Yield to Maturity (YTM)

Yield to Maturity (YTM)

Yield to Maturity (YTM) is the annualized internal rate of return (IRR) on a bond if you hold it to maturity and reinvest coupon payments at the same yield. It equates the present value of all future cash flows (coupon payments and principal) to the bond’s current market price.

Key points

• YTM reflects the total expected return if a bond is held to maturity and coupons are reinvested at the YTM rate.
• It changes with market price; a bond’s coupon rate is fixed, but YTM fluctuates with interest rates and price changes.
• When interest rates rise, YTM tends to rise (bond prices fall); when rates fall, YTM tends to fall (bond prices rise).
• YTM is an estimate; actual realized return can differ if coupon reinvestment rates differ or the bond is sold before maturity.

Approximate YTM formula

An often-used approximation:
YTM ≈ [C + (FV − PV) / t] ÷ [(FV + PV) / 2]

Where:
* C = annual coupon cash flow (dollars per year)
* FV = face (par) value
* PV = current price (present value)
* t = years to maturity

This formula gives an approximate annual yield. For precise YTM, use a financial calculator, Excel’s RATE or YIELD functions, or solve the full present-value equation for the discount rate.

How to calculate YTM (overview)

1. Gather inputs: current market price, face value, coupon rate (or coupon payment), and years to maturity.
2. Use the exact IRR approach by solving for r in:
   PV = Σ (Coupon / (1 + r)^k) + FV / (1 + r)^n
   where k enumerates coupon periods and n is total periods.
3. If you prefer a quick estimate, use the approximation formula above.
4. For bonds with semiannual coupons, convert payments and periods to semiannual terms and annualize the periodic yield.

Example (approximate)

Bond details:
* Face value = $100
* Current price = $95.92
* Coupon = 5% (annual coupon = $5)
* Time to maturity = 2.5 years

Apply the approximation formula:
Numerator = 5 + (100 − 95.92) / 2.5 = 5 + 1.632 = 6.632
Denominator = (100 + 95.92) / 2 = 97.96
YTM ≈ 6.632 / 97.96 ≈ 0.0677 = 6.77% (≈ 6.8%)

This gives a quick estimate; exact calculation with period-by-period discounting or a financial calculator may give a slightly different number.

Variations of YTM

• Yield to Call (YTC): Assumes the issuer will call the bond at the earliest call date; time horizon is until the call date.
• Yield to Put (YTP): Assumes the holder will exercise a put option to sell the bond back to the issuer at the earliest date allowed.
• Yield to Worst (YTW): The lowest yield among possible scenarios (e.g., maturity, call, put) — used to evaluate bonds with embedded options.

Explain Like I’m 5

If you buy a bond, YTM is an estimate of how much money you’ll make each year (as a percentage) if you keep the bond until the issuer repays you and if you reinvest the interest payments at the same rate.

Short FAQs

Q: Is higher or lower YTM better?
A: Higher YTM means a higher expected return but often reflects higher risk or a discounted price. “Better” depends on your return objectives and risk tolerance.

Q: How do I calculate precise YTM?
A: Use a financial calculator, Excel’s RATE/YIELD functions, or solve the present-value equation for the discount rate (IRR). Approximation formulas are useful for quick estimates.

Bottom line

YTM is a standard measure of a bond’s expected annual return if held to maturity and if coupon payments are reinvested at that yield. Use exact IRR methods for precision, and consider YTC, YTP, and YTW when bonds have embedded options.