Basic, lesson 1 of 4
Bonds and how they are priced
A bond is a list of promised cash flows. Its price is what those cash flows are worth today, discounted at the rate the market demands.
8 min, 3 checks
1What a bond actually is
A bond is a loan cut into tradable pieces. The issuer, a government or a company, borrows money today and promises two things: regular interest payments, called coupons, and the return of the borrowed amount at the end, called the face value or par.
Most bonds you will discuss in an interview have a face value of $1,000 or are quoted per $100 of face. A bond quoted at 98 trades at 98% of face, so $980 for a $1,000 bond.
| Term | Meaning | Example |
|---|---|---|
| Face value (par) | What is repaid at maturity | $1,000 |
| Coupon rate | Annual interest as a share of face | 5% |
| Coupon | The cash interest paid each year | $50 |
| Maturity | When face value comes back | 5 years |
| Price | What the bond trades for today | Depends on yields |
The coupon is fixed when the bond is issued. It never changes. What changes every second the market is open is the price, because the return investors demand keeps moving.
2Price is the present value of the cash flows
A dollar in five years is worth less than a dollar today, because you could invest today's dollar and earn a return. So to price a bond, you discount each future cash flow back to today at the market's required rate, the yield, and add them up.
Price = C / (1 + y) + C / (1 + y)^2 + ... + (C + Face) / (1 + y)^n
C is the annual coupon, y is the yield, n is the number of years. Annual coupons keep the math simple; real Treasuries pay twice a year.
Worked example
A 5 year, 5% coupon bond when the market demands 6%
- 1Cash flows: $50 at the end of years 1 to 4, then $1,050 in year 5.
- 2Discount each at 6%: 50 / 1.06 = 47.17, 50 / 1.06^2 = 44.50, 50 / 1.06^3 = 41.98, 50 / 1.06^4 = 39.60, 1,050 / 1.06^5 = 784.62.
- 3Add them: 47.17 + 44.50 + 41.98 + 39.60 + 784.62 = 957.88.
The bond is worth about $957.88. It pays 5% when the market wants 6%, so it has to sell below par to make up the difference.
Check 1
A zero coupon bond pays $1,000 in 2 years and nothing before. If the market yield is 5%, what is its price in dollars?
3When the coupon equals the yield
Run the same 5 year, 5% bond at a 5% yield and every cash flow is discounted at exactly the rate it pays. The price comes out to $1,000, par. That is the anchor to remember: coupon equal to yield means price equal to par.
Run it at 4% and the price rises to about $1,044.52. The bond pays more than the market requires, so buyers pay up for it.
| Market yield | Price | Trades at |
|---|---|---|
| 4% | $1,044.52 | Premium |
| 5% | $1,000.00 | Par |
| 6% | $957.88 | Discount |
Check 2
A bond has a 3% coupon and the market yield on similar bonds is 4.5%. Where does it trade?
4Why traders care
On a rates desk the coupon is old news. What moves P&L is the yield, because the yield sets the price. A trader who is long bonds wants yields to fall; a trader who is short wants them to rise.
Check 3
You own a bond. Yields across the market fall overnight. What happened to your position?
Terms in this lesson: Treasury securities.
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