Math & Analytics

Yield to Call (YTC)

The annualized return on a callable bond if held until its earliest call date and redeemed at the call price.

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Yield to call (YTC) is the annualized return an investor would earn on a callable bond if it is held until its first call date and redeemed at the call price (often par or a slight premium to par).

Formula (similar to YTM, substituting call date and call price): > YTC ≈ [Annual Coupon + (Call Price − Market Price)/Years to Call] ÷ [(Call Price + Market Price)/2]

When is YTC relevant? - YTC matters most for premium bonds (trading above par) where the issuer has an incentive to call (refinance at lower rates). - When the bond is likely to be called, YTC is a more realistic measure of expected return than YTM.

Yield to worst (YTW): The lower of YTM and YTC (and any other potential call dates). Investors use YTW as the most conservative expected return — the worst yield they can receive assuming the issuer acts in its own best interest. > YTW = min(YTM, YTC, yield to each call date)

Impact of callable feature: - Callable bonds typically offer a higher yield than non-callable bonds of similar quality (call premium compensates investors for reinvestment risk). - When rates fall, the issuer calls the bond and refinances at lower rates — leaving the investor to reinvest at lower yields (negative convexity).

Example: Premium bond (price $1,050, par $1,000, 7% coupon, 20 years to maturity, callable in 3 years at $1,010). - YTC will be lower than YTM because the investor receives the call price sooner rather than full coupon stream to maturity.

> Exam tip: For premium bonds, YTC < YTM — the issuer is likely to call. Yield to worst = minimum of YTM and all YTCs. Use YTW as the conservative expected return.

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