OAS, Option Cost and a Volatility View in Two Issuer Bonds
Nadia Okafor compares two senior unsecured bonds of the same issuer, both maturing in 10 years. Bond X is callable at 102 beginning in year 3; Bond Y is straight. Bond X trades at 101.50 with a yield of 6.50% and an OAS of 210 bp. Bond Y trades at 99.20 with a yield of 6.10% and an OAS of 150 bp. The issuer's credit curve is flat and both bonds are equally liquid. Okafor's model uses 18% implied volatility. Effective durations are 4.9 for X and 7.0 for Y; effective convexities are -12 for X and 55 for Y. Her house view is that interest-rate volatility will fall materially over six months while credit spreads are unchanged.
1. Which bond is relatively cheap on an option-adjusted basis? Interpret the 60 bp OAS difference and state the main caveat.
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Bond X looks cheap. OAS removes the value of the embedded option, so two bonds of the same issuer with the same credit risk and comparable liquidity should trade at similar OAS. X's 210 bp versus Y's 150 bp means an investor is paid 60 bp more for bearing the same credit exposure, with the option effect already stripped out.
Caveat. OAS is a model output, not an observable. It depends on the volatility assumption, the call schedule, and the interest-rate model. X's 60 bp could be measurement rather than mispricing if the model overstates the call's value, if the two bonds differ in accrued interest or tax treatment, or if Y's 150 bp reflects a richer market for non-callable paper. The honest conclusion is: X is cheap under this model, and the size of the cheapness should be treated as a range that widens or narrows with the volatility input.
2. Estimate the price change for each bond for a 50 bp decline in yields using effective duration and convexity. Which bond is consistent with Okafor's volatility view?
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Using %ΔP ≈ -D_eff x Δy + 0.5 x C x (Δy)^2 with Δy = -0.005:
Bond X: -4.9 x (-0.005) = +2.450%; 0.5 x (-12) x 0.000025 = -0.015%. Total +2.44%.
Bond Y: -7.0 x (-0.005) = +3.500%; 0.5 x 55 x 0.000025 = +0.069%. Total +3.57%.
Reading. In a rate rally Y wins by about 1.1 percentage points because it has no negative convexity. But Okafor's stated view is falling volatility, not falling rates. Lower volatility reduces the expected value of the call, so X's callable price should rise even with yields unchanged. X therefore expresses the view; Y is a duration bet she has not articulated. Combining the two: X offers relative value plus a volatility tailwind, while Y offers more absolute upside if rates also fall.
3. How would the conclusion change if the 18% volatility input were too high? What if the bonds differed materially in liquidity?
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Too-high volatility. OAS = spread - option cost. Overstating volatility overstates the call's cost, which understates X's computed OAS. The true cheapness of X is therefore larger than 60 bp, strengthening the relative-value case. The reverse applies to Y, which has no option: its OAS is unaffected. A useful discipline is to re-run OAS at 14% and 22% volatility and see whether the ranking survives.
Liquidity differences. If X were the less liquid bond, part of the 60 bp would be an illiquidity premium rather than mispricing, and an investor who does not need to trade could still harvest it. If Y were the less liquid, the 60 bp gap would understate X's cheapness. Because the setup states both are equally liquid and from the same issuer with a flat credit curve, the credit and liquidity explanations are largely controlled for and the option model is the remaining variable of consequence.