Module 4
Corporate bonds & credit spreads
A government bond is (assumed) risk-free. A company might not pay you back — so its bonds must offer extra yieldto compensate. That extra yield over the risk-free curve is the credit spread, and the cleanest way to measure it is the Z-spread: the single constant amount you add to every point on the risk-free curve to make the bond's model price equal its market price. A wider spread means the market sees more risk.
Two more tools professionals use daily:
- CS01 (spread DV01) — the dollar gain or loss if the spread moves 1 basis point. It's your credit risk in dollars, just like DV01 is your rate risk.
- Carry & roll-down — your return if nothing changes: the coupon income you collect (carry) plus the price gain from the bond “rolling down” to a shorter, lower-yield point on the curve. It's why traders say they “get paid to wait.”
Drop the market price below the risk-free price and watch the spread appear.
🎛 Spread explorer
Z-spread
124 bp
over the risk-free curve
CS01 ($/bp)
$4,341
P&L per 1bp of spread
Risk-free price
103.54
if it had no credit risk
Carry & roll-down
Carry (income)
+5.61%
Roll-down
+0.63%
Total return
+6.24%
The Z-spread is the constant extra yield over the risk-free curve that reprices the bond to its market price — your compensation for credit risk. CS01 is what you make or lose per 1bp of spread move. Carry & rollis your return if nothing changes: coupon income plus the price gain from rolling down the curve. Educational tool — not investment advice.
How the Z-spread is actually computed
You can't solve for the Z-spread with a formula — you have to search for it. The Z-spread is the one number zyou add to every point on the risk-free curve so that the bond's model price equals its market price:
market price = Σ cashflowᵢ × DF(tᵢ) × e^(−z · tᵢ)
Since price falls as z rises, we bisect: guess a spread, price the bond, and halve the search range based on whether we're too high or too low — repeating until it matches to the penny.
Worked example — Ford Motor Credit 5.75% ≈ 2030
Take a real issuer whose bonds trade at a meaningful spread: Ford Motor Credit (a BBB-/BB borrower). Say its 5.75% note maturing in ~5 years is quoted around 98.00. Priced off the risk-free curve alone (z = 0) it would be worth 104.64— so the market is charging a discount for Ford's credit risk. The solver walks in, halving the range each step:
z = 1250 bp → price 60.95 (price too low → spread too wide) z = 375 bp → price 88.73 (still too low) z = −63 bp → price 107.59 (too high → spread too tight) z = 156 bp → price 97.67 (very close) z = 102 bp → price 100.05 …converges to z = 148 bp → price 98.00 ✓
So this bond's Z-spread is 148 bp — Ford pays 1.48% a year over Treasuries for the risk you take. Its CS01 is ≈ $4,319per $10 M per basis point: if the spread widens 10 bp, you lose about $43,000.
How carry and roll-down are computed
“Carry & roll” is your return if nothing moves — the market just sits still and time passes. It has two parts:
1. Carry (income).The coupon you collect over the holding period. For our Ford bond over one year, that's simply the coupon: 5.75% × 100 = 5.75 per 100 face.
2. Roll-down. A year from now — if the curve and spread are unchanged— the bond is no longer a 5-year; it's a 4-year. On an upward-sloping curve a 4-year is discounted at lower rates, so it's worth more. We reprice it as a 4-year at the same 148 bp spread:
price today (5y, 148 bp) = 98.00 price in 1y (4y, same 148 bp) = 98.61 roll-down = +0.61
Add them up: (5.75 income + 0.61 roll) / 98.00 = 6.49%total return over the year, earned just for holding — no view on rates or spreads required. That's why traders say a steep curve and a fat spread “pay you to wait.” The calculator above runs exactly this math for any bond you dial in.
Things to try
- • Enter the Ford example above — coupon 5.75, maturity 5, price 98 — and confirm you get a ~148 bp Z-spread.
- • Lower the market price — the Z-spread widens. That's what happens when a company's risk rises.
- • Raise the maturity — CS01 grows, because a longer bond is more sensitive to the same spread move.
- • Extend the horizon — see carry & roll compound. A steep curve makes roll-down bigger.