Discount vs Premium Bonds
Discount vs Premium Bonds
A bond trading below par (face value) is trading at a discount. A bond trading above par is trading at a premium. The discount or premium reflects the difference between the bond's coupon and the market's current yield requirement. At maturity, both converge to par.
Key takeaways
- A discount bond trades below par because its coupon is lower than the market's required yield; you earn a capital gain at maturity
- A premium bond trades above par because its coupon is higher than the market's required yield; you suffer a capital loss at maturity
- The size of the discount or premium depends on the difference between the coupon and the market yield and the bond's maturity
- Long-maturity bonds discount or premium more than short-maturity bonds when yields change
- All bonds converge to par at maturity, so owning a discount bond is a way to capture a known capital gain
Discount bonds: buying a bargain
A discount bond trades below its par (face value). If a $1,000 par bond is trading at $950, the discount is $50 or 5%.
Discount bonds arise when interest rates have risen since the bond was issued. Suppose a bond was issued at par with a 3% coupon. If market interest rates rise to 4%, new bonds are issued with 4% coupons. The old 3% bond is less attractive. To sell it, the issuer (or you, the bondholder, if selling in the secondary market) must accept a lower price.
The new price will be low enough that the yield to maturity (combining the coupon and the capital gain) equals the market's required yield of 4%. If the 3% bond has 5 years to maturity, the price might fall to $956 (a $44 discount). You earn $30 per year in coupons plus $44 in capital gains at maturity, totaling $194 over 5 years on a $956 investment. That is a 4% annualized return.
The capital gain at maturity is certain (barring default). You know that in 5 years, you will receive $1,000. You paid $956 today. The $44 profit is built into the investment.
Premium bonds: overpaying for high coupons
A premium bond trades above par. If a $1,000 par bond is trading at $1,050, the premium is $50 or 5%.
Premium bonds arise when interest rates have fallen since the bond was issued. A bond issued at par with a 4% coupon is attractive when market rates fall to 3%. New bonds issued today have only 3% coupons. The old 4% bond is sought-after. Its price rises.
The new price will be high enough that the yield to maturity (combining the coupon and the capital loss at maturity) equals the market's required yield of 3%. If the 4% bond has 5 years to maturity, the price might rise to $1,044 (a $44 premium). You earn $40 per year in coupons, but you lose $44 at maturity (because you paid $1,044 but receive $1,000), for a net of $160 over 5 years on a $1,044 investment. That is a 3% annualized return.
The capital loss at maturity is certain. You will lose the $44 premium when the bond is redeemed at par.
The discount/premium formula
The size of the discount or premium is determined by the difference between the coupon and the market yield and the bond's maturity.
Long-maturity bonds discount or premium more than short-maturity bonds. A 3% coupon bond in a 4% yield environment will be deeper in discount if it matures in 20 years than if it matures in 2 years.
A 3% coupon bond in a 4% yield environment has a YTM of 4%. The difference (1%) compounds over time. The longer the maturity, the larger the discount needed to achieve that 4% YTM.
For a rough approximation:
Discount ≈ (Coupon − YTM) × Duration (in years)
A 3% coupon, 4% YTM bond with a duration of 5 years would have a discount of roughly (3% − 4%) × 5 = 5%, or $50 on a $1,000 par bond.
This is not exact (the precise calculation requires discounting cash flows), but it gives the intuition: larger coupon/yield differences produce larger discounts/premiums, and longer-maturity bonds are more sensitive.
Tax implications of discounts and premiums
In the U.S., the tax treatment of discount and premium bonds differs:
- Discount bonds — If you buy a bond at a discount and sell it above your purchase price but below par, the gain is ordinary income, not a capital gain. If you hold to maturity, the discount is treated as interest income. Tax-deferred accounts (IRAs, 401(k)s) eliminate this complication.
- Premium bonds — If you buy a bond at a premium, you can elect to amortize the premium over the bond's life, deducting a portion each year. This reduces your taxable interest income. The premium is amortized and deducted from the bond's cost basis.
International tax rules vary. The UK, Canada, Australia, and other countries have different treatments. A bond investor in multiple jurisdictions should consult a tax advisor.
Original issue discount (OID)
Original issue discount bonds are issued at a discount. The U.S. Treasury might issue a 4-week T-bill at a 4.5% discount rate, meaning you pay $9,887.50 for a $10,000 face value. The discount ($112.50) is your income; there is no coupon.
Corporate bonds can also be issued at a discount if the coupon is set below the market yield at issuance. Over time, the bond's price accretes toward par (assuming no other changes).
Convergence to par at maturity
A key insight: all bonds converge to par at maturity. A discount bond that was trading at $950 will pay $1,000 at maturity. A premium bond trading at $1,050 will pay $1,000 at maturity. Time brings all bonds to par.
This is relevant for buy-and-hold investors. If you buy a discount bond and hold it to maturity, you earn not just the coupons but also the capital gain. If you buy a premium bond and hold to maturity, you earn the coupons but suffer the capital loss.
For short-term traders, the convergence matters because it sets a price ceiling. A bond cannot trade at a discount indefinitely; as maturity approaches, the bond's price must rise toward par (otherwise there would be an arbitrage opportunity).
Duration and discount/premium sensitivity
A bond's duration (a measure of interest rate sensitivity) is related to the discount or premium. A deeply discounted bond might have high duration because the coupon is low and most of the cash flow is back-loaded to the maturity payment.
When interest rates change, a deeply discounted bond's price swings more (in percentage terms) than a bond at par. Understanding this dynamic helps you anticipate price moves.
Discount bonds as a buy-and-hold strategy
Some investors deliberately seek discount bonds, especially in declining rate environments. A discount bond offers an implicit capital gain if held to maturity. If you buy at $950 and hold to maturity, you will receive $1,000, a guaranteed 5% gain (plus the coupon income).
In the 2020–2022 period, after the Federal Reserve cut rates to zero and then raised them sharply, many bonds traded at discounts. Investors buying these discounted bonds in 2022 locked in attractive yields and known capital gains if they held to maturity.
Premium bonds and callable risk
Premium bonds are particularly vulnerable to callable risk. A bond trading at a $50 premium ($1,050) is attractive to the issuer if it is callable. If rates fall further, the issuer will call, you receive $1,000 (par), and you lose the $50 premium. The premium is capped; you cannot earn the full $50 gain.
Investors who buy premium bonds must carefully assess callable risk. For non-callable bonds (like Treasuries), the premium is safe. For callable bonds, the premium is at risk if rates fall.
Amortization of premium and discount
Accounting and tax rules require amortization of premium and discount. For an investor:
- A premium is amortized downward over the bond's life, reducing the cost basis.
- A discount is accreted upward over the bond's life, increasing the cost basis.
This is important for accurate return calculation and for tax planning.
Example: comparing two bonds
Bond A: Discount bond
- Par: $1,000
- Coupon: 3%
- Maturity: 5 years
- Price: $950
- YTM: 4.27%
You earn $30 per year in coupons plus a $50 capital gain at maturity. Total return: ($150 coupons + $50 gain) / 5 years = $40 per year average, on a $950 investment = 4.27% annualized.
Bond B: Premium bond
- Par: $1,000
- Coupon: 5%
- Maturity: 5 years
- Price: $1,050
- YTM: 4.27%
You earn $50 per year in coupons but suffer a $50 capital loss at maturity. Total return: ($250 coupons − $50 loss) / 5 years = $40 per year average, on a $1,050 investment = 4.27% annualized.
Both have the same YTM (4.27%), but they are different investments. Bond A offers income plus capital gain; Bond B offers income with capital loss. If you expect rates to fall (bond prices to rise), Bond A (discount) is riskier—it will enjoy less price appreciation. If you expect rates to rise (bond prices to fall), Bond A is safer—the capital gain at maturity is unaffected.
Market psychology and discounts/premiums
Discount bonds sometimes feel like a bargain—you are paying below par. Premium bonds feel like you are overpaying. Psychologically, investors prefer discount bonds. But mathematically, if two bonds have the same YTM, they offer the same return; the difference is in the composition (coupon vs. capital gain).
This preference can create inefficiencies. Deep discount bonds sometimes trade at higher yields than premium bonds, even when the bonds are otherwise equivalent. Sophisticated investors exploit this by buying discount bonds at favorable yields.
Callable bond premiums
For a callable bond, the premium is at risk. The issuer will call if the bond is in-the-money (trading well above the call price). For a callable bond, the premium should be smaller than for a non-callable bond, because the upside is capped.
A non-callable bond trading at $1,050 can be held, and the premium is yours. A callable bond trading at $1,050 might be called, and the premium evaporates when you are forced to take par back.
Conclusion: discounts and premiums tell a story
Discounts and premiums are not mysteries; they are the market's way of reconciling different coupons with different yields. A discount reflects a coupon below the market yield; a premium reflects a coupon above the market yield. At maturity, both converge to par. Understanding discounts and premiums helps you spot opportunities (overly discounted bonds with solid credit) and risks (premium bonds subject to call risk).
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Related concepts
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We have covered discount and premium bonds—bonds where the coupon is out of line with market rates. Par bonds are the special case where the coupon exactly matches the market yield, creating a unique set of properties and a sense of equilibrium in bond valuation.