Bond pricing calculator: price, duration, and convexity

• The price is the present value of every coupon plus the face value paid at maturity, each discounted at the market yield you enter, split into the number of payments per year you pick.
• Current yield is the annual coupon divided by that price. Yield to maturity is the market yield you typed in: the lab starts from the yield and works out the price, so the two always agree.
• Modified duration is the weighted average time to each payment, scaled by the yield, and tells you the percent price change for a one-point move in rates. Convexity adds the second-order correction, since price does not fall in a straight line as yields rise.
• The rate-sensitivity lines apply duration and convexity to a 1-point and a 2-point rise in yield. Accrued interest is the coupon earned since the last payment, counted over a 365-day year.
• Open the advanced options to add a call price and call date, which gives a yield to call, or to mark the bond tax-free, which gives the taxable yield that would leave you the same amount after the tax rate you enter.

Take the lab's starting numbers: a $1,000 bond with a 5% coupon, 10 years to maturity, semiannual payments, and a market yield of 4.5%. The price comes to $1,039.91, which is above face value because the coupon beats the market yield. Current yield is 4.81%. Modified duration is 7.86 years, so a 1-point rise in yield moves the price by about -7.49%, and a 2-point rise by about -14.23%. Accrued interest after 90 days is $12.33, and the estimated one-year total return at an unchanged yield is 4.55%.

• The price assumes a full coupon period remains until the next payment. Accrued interest is shown on its own line and is not added to the price.
• A single market yield discounts every payment, so the lab does not model a yield curve where short and long payments are discounted at different rates.
• Price changes use duration plus convexity, an estimate that is close for small moves and drifts for large ones. The lab labels a duration of 7 years or more as high risk, which is a rule of thumb in the lab, not a market standard.
• Tax-equivalent yield uses one federal rate and ignores state tax, the alternative minimum tax, and any phase-outs.
• Yield to call is the rate that makes the coupons to the call date plus the call price worth today's price. It does not account for what you do with the cash when the bond is called.

Finance Quest is educational. It is not financial advice, and no calculator here knows your full situation.

A 5% coupon sounds like a 5% return, but the bond in the example costs $1,039.91 and repays $1,000. The coupon is paid on face value, so the return you earn is the yield, 4.5% here. Current yield, 4.81%, still ignores the $39.91 premium you give back at maturity. Compare bonds by yield to maturity, and by yield to call when the issuer can redeem early.

The lesson for this lab is in Chapter 14, Bonds & Fixed Income. Read the lesson

• BondYield-to-maturity and rate sensitivity.
• Bond ladderBuild a ladder of maturities and see the cost, yield, and cash flow by year.
• Asset allocationSet a stock, bond and cash mix against horizon and risk tolerance.