In 2022 a fund of high-quality US bonds, the kind many people hold as the safe part of a portfolio, lost about 13 % in a year. Nothing defaulted. The loss came from one thing: interest rates went up, and when rates go up, the prices of bonds already issued go down. This chapter explains that link from the ground up. We start with what a bond is, then show how a change of a hundredth of a percentage point turns into dollars, and finish by rebuilding four historical episodes with the same arithmetic. The overview article introduced bonds as a class; here we go one step deeper each level.
Level 1 Plain words
For every reader: the idea in plain words, no formulas.
A bond is a loan with a price
When you buy a bond you lend money. The borrower, a government or a company, promises two things: a fixed payment every year, called the coupon, and your money back on a set date, called maturity. A 10-year Treasury note with a 4 % coupon and $1,000 of face value pays $40 a year (in two $20 halves) for ten years and then returns the $1,000.
What makes a bond more than a loan is that you can sell it before maturity. Someone else takes over the payments and pays you a price for them. That price moves every day, and the main reason it moves is the level of interest rates.
Who borrows, and why it matters
The US Treasury borrows to fund the federal government, and markets treat its bonds as free of default risk in dollars. Federal agencies and the mortgage giants issue bonds backed by home loans. States and cities issue municipal bonds, whose interest is usually free of federal income tax. Companies issue corporate bonds, which pay more because the company might fail to pay. Each step away from the Treasury adds a credit spread on top of the Treasury yield (Chapter 9 covers spreads). Every bond, whoever issues it, shares the rate risk this chapter describes.
Why prices fall when rates rise
Picture holding that 4 % note when new 10-year notes start paying 5 %. Nobody will pay you $1,000 for $40 a year when $1,000 buys $50 a year elsewhere. Your note still pays its $40, so the only thing that can adjust is its price. It falls until a buyer who pays the lower price earns about 5 % a year on it, counting the extra gain at maturity when the note repays its full $1,000.
It works in reverse too. If new notes pay only 3 %, your 4 % coupon looks generous and buyers bid its price above $1,000. Bond prices and interest rates sit on opposite ends of a see-saw. The rate a buyer earns at today's price is the bond's yield.
What a basis point is
Rates move in small steps, so the market counts them in basis points. One basis point is one hundredth of a percentage point: a yield going from 4.00 % to 4.25 % has risen 25 basis points, written 25 bp. The Federal Reserve moves its policy rate in multiples of 25 bp, and in 2022 it raised that rate by 425 bp in nine months (Chapter 7 tells that story).
How much does one basis point matter in dollars? For a $1 million holding of a 10-year note like ours, each basis point is worth about $818. A 25 bp rise costs the holder about −2.04 % of the price; a 200 bp rise, the size of the 2022 move, costs about −14.9 %. Longer bonds move more. That sensitivity has a name, duration, and most of this chapter is about it.
A 10-year, 4 % bond: twenty half-yearly coupons of $20 per $1,000 and the face value at the end.Show the numbers
Year
Cash ($)
0.5
20
1
20
1.5
20
2
20
2.5
20
3
20
3.5
20
4
20
4.5
20
5
20
5.5
20
6
20
6.5
20
7
20
7.5
20
8
20
8.5
20
9
20
9.5
20
10
1020
Source: computed: face $1,000 x 4 % / 2 = $20 per half year, as of 2026-10-28.
The last bar is cut: drawn to scale it would be 51 times as tall as a coupon.
Level 2 How it works
For readers who want the mechanism, with the diagrams.
Beginner path stops here
The cash flows
Every plain bond is a schedule of payments: a coupon each period and the face value at the end. Its price today equals each of those payments discounted back to today at the bond's yield. A payment due in ten years counts for less than one due next year, because money in hand can earn interest in the meantime (Chapter 4 works through discounting).
That one sentence explains most of bond behaviour. Raise the discount rate and every future payment is worth less today, and the far ones lose the most, because they are discounted the most times.
Coupon, yield and price: par, premium, discount
Three numbers describe a bond's return, and beginners mix them up.
Name
What it measures
Our 10-year note at a 5 % market yield
Coupon rate
the fixed payment over face value
4 %
Current yield
the coupon over today's price
about 4.3 %
Yield to maturity
the single discount rate that makes the cash flows equal the price
5 %
When the yield equals the coupon, the bond trades at par, $100 per $100 of face. When market yields rise above the coupon, the bond trades at a discount; when they fall below it, at a premium. At a 5 % yield our 4 % note is worth $92.21 per $100; at 3 % it is worth $108.58. As maturity approaches, a discount or premium bond's price drifts back toward par, because the face value is the last payment and nothing can change it.
The price-yield curve
Plot a bond's price against its yield and you get a curve that slopes down and bends upward, like the side of a bowl. The slope at any point tells you how much the price changes for a small yield change. The bend means the slope is not constant: as yields rise, the curve flattens, so each further rise costs a little less; as yields fall, it steepens, so each further fall gains a little more.
Price of the 10-year 4 % bond against its yield. The straight line touching the curve at 4 % is the duration estimate; the gap between line and curve is convexity.Show the numbers
Yield
Price
Tangent (duration only)
0 %
140
132.7
2 %
118.05
116.35
3 %
108.58
108.18
4 %
100
100
5 %
92.21
91.82
6 %
85.12
83.65
8 %
72.82
67.3
10 %
62.61
50.95
Source: computed: semi-annual 4 % coupon, 10 years; Macaulay 8.34 years, modified 8.18, as of 2026-10-28.
Duration in one idea
Duration measures how far a bond's price moves when its yield moves. A modified duration of 8 means a 1 percentage point rise in yield cuts the price by about 8 %. Our 10-year 4 % note has a modified duration of 8.18 years.
Duration also has a time meaning. Macaulay duration is the average date of the cash flows, each weighted by its share of the price. For our note that comes to 8.34 years: earlier than the ten-year maturity, because the coupons pull the average forward. A zero-coupon bond pays nothing until maturity, so its Macaulay duration equals its maturity, and it is the most rate-sensitive bond of a given term.
What makes duration longer:
a longer maturity, because more of the value arrives late;
a lower coupon, because less of the value comes back early;
a lower yield level, because distant payments are discounted less and so carry more weight.
The last point surprises people. The same 10-year bond has a duration near 9.72 years at a yield of half a percent, and under five years at the 16 % yields of 1981. Low-rate worlds make bonds riskier per basis point.
Convexity
Duration draws a straight line under a curve. Over small moves the line and the curve agree; over big moves the curve stays above the line whichever way yields go. That gap is convexity, and it favours the holder of a plain bond: when yields jump, the price falls a little less than duration says, and when they drop, it rises a little more.
The price change of the 10-year 4 % bond for yield moves of 25, 100 and 200 bp in each direction: the duration-only estimate against the estimate with convexity.Show the numbers
Move (bp)
Duration only (%)
With convexity (%)
Full repricing (%)
-200
16.35
17.93
18.05
-100
8.18
8.57
8.58
-25
2.04
2.07
2.07
+25
-2.04
-2.02
-2.02
+100
-8.18
-7.78
-7.79
+200
-16.35
-14.77
-14.88
Source: computed: ΔP/P ≈ −D Δy + ½ C Δy², D = 8.18, C = 78.9; 10-year 4 % semi-annual par bond, as of 2026-10-28.
On a 25 bp move the convexity correction is tiny, +0.025 %. On a 200 bp move it grows to +1.6 %, too large to leave out. Some bonds have negative convexity. Mortgage bonds are the main example: when rates fall, homeowners refinance and repay early, so the bond's price rises less than a plain bond's would (Chapter 17 covers this).
Callable bonds behave the same way. A company that issues a 10-year bond it may repay after three years holds an option, and it uses that option when rates fall. Suppose such a bond pays a 6 % coupon and trades at $108. Its yield to maturity is 4.97 %, yet if the issuer calls it at par in three years, the buyer earns only 3.18 %. Dealers quote the lower of the two, the yield to worst, for that reason.
Yields differ by maturity
Treasuries of different maturities pay different yields. Plot them against maturity and you get the yield curve. Usually it slopes up, since lenders ask more to tie money up for longer. Sometimes short yields sit above long ones, an inverted curve, which has come before most US recessions since the late 1960s (Chapter 7 tells that history). For bond maths the curve matters because a "rate rise" rarely raises every maturity by the same amount. In 2022 the 2-year yield rose more than the 10-year. A portfolio of short bonds then lost less than duration alone would suggest for a long one, yet more than its holders expected from "safe" short paper.
Ladders, bullets and barbells
How you spread money across maturities changes your exposure to rates even at the same average duration.
A ladder holds equal amounts maturing every year, say from one to ten years. Each year one rung matures and gets reinvested at the far end. Income rises and falls slowly with rates.
A bullet concentrates the money around one maturity, which suits a known future bill such as tuition in five years.
A barbell splits the money between short and long bonds and holds nothing in the middle.
Three ways to hold the same amount of bonds: a ladder across ten years, a bullet at five years, and a barbell at two and ten years.Show the numbers
Maturity (years)
Ladder ($)
Bullet ($)
Barbell ($)
1
10
0
0
2
10
0
50
3
10
0
0
4
10
0
0
5
10
100
0
6
10
0
0
7
10
0
0
8
10
0
0
9
10
0
0
10
10
0
50
Source: computed: three illustrative ways to place $100, as of 2026-10-28.
A barbell and a bullet can have the same duration, so a small parallel move hurts them alike. The barbell has more convexity, which helps on big moves, and it gives that up when the curve's middle moves differently from its ends. Level 3 puts numbers on the trade.
Reinvestment risk
A bond's yield to maturity assumes that every coupon gets reinvested at that same yield. If rates fall after you buy, the coupons earn less and your realised return falls short of the yield you bought. If rates rise, your bond's price drops but the coupons earn more. These two effects pull against each other. Over a holding period equal to the bond's Macaulay duration, they roughly cancel, which is why insurers and pension funds match the duration of their bonds to the timing of what they owe. That practice is called immunization.
TIPS and breakeven inflation
A Treasury Inflation-Protected Security, or TIPS, adjusts its face value with the consumer price index, and pays its coupon on the adjusted amount. Its yield is a real yield: a return over inflation. An ordinary Treasury pays a nominal yield, with no adjustment.
The gap between the two yields of the same maturity is breakeven inflation. If inflation runs above the breakeven, TIPS beat nominal Treasuries; if it runs below, nominal Treasuries win. At the end of 2021 the 10-year nominal yield was 1.52 % and the 10-year TIPS yield was −1.04 %, a breakeven of 2.56 percentage points (FRED series DGS10 and DFII10). Inflation in 2022 ran far above that.
The 10-year Treasury yield less the 10-year TIPS yield, the market's breakeven inflation rate, from FRED.Show the numbers
Month
10-year nominal (%)
10-year real (%)
Breakeven (%)
2003-12
4.27
1.98
2.28
2004-12
4.23
1.67
2.56
2005-12
4.47
2.12
2.34
2006-12
4.56
2.25
2.31
2007-12
4.1
1.79
2.31
2008-12
2.42
2.17
0.25
2009-12
3.59
1.36
2.22
2010-12
3.29
1.04
2.25
2011-12
1.98
-0.03
2.01
2012-12
1.72
-0.76
2.48
2013-12
2.9
0.74
2.16
2014-12
2.21
0.51
1.7
2015-12
2.24
0.73
1.51
2016-12
2.49
0.56
1.94
2017-12
2.4
0.5
1.9
2018-12
2.83
1.02
1.82
2019-12
1.86
0.14
1.72
2020-12
0.93
-0.98
1.92
2021-12
1.47
-0.99
2.46
2022-12
3.62
1.36
2.26
2023-12
4.02
1.84
2.18
2024-12
4.39
2.09
2.3
2025-12
4.14
1.9
2.24
2026-10
5.16
2.82
2.35
Source: Federal Reserve Bank of St. Louis, FRED, series DGS10 (10-year Treasury constant-maturity yield, percent; monthly mean of daily values); Federal Reserve Bank of St. Louis, FRED, series DFII10 (10-year TIPS yield (real), percent; monthly mean of daily values), as of 2026-10-26.
Monthly means of daily yields; the table shows each December and the latest month.
TIPS protect against inflation, yet they are still bonds with duration. When real yields rise, TIPS prices fall, and in 2022 they fell hard (Level 4).
Level 3 The math
For Series 65 and CFA readers: formulas and worked examples.
Series 65 path stops here
Pricing a bond
Take a bond with coupon per period, face value , yield a year compounded times a year, and periods left. We write its price as a sum.
In words, a bond's price equals every coupon and the face value added up, each one divided by one plus the period yield once for every period until it arrives.
Worked example A 10-year 4 % note at three yields
Coupons come to $2 per $100 every half year for periods. With the period yield equals the period coupon and the price comes to $100.00, par. Raise the yield to 5 % and we discount every payment at 2.5 % a period; the price drops to $92.21. Cut it to 3 % and the price rises to $108.58. A one-point fall in yield gains more than a one-point rise loses, which is convexity showing up already.
Macaulay and modified duration
Macaulay duration weights each payment date (in years) by the share of the price that payment supplies.
In words, Macaulay duration is the average time until the bond's cash arrives, with each date weighted by the present value of the payment due then.
Modified duration converts that time into a price sensitivity.
In words, modified duration is Macaulay duration divided by one plus the period yield, and it equals the percentage fall in price for each unit rise in the yield.
Worked example Duration of the 10-year 4 % note
Working through the twenty cash flows at a 4 % yield gives 8.34 years. Dividing by gives 8.18 years. So a 1 percentage point rise in yield costs about 8.2 % of the price, and a 1 bp rise costs about 0.082 %.
Convexity and the second-order estimate
Convexity is the curvature of the price-yield curve, scaled by price.
In words, convexity measures how fast duration itself changes as the yield moves, per dollar of price.
Together the two give the standard estimate of a price change for a yield change .
In words, the percentage price change is about minus duration times the yield change, plus half the convexity times the yield change squared.
The first term changes sign with the move; the second is always positive for a plain bond, because a squared change is positive whichever way the yield goes.
Worked example A 25 bp rise, three ways
Our note has 78.9 (in years squared) and 8.18 years. Set .
Piece
Calculation
Result
Duration term
−2.04 %
Convexity term
+0.025 %
Both together
sum of the two
−2.02 %
Full repricing at 4.25 %
the bond-price formula again
−2.02 %
The duration-only estimate is off by about 0.024 % of the price, small enough that traders quote rate risk by duration alone for moves this size. A 25 bp fall gives +2.07 %: larger in size than the loss from the rise.
Worked example A 200 bp rise, the size of 2022
With the duration term is −16.4 % and the convexity term +1.6 %, so the estimate becomes −14.8 %. Full repricing at a 6 % yield gives −14.9 %. Duration alone overstates this loss by more than a percentage point; with convexity the estimate lands within a tenth of a point.
DV01: one basis point in dollars
Desks run rate risk in dollars per basis point.
In words, DV01 is the market value of the holding times its modified duration times one basis point, the dollar change for a 0.01 percentage point move in yield.
Worked example A $1 million position
At par the market value is $1,000,000, so , about $818. To hedge, a manager who holds this note and wants no rate exposure sells enough of another instrument to carry the same DV01 the other way. DV01s add across positions, which is why risk reports total them.
Portfolio duration and hedging with DV01
The duration of a portfolio is the market-value weighted average of its bonds' durations. A mix of 60 % in a 2-year note and 40 % in a 30-year bond, both 4 % par bonds, has a duration of 8.09 years, close to the 10-year's 8.18 years even though it holds no 10-year bond at all. Half in a 2-year and half in a 10-year gives 5.04 years.
Hedging uses DV01. A $1 million 5-year 4 % note has a DV01 of $449, against $818 for the 10-year. To offset the rate risk of $1 million of 10-year notes with 5-year notes, a desk sells about 1.82 times as much face value, about $1,820,348. The hedge protects against parallel moves only. If 5-year yields rise and 10-year yields stay put, the hedged position gains or loses anyway; this leftover is curve risk.
Effective duration
For bonds whose cash flows change with rates (callable bonds, mortgage bonds), the formula for Macaulay duration does not apply. We instead reprice the bond with yields shifted up and down and measure the slope.
In words, effective duration is the price with yields down minus the price with yields up, divided by twice the starting price times the shift.
For our plain note a 25 bp shift gives 8.18 years, matching the formula, as it should. For a mortgage bond the two numbers part company, because the cash flows move when rates move.
Zero-coupon bonds and long duration
Consider a 30-year zero-coupon Treasury strip at a 4 % yield. It costs $30.48 per $100 of face value, its modified duration is 29.41 years, and a 100 bp rise cuts its price by −25.4 %. Pension funds that owe money in thirty years hold these bonds because they move like the liability. For a saver with no such liability, one of these strips is a large bet on rates.
The math Barbell against bullet
Start from a 5-year 4 % bullet with 4.49 years. We match that duration with 59 % in a 2-year note and 41 % in a 10-year note. The barbell's convexity comes to 35.3 against the bullet's 23.5, so in a large parallel move the barbell does better. Markets know this, and a barbell usually yields a little less than the bullet: investors pay for convexity with yield.
Reinvestment and the realised yield
Hold the 10-year 4 % note to maturity and reinvest every coupon at a rate . The ending wealth per $100 is the face value plus the future value of twenty $2 coupons. With the realised yield is 4.00 %, the yield bought. At it drops to 3.68 %; at it rises to 4.35 %. Over ten years the coupons supply a large part of the total, so the reinvestment rate matters more than many holders expect.
Breakeven inflation and the Fisher relation
Irving Fisher linked nominal and real rates through expected inflation .
In words, one plus the nominal rate equals one plus the real rate times one plus inflation.
So breakeven inflation is about . At the end of 2021 that difference was 2.56 percentage points, and the exact Fisher form gives 2.59 %; FRED's own breakeven series (T10YIE) read 2.56 % that day. With a nominal yield of 4.3 % and a real yield of 1.9 %, inflation of 3 % would leave a TIPS holder +0.66 percentage points a year ahead of a nominal holder.
The math Taxable-equivalent yield
Interest on most municipal bonds is free of federal income tax. To compare it with a taxable bond, divide by one minus the tax rate .
In words, the taxable-equivalent yield is the tax-free yield divided by one minus the investor's tax rate.
A 3.5 % muni for an investor in the 32 % bracket is worth 5.15 % in taxable terms. Chapter 9 uses this for credit, and Chapter 22 for where to hold what.
Level 4 History, analysed
For readers who want past episodes run through the Level 3 math.
1981: the highest yields in the series
1981Ten-year Treasury yields peak at 15.84 %
On 30 September 1981 the 10-year Treasury yield closed at 15.84 %, the highest value in FRED's daily series, as the Federal Reserve under Paul Volcker held policy tight to break inflation. A buyer of a new 10-year note that day bought a bond with a modified duration of only 4.94 years, because high coupons return much of the value early. A year later the yield stood at 11.73 %, a fall of −411 bp. Repriced as a 9-year bond, the note had gained +22.5 % in price, and with a year of coupons the total return came to +38.3 %.
Two lessons sit in that year. High yields shorten duration, so the same rate move does less damage per basis point than it would today. And the investors who earned those returns were the ones willing to lock in long bonds when inflation fears were at their worst; a holder of short bills rolled into lower yields instead.
1994: the great bond sell-off
1994The Fed starts hiking and bonds lose a year of income
The Federal Reserve raised its target rate on 4 February 1994, its first hike in five years, and kept going until it reached 6 % on 1 February 1995, double the 3 % where it started. The 10-year yield had touched 5.19 % on 15 October 1993; by 7 November 1994 it was 8.05 %, a rise of +286 bp.
We run the move through the Level 3 tools for a 10-year note bought at par at the low.
Measure
Result
Duration-only estimate, instant move
−22.1 %
Full repricing, instant move
−19.4 %
Repriced a year later as a 9-year bond
−18.1 %
Total return over the year with coupons
−12.9 %
Three things soften the duration estimate. Convexity cuts the loss by almost three points for a move this large. A year of ageing shortens the bond. And a year of coupons pays back a slice. Still, a holder of the safest bond in the world lost about an eighth of the money in a year. Leveraged holders lost far more. Orange County, California, had borrowed to buy bonds that paid off only if rates stayed low, and it filed for bankruptcy in December 1994 (the size of its loss is in Gaps).
March 2020: even Treasuries can wobble
2020The dash for cash in the Treasury market
As the pandemic shut economies in March 2020, investors sold whatever they could turn into cash, including Treasuries. The 10-year yield fell to 0.54 % on 9 March 2020 and then rose to 1.18 % by 18 March, a move of +64 bp in nine days, while stocks were also falling.
At a yield near half a percent, a 10-year bond priced at par has a duration of 9.72 years. Repricing it from 0.54 % to 1.18 % gives −6.0 %, a loss for the asset that portfolios hold to cushion a stock crash, in the very week the cushion was needed. The Federal Reserve then bought Treasuries in large amounts, announcing on 23 March 2020 that it would buy them in the amounts needed, and the market calmed. The episode shows a liquidity risk that no duration number captures: in a panic, even the deepest market can briefly struggle to absorb sellers.
2022: the year bonds failed as a cushion
2022Rates jump and the bond index loses about 13 %
The Federal Reserve raised its target from 0 to 0.25 % on 16 March 2022 to 4.25 to 4.50 % on 14 December 2022. The 10-year yield went from 1.52 % at the end of 2021 to 3.88 % at the end of 2022, a rise of +236 bp (FRED DGS10). The Bloomberg US Aggregate bond index returned about minus 13.0 % for the year, its worst calendar year since the index began in 1976.
We can rebuild most of that loss. At the end of 2021 the Aggregate's duration stood at about 6.6 years. Multiplying by the 10-year's move gives a price effect of −15.6 %. Adding about 2 % of coupon income (an assumption; the index's own income return is in Gaps) gives −13.6 %, within 0.6 percentage points of the reported loss. We leave convexity out on purpose: mortgage bonds make up about a quarter of the index and their convexity is negative, while the rest is positive, so the two partly cancel. Using the 10-year as a proxy for the whole index simplifies things too, since short yields rose more than long ones that year.
TIPS did not escape. Over 2022 the 10-year real yield rose from −1.04 % to 1.58 %, a move of +262 bp. With a duration near seven years for a broad TIPS fund, that move cost far more than the inflation adjustment added. Investors who bought TIPS as "inflation insurance" learned that it covers the inflation part of the yield and leaves the real part exposed (Chapter 20 works the TIPS case through).
What should a reader take from 2022? A bond fund's duration tells you, in advance, roughly what a given rate rise will cost. In 2021 an Aggregate duration of about 6.6 told every holder that a two-point rise in yields would cost around 13 %. A yield of about 1.5 % offered very little income to absorb such a move. Anyone could have run this arithmetic before the losses arrived.
What the four cases share
Put the four episodes side by side and one variable explains most of each outcome: the yield change multiplied by the duration. In 1981 a falling yield and a short duration gave a large gain. In 1994 and 2022 rising yields and longer durations gave the worst bond years in living memory. March 2020 shows that the same arithmetic applies over nine days as over a year.
Two second-order effects shift the totals. Convexity trims large losses and pads large gains for plain bonds, and it works against mortgage bonds. Income offsets part of a loss, and it offsets more when starting yields are high; the 1994 holder started at 5.19 %, the 2022 holder at about 1.5 %. When a reader sees a bond fund's duration and yield on a fact sheet, those two numbers give a rough range for the next year: the yield is the income, and duration times a plausible yield change gives the swing in price.
Board of Governors of the Federal Reserve System, FOMC statements of 4 February 1994, 1 February 1995, 23 March 2020, 16 March 2022 and 14 December 2022.
Bloomberg US Aggregate Bond Index, calendar-year 2022 total return as published by Bloomberg.
Frederick R. Macaulay (1938), Some Theoretical Problems Suggested by the Movements of Interest Rates, Bond Yields and Stock Prices in the United States since 1856, National Bureau of Economic Research.
Frank J. Fabozzi, Bond Markets, Analysis, and Strategies, for duration, convexity and immunization.
Irving Fisher (1930), The Theory of Interest.
Gaps
The Bloomberg US Aggregate's effective duration at the end of 2021 (we use about 6.6 years) and its income return for 2022 (we assume about 2 %) come from Bloomberg's index reports, which we did not have; the rebuild of 2022 is approximate on both counts.
The duration of a broad TIPS fund at the end of 2021 (we say near seven years) is a round figure; fund fact sheets give the exact value.
Orange County's 1994 loss is usually reported at about $1.6 billion to $1.7 billion; we leave the exact figure to the county's bankruptcy filings.
We treat each historical move as a parallel shift of one yield. Real curves twist, and an index holds many maturities.
Terms
coupon
the fixed interest payment a bond makes, quoted as a yearly percentage of face value.
maturity
the date a bond repays its face value and stops paying coupons.
yield
the return a buyer earns at today's price if the bond pays as promised and is held to maturity; also called yield to maturity.
basis point
one hundredth of a percentage point (0.01 %); 100 basis points make one percentage point.
par
a price equal to face value, which happens when a bond's yield equals its coupon rate.
discount bond
a bond trading below face value because market yields are above its coupon.
premium bond
a bond trading above face value because market yields are below its coupon.
duration
a measure of how much a bond's price changes when its yield changes; also the weighted average time until its cash arrives.
modified duration
the percentage price change for a one percentage point change in yield, with the sign reversed.
Macaulay duration
the average time until a bond's cash flows arrive, weighted by their present values, in years.
zero-coupon bond
a bond that pays no coupons and returns its face value at maturity; its duration equals its maturity.
convexity
the curvature of the price-yield relationship; it makes a plain bond gain more when yields fall than it loses when they rise by the same amount.
DV01
the dollar change in a position's value for a one basis point change in yield.
ladder
a bond portfolio with equal amounts maturing at regular intervals.
barbell
a bond portfolio concentrated at the short and long end of the maturity range with little in the middle.
immunization
matching the duration of bonds to the timing of a liability so that rate moves affect both alike.
TIPS
Treasury Inflation-Protected Securities, whose face value rises and falls with the consumer price index.
real yield
a yield measured over inflation; what a TIPS pays.
nominal yield
a yield in plain dollars, with no adjustment for inflation.
breakeven inflation
the inflation rate at which a TIPS and a nominal Treasury of the same maturity would return the same; about the nominal yield less the real yield.
credit spread
the extra yield a bond pays over a Treasury of the same maturity, for the risk that the borrower fails to pay.
yield curve
Treasury yields plotted against maturity; usually upward sloping, sometimes inverted.
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