Potato April 28, 2017 at 7:59 am #

    @Kyle: It certainly makes a different how long you hold a bond fund, as with any investment. Over any holding period, a bond fund (unlike with an individual bond) the return is not knowable in advance, as it depends on interest rate movements.

    In my opinion it’s not wise to use a dollar-cost averaging strategy with bonds, as it might be with stocks, which are far more volatile. Nor do I feel one need to diversify away from Canadian bonds:
    http://canadiancouchpotato.com/2014/08/29/ask-the-spud-should-i-use-global-bonds/

  28. Dipu April 29, 2017 at 2:59 pm #

    HI Dan,
    Thanks for this article . It is now clear when interest rate rise bond price falls and yield will rise and vice versa.

    But here is my confusion. lets say i buy 100 bond ETF ZAG.TO today @15.90 per etf my total investment is $1590.
    It pays monthly dividend of 0.038 so 12 months from now I would have collected $45.60 ( 0.038*100*12) which is a return of 2.86% but lets say interest rate rised and due to this bond price declined .
    ZAG.TO is now trading at lower price of $15.40 . I decided to sell this ETF that I am only getting $1540. ( rather a loss of $50 while i only collected $45.60 in divided) so why would anyone buy bond in this market as there is for sure interest rate is going to rise in canada, which will only reduce bond price for investor during time of sell. Am i missing anything here?

  29. Canadian Couch Potato April 29, 2017 at 3:09 pm #

    @Dipu: You are assuming that interest rates are “sure to rise,” which is the same assumption people have been making for years:
    http://canadiancouchpotato.com/2014/07/04/bond-bears-admit-you-were-wrong/

    It’s also not clear why you have assumed that the price of the ETF would fall from $15.90 to $15.40. Where do these numbers come from?

    Finally, you are also assuming that the investor would buy a bond ETF with an average maturity of 10 years with the intention of selling it after one year, which is a flawed strategy to begin with:
    http://canadiancouchpotato.com/2011/07/07/holding-your-bond-fund-for-the-duration/

  30. Dipu April 29, 2017 at 10:24 pm #

    Hi Dan, Thanks for taking time to message back, but I was really hoping for some guidance on bond price and interest rate relationship
    Yes, i had assumed that the interest rate will rise but that was just to get some clarity on what happens if it goes up- just using as an example . Interest rate could go up, down or remain unchanged it really doesn’t matter to me that was not the focus of my question.

    Also taking into consideration interest rate will go up means bond price will go down (as this is the reality )
    so when I said that the bond price will go down from 15.9 to 15.4 that was just an assumption for learning purpose. Thats why I used the word “Lets say” . I know this forum is mostly for the experts so you might have looked for mathematically correct calculation but just to make it clear I am a 26 year old recent graduate who is 100% invested in stocks lately I am considering to allocate 10% -20% of my portfolio on bond and was thinking about buying bond etf ZAG. SO my question was what if I buy at todays price and keep collecting dividend and IF decide to sell it in 1-2 years (assuming the interest rate rises )I would be selling at a lower price than what I bought for . so is it really worth buying ZAG unless I decide to buy and hold it for another 10 years?? I would appreciate if u can share some of your thoughts on this. Thank you!

  31. Canadian Couch Potato April 30, 2017 at 9:18 am #

    @Dipu: Thanks for clarifying your question. Yes, if you buy a bond ETF today and interest rates rise, you will be at risk of losing money over short periods. However, as long as you hold the ETF for at least as long as its duration (in the case of ZAG, about 7 to 8 years) you will not lose your original investment.

Trackbacks/Pingbacks

  1. Weekend reading: Invest every month, come what may, once more with feeling – Frozen Pension - April 15, 2017

    […] Bond basics: Why prices fall when rates rise – Canadian Couch Potato […]

  2. Easter Weekend Reading - April 15, 2017

    […] Canadian Couch Potato Dan Bortolotti offers some bond basics: Why do bond prices fall when rates rise? […]

Leave a Reply