Key takeaways
– Yield-to-average life (YAL) is the yield calculated by treating an amortizing or prepaid security as if it repays principal in a single lump sum at the security’s weighted average life (WAL or WAM) rather than at its final stated maturity.
– YAL helps estimate the effective return when principal is repaid before the legal maturity (sinking funds, amortizing bonds, mortgage‑backed securities).
– To compute YAL you first calculate the weighted average life (WAL), then solve a yield (YTM-style) using that WAL and the average redemption price — or, more accurately, compute the internal rate of return (IRR) of the actual cash flows.
– YAL is useful for comparing securities with different repayment profiles, and for stress‑testing returns under different prepayment scenarios (especially with MBS). But it is sensitive to prepayment assumptions and reinvestment risk.
Definition and intuition
– Weighted average life (WAL) = the average time until principal is returned, weighted by the principal amounts returned at each payment date. It tells you how long, on average, a dollar of principal remains outstanding.
– Yield‑to‑average life (YAL) = the yield you get if you assume the instrument is a single‑maturity bond that pays the same coupons but returns principal at the WAL (at an average redemption price). Practically, it replaces the bond’s stated maturity with the WAL in a YTM calculation.
– YAL summarizes how early/late principal returns affect your effective yield. Faster principal repayment (shorter WAL) reduces interest‑rate duration and default exposure but increases reinvestment risk.
When YAL is used
– Bonds with sinking funds or scheduled amortization (corporate sinking‑fund bonds, serial bonds).
– Amortizing securities (some municipal or corporate amortizing issues).
– Mortgage‑backed securities (MBS, CMOs) and other pass‑throughs where borrowers prepay mortgages — the timing of principal cash flows depends heavily on homeowner refinancing and prepayment behavior.
How to compute YAL — two approaches
Approach A (simplified YAL using WAL inserted into YTM formula)
1. Compute WAL:
WAL = (Σ principal_payment_i × time_i) / (total principal)
where time_i is measured in years (or fractions) from purchase.
2. Determine the average redemption price (if principal is redeemed at par, use par; if the issuer repays at varying prices, compute a weighted average redemption price).
3. Use the standard yield‑to‑maturity formula (or a financial calculator/YIELD function) substituting WAL for maturity and the average redemption price for par. Solve for the yield r that satisfies:
Price = Σ coupon/(1+r)^t + redemption/(1+r)^WAL
(This approach is the definition of YAL used in many references and is often a good approximation.)
Approach B (recommended — exact IRR of actual cash flows)
1. Build the actual projected cash‑flow schedule: each coupon and each principal repayment (dates and amounts). For MBS, project prepayments using chosen prepayment speeds (PSA, CPR, or model).
2. Compute the internal rate of return (IRR) that sets PV(cash inflows) = purchase price. In Excel use IRR (regular intervals) or XIRR (irregular dates). This IRR is the true expected yield given your cash‑flow assumptions.
3. If you want to report a single number comparable to YTM, you can also compute the WAL of those cash flows and call the IRR the YAL — but the IRR is the rigorous measure.
Practical numeric example (illustrative)
– Bond principal: $1,000. Annual coupon 5% (paid on outstanding principal). Price = $1,020.
– Principal repay schedule (equal principal): $200 at end of each year for 5 years.
– WAL = [200×1 + 200×2 + 200×3 + 200×4 + 200×5] / 1000 = 3.0 years.
Simplified YAL (treat as bullet at 3 years): solve for r in PV of 50/year for 3 years + 1000 redemption = 1020. That gives r ≈ 4.27%.
Exact IRR using the actual per‑year cash flows (coupons on declining balances + principal amounts) yields about r ≈ 4.26% — close in this example. For uneven or more complex schedules, the IRR approach is preferred.
Practical steps for investors — evaluating a sinking‑fund bond or MBS
1. Obtain or project the principal‑repayment schedule:
• For sinking funds: use the indenture schedule or trustee purchase plan.
• For MBS: choose prepayment assumptions (PSA speeds or a model) and simulate monthly cash flows.
2. Compute WAL using the principal repayment amounts and their timings.
3. Compute yields:
• Quick estimate: plug WAL into a YTM formula with appropriate coupon and average redemption price (use for rapid comparison).
• Accurate estimate: calculate IRR (Excel XIRR or a financial calculator) of the full cash‑flow stream.
4. Compare YAL/IRR under multiple prepayment scenarios (fast, slow, base) to see sensitivity.
5. Consider reinvestment risk: earlier principal returns must be reinvested at prevailing market rates, which may be higher or lower.
6. For premium/discount purchases:
• If you buy at a premium, faster principal repayment tends to reduce your realized yield (you recover more of the premium sooner).
• If you buy at a discount, faster principal repayment tends to increase your realized yield.
7. Assess credit and call risk, liquidity, and tax considerations alongside YAL to make a holistic decision.
YAL for MBS — special considerations
– MBS cash flows depend heavily on homeowner prepayment behavior (refinancing, turnover). WAL is very sensitive to prevailing interest rates: falling rates → faster prepayments (shorter WAL); rising rates → slower prepayments (longer WAL).
– Commonly used prepayment benchmarks and models include the PSA (Public Securities Association) speed schedule and CPR (conditional prepayment rate). Use multiple speeds (e.g., 50% PSA, 100% PSA, 150% PSA) to generate a range of WALs and yields.
– Prepayment variability creates extension risk and contraction risk: yields can fall if prepayments accelerate when you bought at a premium, or yields can rise if prepayments slow when you bought at a discount.
Interpretation — what YAL tells you (and what it doesn’t)
– Tells you an expected effective yield based on average timing of principal return. Useful for comparability across different amortizing issues.
– Gives an idea of interest‑rate duration (shorter WAL → lower interest‑rate sensitivity).
– Does not remove uncertainty: it compresses a stream of uncertain cash flows into a single average date. Realized results can diverge materially if prepayments deviate from assumptions.
– Use scenario analysis rather than relying on a single YAL number when evaluating MBS or callable/sinking‑fund securities.
Pros and cons of using YAL
Pros:
– Summarizes amortizing or prepaid securities in a comparable yield metric.
– Helpful for trustees deciding buybacks under sinking fund rules.
– Quick way to compare securities with different amortization or prepayment profiles.
Cons:
– Depends on assumptions about principal timing (prepayments), which can be highly uncertain (especially for MBS).
– The “single maturity” approximation can obscure the timing and magnitude of intermediate cash flows; IRR is more exact.
– Reinvestment risk and the path of interest rates still matter even if WAL is short.
Tools and formulas (practical)
– WAL formula (Excel): =SUMPRODUCT(principal_payments, times)/SUM(principal_payments)
– Exact yield (IRR): Excel IRR(range_of_cashflows) for equal intervals, or XIRR(cashflows, dates) for real calendar dates.
– YTM with WAL: use financial calculator with N = WAL (in years), PMT = coupon, FV = average redemption, PV = −price, then compute I/Y.
– Prepayment simulation: many fixed‑income analytics platforms provide MBS prepayment modeling; Excel users can implement PSA/CPR schedules and amortize monthly.
Quick checklist for an investor evaluating a candidate MBS or sinking fund bond
1. Get the instrument prospectus/indenture and historical prepayment data if available.
2. Model several prepayment scenarios (slow/base/fast).
3. Compute WAL for each scenario.
4. Compute YAL (simplified) and IRR (exact) for each scenario.
5. Evaluate how premium vs discount affects sensitivity to prepayments.
6. Assess reinvestment risk, duration, credit risk, liquidity, taxes.
7. Make a decision based on the full range of outcomes, not a single YAL number.
Common pitfalls to avoid
– Treating YAL as a guaranteed maturity — it’s an expectation based on timing assumptions.
– Using WAL without stress testing prepayment scenarios.
– Forgetting the effect of coupon timing and declining outstanding balances; for accuracy, compute IRR of actual cash flows.
– Ignoring call or refunding provisions in the indenture that can alter actual repayment timing.
References and further reading
– Investopedia, “Yield‑to‑Average Life” (source provided):
– Freddie Mac and Fannie Mae documentation on MBS structures and prepayment models (for technical details on PSA/CPR and prepayment assumptions).
– Fixed‑income textbooks and CFA curriculum sections on amortizing securities, YTM, and prepayment risk.
Editor’s note: The following topics are reserved for upcoming updates and will be expanded with detailed examples and datasets.