The math
Your bond fund fell because it is about to pay you more.
When interest rates rise, a bond fund loses value at once and earns it back slowly. How slowly has a name, it is printed on the fund's fact sheet, and almost nobody reads it.
What happens on the day rates rise
A bond is a fixed stream of payments. When market interest rates rise, new bonds pay more, so nobody will pay full price for your old one paying less. Its price falls until its yield matches the market. That is the whole mechanism, and it is not a malfunction. It is the market marking your bond to what it is now worth.
Take a ten-year ladder, which is ten bonds maturing one a year, a simple stand-in for an intermediate-term bond fund. Every year the bond that matures and all the coupons get reinvested in a new ten-year bond at whatever rates are that day. Start it at a 4% yield, then move every rate up two percentage points overnight and leave it there.
The day rates rise
$100,000 in a ten-year bond ladder, yields 4% to 6%
- Value the next morning
- $91,200
- Loss
- -8.8%
- Fund duration
- 4.9 years
For the price effect you use modified duration, which is duration divided by one plus the yield: 4.72 here. Multiplied by the two-point move, it predicts -9.4%. The actual loss is a little smaller because bond prices curve rather than fall in a straight line, which is called convexity and which works in the holder's favor in both directions.
That number, duration, is the one that matters, and it means two things at once. Adjusted slightly, it is the percentage the fund loses for each point that rates rise. Unadjusted, it is the weighted average number of years until the fund's money comes back to it. Those turn out to be almost the same number, for a reason that is the whole point of this essay.
And then what happens
The fund that just lost money now owns bonds yielding 6% instead of 4%, and every year it reinvests at 6%. So it starts out behind and catches up. Here is the same $100,000 under three paths: rates up two points, rates unchanged, and rates down two points.
| Rates up 2 points | Unchanged | Rates down 2 points | |
|---|---|---|---|
| Before | $100,000 | $100,000 | $100,000 |
| Instant after | $91,200 | $100,000 | $110,174 |
| Year 1 | $96,672 | $104,000 | $112,378 |
| Year 2 | $102,473 | $108,160 | $114,625 |
| Year 3 | $108,621 | $112,486 | $116,918 |
| Year 4 | $115,138 | $116,986 | $119,256 |
| Year 5 | $122,047 | $121,665 | $121,641 |
| Year 7 | $137,132 | $131,593 | $126,555 |
| Year 10 | $163,326 | $148,024 | $134,302 |
| Year 15 | $218,567 | $180,094 | $148,280 |
The fund that took the loss is ahead of the fund that never took it by year 5. Interpolated, the crossover is at 4.8 years. The fund's duration was 4.9 years. That is not a coincidence. It is what duration is.
Duration is the number of years after which you stop caring what rates did.
Which makes it a question about when you need the money
If you need the money before one duration has passed, a rise in rates cost you. Over three years the shocked fund returned 2.8% a year against 4.0% for the unchanged one. If you need it after, the rise was the best thing that could have happened: over fifteen years the shocked fund returned 5.4% a year against 4.0%.
The falling-rate path is the same story in reverse, and it is the one people get wrong. That fund jumped 10.2% overnight, which feels like winning. But it now reinvests at 2%, the unchanged fund catches it in year 5, and over fifteen years it returned 2.7% a year. A rate cut is not a gift to a long-term bond holder. It is a refund of future interest, paid early.
So the useful rule is simple. Match the fund's duration to when you will spend the money. Money you need in two years does not belong in a fund whose duration is six, because a rate rise between now and then is a loss you will not be around to earn back. Money you will not touch for fifteen years can sit in an intermediate fund and treat every rate rise as a pay raise.
Holding the bond to maturity does not avoid any of this
The common objection is that an individual bond held to maturity cannot lose money, because you get your full face value back at the end. That is true, and it is the most expensive true statement in personal finance, because it confuses not seeing a loss with not having one.
Buy a single ten-year bond at par yielding 4%, and let rates go to 6% the next day. Your statement keeps showing face value plus the coupons you have collected and reinvested. The market would pay considerably less.
| Year | What the statement shows | What it is worth | Loss not shown |
|---|---|---|---|
| 0 | $100,000 | $85,280 | -$14,720 |
| 1 | $104,000 | $90,397 | -$13,603 |
| 3 | $112,734 | $101,570 | -$11,165 |
| 5 | $122,548 | $114,124 | -$8,425 |
| 7 | $133,575 | $128,229 | -$5,346 |
| 9 | $145,965 | $144,078 | -$1,887 |
| 10 | $152,723 | $152,723 | $0 |
The hidden loss shrinks to zero at maturity, which is why it feels like it went away. It did not go away. It was paid, a little every year, in the form of a 4% coupon on a bond that the market would have paid you 6% to hold.
Where the loss went
One ten-year bond at 4%, rates to 6%, held to maturity
- Market loss on day one
- $14,720
- Compounded at 6%, 10 years
- $26,362
- Shortfall at maturity
- $26,362
Against simply owning a new 6% bond from the same day, the holder ends $26,362 behind. That is the day-one loss, to the dollar, plus ten years of interest on it. Holding to maturity converts a loss you can see into a below-market return you cannot, and charges you interest for the privilege.
A bond fund and an individual bond with the same duration take the same hit on the day rates move. The fund simply tells you about it every day. If that is unbearable, the answer is a shorter duration, not a different wrapper.
How much each maturity moves
Duration rises with maturity, but not one for one, because the coupons arrive along the way. Here is the price change for a one-point move in rates on a bond yielding 4%.
| Maturity | Duration (years) | Rates up 1 point | Rates down 1 point |
|---|---|---|---|
| 1 year | 1.0 | -1.0% | +1.0% |
| 2 years | 2.0 | -1.9% | +1.9% |
| 5 years | 4.6 | -4.3% | +4.6% |
| 10 years | 8.4 | -7.7% | +8.5% |
| 20 years | 14.1 | -12.5% | +14.9% |
| 30 years | 18.0 | -15.4% | +19.6% |
Two things to notice. A two-year bond barely moves, -1.9% for a one-point rise, which is why short-term money belongs in short-term instruments. And a thirty-year bond is a different animal: a one-point rise costs 15.4%, which is a stock-market-sized move on something sold as safe. Note too that every row gains more when rates fall than it loses when they rise by the same amount. That asymmetry is convexity, and it is free.
What to actually do
Look up the duration. Bond funds publish it, usually on the fact sheet. It tells you, before anything happens, roughly what a one-point rise will cost and how long it will take to earn back.
Match it to the date you need the money. Near-term money goes in Treasury bills, a high-yield savings account or a ladder of bills maturing within the year, where duration is measured in months. We covered the options in where to keep cash. Long-term money can take duration because it has time to collect on it.
Do not sell after the fall. Selling a bond fund after rates rise locks in the loss and walks away from the higher yield that was going to repay it. It is the bond version of selling stocks at the bottom, with one difference: here the source of the recovery is known in advance, because it is the higher yield the fund now earns.
Rebalance into it, if anything. A fall in the bond fund after a rise in rates is precisely when a rebalancing rule buys more of it, at a higher yield. See rebalancing.
What this leaves out
The model holds every rate at one level and moves them all together. Real yield curves twist, so short and long rates rarely move by the same amount. It assumes government-quality bonds: corporate and especially high-yield bond funds also carry credit risk, which tends to hurt at exactly the moment stocks do, and no amount of waiting one duration fixes a default. It ignores inflation, which is the reason rates usually rise in the first place and which erodes the real value of every fixed payment, the case for inflation-protected bonds. And it ignores taxes on the coupons, which depend on the account the fund sits in.
None of that changes the central point. A rate rise is a loss now and a gain later, the exchange rate between the two is set by duration, and your horizon decides which side of it you are on.