Synthesis

Quick Answer

Work fixed income exam questions in order: find the price relationship (premium, discount, or par), pick the right yield (YTC for a premium callable bond likely to be called, YTM for discount), assess risk (duration, credit rating, spread, call features, maturity), then factor in special features like convertibility or a zero coupon.

This four-step sequence prevents the most common exam error: picking a yield or risk answer before establishing whether the bond trades at a premium or discount in the first place.

Step 1: Determine Price Relationship

If You Know...Then...
Yield to Maturity (YTM) > CouponBond is at discount
YTM < CouponBond is at premium
YTM = CouponBond is at par
Current Yield (CY) > CouponBond is at discount
CY < CouponBond is at premium

Step 2: Apply the Appropriate Yield

Bond Trading AtFocus On
DiscountYTM (issuer will not call)
Premium, callable, likely to be calledYield to Call (YTC), since it trades above the call price
Premium, not callable (or not likely to be called)YTM; there is no YTC on a noncallable bond
ParNominal yield, current yield, and YTM are equal; calculate YTC separately if callable

Step 3: Assess Risk Profile

Risk FactorKey Question
DurationHow sensitive is this bond to rate changes?
Credit ratingHow likely is default?
Credit spreadHow much extra yield for the credit risk?
Call featuresCould reinvestment risk materialize?
MaturityHow long is the investor exposed?

Step 4: Consider Special Features

FeatureKey Consideration
CallableReinvestment risk; YTC most relevant for a premium bond likely to be called; use effective duration
PuttableBenefits bondholder when rates rise; lower coupon than comparable bonds
ConvertibleUse par value for conversion ratio; trades at greater of bond value or conversion value
Zero-couponNo reinvestment risk but highest volatility; phantom income tax; best for tax-deferred accounts

The Master Yield Ranking

Discount: Nominal<CY<YTM<YTC\text{Discount: } \text{Nominal} < \text{CY} < \text{YTM} < \text{YTC} Premium: Nominal>CY>YTM>YTC\text{Premium: } \text{Nominal} > \text{CY} > \text{YTM} > \text{YTC} Par: Nominal = CY = YTM\text{Par: Nominal = CY = YTM}

Key Formulas

Current Yield=Annual InterestMarket Price\text{Current Yield} = \frac{\text{Annual Interest}}{\text{Market Price}} Taxable Equivalent Yield (TEY)=Tax-exempt Yield1−Marginal Tax Rate\text{Taxable Equivalent Yield (TEY)} = \frac{\text{Tax-exempt Yield}}{1 - \text{Marginal Tax Rate}} Conversion Ratio=Par ValueConversion Price\text{Conversion Ratio} = \frac{\text{Par Value}}{\text{Conversion Price}} Conversion Value=Conversion Ratio×Stock Price\text{Conversion Value} = \text{Conversion Ratio} \times \text{Stock Price} Credit Spread=Corporate Bond Yield−Treasury Yield\text{Credit Spread} = \text{Corporate Bond Yield} - \text{Treasury Yield} Price Change≈−Duration×Change in Yield\text{Price Change} \approx -\text{Duration} \times \text{Change in Yield}

Exam Tip: Gotchas

  • Yield to Worst (YTW) is always the LOWEST possible yield - the most conservative measure. It is the lesser of YTM, YTC, or any yield to a put date.
  • Discounted Cash Flow (DCF) value > market price means undervalued (buy). DCF value < market price means overvalued (sell).

What Should You Check on Exam Day?

  • Work the four steps in order: price relationship, then yield, then risk, then special features. Do not jump straight to a yield answer.
  • Confirm the yield ranking direction matches the price relationship you found in Step 1: discount climbs, premium dips.
  • Double-check that a callable or puttable feature does not change which yield or which duration measure applies.