Pull to par
Also written Pulled to par · Pull to par effect
The movement of a bond's price toward its face value as maturity approaches — premium bonds drift down to par, discount bonds drift up to par, and at maturity every bond is worth face value.
In plain language
On the day a bond matures, the issuer pays face value. Not the market price the bond fetched last year, not what the buyer paid — face value. So whatever price a bond trades at today, it has to arrive at par by the maturity date.
The workbook calls this the "pulled to par" concept: the movement of a bond's price toward its face value as it approaches its maturity date.
- A premium bond, trading above par, decreases in price as maturity approaches.
- A discount bond, trading below par, increases in price as maturity approaches.
- A par bond stays at par.
Market yields can push a bond's price around along the way. The pull to par is the steady force underneath, and it wins at the end.
How it works
Whether a bond is at premium or discount depends on its coupon against the market yield:
| Relationship | Price |
|---|---|
| Coupon rate = yield | At par |
| Coupon rate < yield | At discount |
| Coupon rate > yield | At premium |
The workbook traces the price path of an original 10-year, 9% annual coupon bond priced to three different yields, holding each yield constant until maturity:
| Years to maturity | Discount (yield 11%) | Par (yield 9%) | Premium (yield 7%) |
|---|---|---|---|
| 10 | 88.2220 | 100.00 | 114.05 |
| 8 | 89.7080 | 100.00 | 111.94 |
| 5 | 92.6080 | 100.00 | 108.20 |
| 3 | 95.1130 | 100.00 | 105.25 |
| 1 | 98.1980 | 100.00 | 101.87 |
| 0 | 100.0000 | 100.00 | 100.00 |
The discount bond climbs and the premium bond falls, with no change in yield at all. The movement also speeds up near the end: the premium bond loses 1.02 in its first year (114.05 to 113.03) but 1.87 in its final year (101.87 to 100.00).
The workbook draws a risk conclusion from this in section 1.12: if the bond is held until maturity, there will be no price risk — the pull to par guarantees the redemption price, whatever happened in between.
A worked example
The workbook's price path, applied to Rs 10 lakh of face value (10,000 bonds of Rs 100).
Two investors buy the same 10-year, 9% annual coupon bond on the same day, at different yields.
Mrs Pillai buys at a yield of 11 percent — a discount price of Rs 88.2220.
Cost = 10,000 × 88.2220 = Rs 8,82,220
Value at 5 years left (yield unchanged) = 10,000 × 92.6080 = Rs 9,26,080
At maturity = 10,000 × 100 = Rs 10,00,000
Pull-to-par gain over the life = Rs 1,17,780
On top of that she receives the 9 percent coupon — Rs 90,000 a year.
Mr Kohli buys at a yield of 7 percent — a premium price of Rs 114.05.
Cost = 10,000 × 114.05 = Rs 11,40,500
At maturity = Rs 10,00,000
Pull-to-par loss over the life = Rs 1,40,500
He receives the same Rs 90,000 a year in coupons, so over ten years Rs 9,00,000 of coupon partly offsets a Rs 1,40,500 price decline built into his purchase.
Neither investor made a mistake. The premium Mr Kohli paid was the price of a coupon above the market yield, and the pull to par hands that premium back to the issuer a little each year.
Why NISM asks about it
Chapter 1 (Introduction to Interest Rate, Interest Rate Instruments and Fixed Income Markets) introduces pull to par in section 1.11.7, "Price Time Path of a Bond", with the 10-year 9% bond table at 11, 9 and 7 percent. Section 1.11.6 supplies the coupon-versus-yield rule for premium and discount, and section 1.12 uses pull to par to argue that a bond held to maturity carries no price risk. Expect a question on which direction a premium or discount bond moves as maturity nears.
Common exam traps
- Premium bonds fall toward par; discount bonds rise toward par. Not the other way round.
- Pull to par happens with yields unchanged. It is a time effect, not a rate effect.
- Coupon above yield = premium; coupon below yield = discount.
- At maturity every bond is worth face value, whatever it traded at before.
- No price risk if held to maturity is the workbook's conclusion — it does not remove credit risk or reinvestment risk on coupons.
- The drift accelerates near maturity. The last year's move is larger than the first year's.
Where this is taught
Free preparation for NISM Series IVRelated terms
- Face valueThe denomination a company's capital is divided into and carried in its books — fixed, printed on the certificate, and the base on which dividend percentages and stock splits are computed.
- Reinvestment riskThe risk that the coupons or other intermediate cash flows from an investment have to be put back to work at a lower rate than the original investment earned, pulling the total return below the promised yield.
- Yield to MaturityThe single discount rate at which a bond's future coupons and redemption amount add up to exactly its market price today — the return you actually earn if you hold it to maturity.
- Zero coupon bondA bond that pays no coupons: it is issued below face value and repays the face value at maturity, so its duration equals its maturity.
- Coupon rateThe rate of interest a bond pays, applied to its face value and never to its market price — which is why the coupon tells you the cash flow but not the return.
- ConvexityThe curvature of the price-yield relationship — the correction duration misses, because duration is a straight line and the true relationship bends.
- Coupon effectThe fact that two bonds with the same issuer and maturity but different coupons show different yields to maturity even when both are priced correctly off the same zero curve — why YTM cannot judge mispricing.
- Redemption valueWhat the issuer pays at maturity other than the coupon. Above face value the bond is redeemed at a premium, below it at a discount, and equal to it at par.