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How do you value an expansion option embedded in a capital project, and when does it materially affect the NPV decision?
An expansion option lets management scale up a project if demand is strong. Strategic NPV equals the base NPV plus the expansion option value. This option is most valuable under high uncertainty with modular project design.
How does bootstrapping estimate the standard error of a statistic without relying on distributional assumptions?
Bootstrapping estimates standard errors by treating your observed sample as a proxy for the population and repeatedly resampling with replacement. The standard deviation across thousands of resampled statistics approximates the true sampling distribution's spread.
How does tax loss harvesting work as a portfolio management strategy, and what are the wash sale rules that constrain it?
Tax loss harvesting realizes capital losses by selling depreciated positions and replacing them with similar (but not substantially identical) securities to maintain exposure. The wash sale rule prevents repurchasing the same security within 30 days. TLH can add 0.5-1.5% annually to after-tax returns.
What is a cross-default clause in a bond indenture, and how does it affect credit risk analysis?
A cross-default clause triggers a default on the bond if the issuer defaults on any other material debt above a specified threshold. While protective for individual creditors by providing early warning, it can amplify systemic risk by causing simultaneous defaults across all facilities from a single trigger event.
What is double leverage in a holding company structure, and why does it concern credit analysts?
Double leverage occurs when a holding company uses parent-level debt to fund equity investments in subsidiaries, measured as subsidiary equity investment divided by HoldCo equity. Ratios above 1.0x indicate the capital base is leveraged twice, creating cash flow dependency on subsidiary dividends.
How do you modify the dividend discount model to account for companies that return cash primarily through share repurchases?
The total payout model modifies the DDM by discounting dividends plus net share repurchases instead of dividends alone. This prevents systematic undervaluation of companies that return most cash through buybacks, and produces values consistent with FCFE models when all free cash flow is distributed.
What is the forward earnings yield, and how is it used to estimate the equity risk premium in the Fed Model?
The forward earnings yield is the inverse of the forward P/E ratio. The Fed Model compares this yield to the 10-year Treasury yield as a valuation signal, but is theoretically flawed because it compares a real return (equities) to a nominal return (bonds) and ignores growth and risk differentials.
What determines the steady state in the Solow growth model, and why can't capital accumulation alone drive permanent growth?
The Solow model's steady state occurs where investment equals depreciation, and diminishing returns to capital prevent capital accumulation alone from driving permanent per-capita growth. Only technological progress can sustain long-run growth in output per worker.
How does an iron condor generate profit, and what are the breakeven points?
An iron condor sells a put spread and a call spread simultaneously, collecting net premium that represents the maximum profit if the underlying stays between the short strikes. Breakeven points equal the short put minus net premium (lower) and the short call plus net premium (upper).
What are the key financial reporting differences between defined benefit and defined contribution pension plans?
Defined contribution plans create simple expense entries equal to employer contributions, while defined benefit plans require complex actuarial calculations, balance sheet liabilities for the funded status, and multi-component pension cost recognition on the income statement.
What is the disposition effect, and why do investors consistently sell winning positions too early while holding losers too long?
The disposition effect is investors' tendency to sell winners too early and hold losers too long, driven by prospect theory's asymmetric risk attitudes in gain vs. loss domains. Measured by comparing PGR to PLR, it leads to suboptimal tax outcomes and lower returns.
What are fallen angel bonds and why do they create investment opportunities?
Fallen angels are bonds that were originally issued with investment-grade ratings but have been downgraded to high-yield. They represent a distinct segment of the HY market...
What is a credit-implied rating and how does it differ from agency credit ratings?
A credit-implied rating is derived from a bond's observed market spread by mapping it to the average spread for each rating category. If a BBB-rated bond trades at...
How do you decompose a bond's total risk into spread risk and interest rate risk?
A corporate bond's total yield is the sum of the benchmark risk-free rate and the credit spread. Total price risk can be decomposed into the portion driven by benchmark...
What is empirical duration and when is it more useful than analytical duration?
Empirical duration is estimated by regressing observed bond price changes against changes in benchmark yields using historical market data. Unlike analytical duration...
What is credit spread duration and how does it differ from interest rate duration?
Credit spread duration measures a bond's price sensitivity to changes in its credit spread, while interest rate duration measures sensitivity to changes in the benchmark...
Why does a floating rate note have an effective duration near zero and what are the exceptions?
A floating rate note's coupon resets periodically to a reference rate plus a fixed spread. At each reset date, the FRN's price returns to approximately par because its...
How do you calculate the cost of an embedded option using OAS and Z-spread?
The option cost embedded in a bond is the spread difference between the Z-spread and the OAS. This difference represents the yield the investor gives up or gains due to...
What is one-sided duration for callable bonds and why does it reveal asymmetric risk?
One-sided duration calculates the price sensitivity separately for yield increases and yield decreases. For callable bonds, these two values differ significantly because...
How do you calculate effective convexity and why does it matter for bonds with embedded options?
Effective convexity measures the second-order curvature effect of yield changes on bond price, estimated numerically using an option-adjusted valuation model rather than...
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