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CFA Level II Updated
How does gradient descent work in training financial models, and what are the key variants I should know for the CFA exam?
Gradient descent minimizes a loss function by iteratively adjusting parameters in the direction of steepest descent. The three main variants — batch, stochastic, and mini-batch — differ in how much data they use per update, balancing speed against stability.
When do I use consolidation vs the equity method vs financial instruments treatment? I need a clear decision framework.
The accounting treatment for intercorporate investments depends on the degree of influence or control. Below 20% is typically a financial instrument, 20-50% uses the equity method, and above 50% requires full consolidation, but exceptions based on actual influence can override these thresholds.
When should implementation costs for a cloud computing SaaS arrangement be capitalized versus expensed?
Under ASC 350-40, implementation costs for SaaS arrangements follow a three-phase model: preliminary project costs are expensed, application development stage costs may be capitalized, and post-implementation costs are expensed. Analysts should scrutinize the capitalization assumptions and hosting term estimates.
How does the binomial option pricing model converge to the Black-Scholes formula as the number of steps increases?
The binomial model converges to Black-Scholes as the number of steps N approaches infinity because the sum of many small binomial up-down moves converges to a log-normal distribution via the Central Limit Theorem. Numerically, 100 or more steps produce prices indistinguishable from the BSM analytical solution.
How do you calculate the funded status of a defined benefit pension, and what hits the income statement vs. OCI?
Pension accounting is one of the densest topics in CFA Level II, but once you see the framework, it becomes very systematic. The funded status equals the fair value of plan assets minus the projected benefit obligation (PBO), and what hits the income statement vs. OCI follows a clear set of rules.
What is the two-fund separation theorem, and how does it simplify portfolio selection for all investors?
The two-fund separation theorem states that all mean-variance investors hold the same tangency portfolio, differing only in their allocation between this portfolio and the risk-free asset. This reduces multi-asset allocation to a two-step decision.
How does signaling theory explain the market reaction to dividend changes, and what makes a dividend signal credible?
Signaling theory explains that dividend changes convey credible information because they are costly to imitate — firms must sustain higher payouts or face severe market penalties. The asymmetric cost of cutting dividends makes increases a credible positive signal.
How are indefinite-lived intangible assets tested for impairment, and why aren't they amortized?
Indefinite-lived intangibles are not amortized because their cash-flow-generating period has no foreseeable limit, but they must be tested for impairment annually by comparing carrying value to fair value (GAAP) or recoverable amount (IFRS).
How do companies determine their target capital structure, and what factors push the optimal debt ratio higher or lower?
Companies determine target capital structure by minimizing WACC through a combination of modeling at different debt levels, peer analysis, credit rating constraints, and stress testing. The optimal ratio balances tax shields against financial distress costs.
Why is stepwise regression considered dangerous, and what are the main pitfalls of automated variable selection?
Stepwise regression is dangerous because it tests hundreds of variable combinations, inflating the probability of false discoveries. Reported p-values become invalid, coefficients are biased upward, and models that look great in-sample often fail out-of-sample.
How does the dependency ratio affect fiscal policy, savings rates, and investment returns across countries?
Rising dependency ratios reduce national savings, increase fiscal pressure through pension and healthcare costs, push real interest rates lower, and may compress long-term equity returns. Portfolio managers should incorporate demographic trend analysis into country allocation and sector selection.
How does a diagonal spread exploit time decay differences between near-term and far-term options?
A diagonal spread sells a near-term OTM option (high theta decay) and buys a longer-term option at a different strike (lower theta), profiting from the faster decay of the short leg. The expiration mismatch allows rolling the short leg for recurring premium income.
How do you construct a vega-neutral options portfolio, and why would you want one?
A vega-neutral portfolio eliminates sensitivity to implied volatility changes by offsetting positive and negative vega positions. Construction involves calculating total portfolio vega and adding options with opposite vega exposure in sufficient quantity to reach zero net vega.
What are balloon payment bonds and what unique refinancing risk do they carry?
Balloon payment bonds are partially amortizing, with a large principal payment due at maturity. The primary risk is refinancing risk — the borrower typically plans to refinance the balloon, which can fail if interest rates rise or credit conditions tighten.
How do warrants differ from options, and what impact does exercise price have on dilution?
Warrants and exchange-traded options differ fundamentally in that warrants cause dilution by creating new shares when exercised, while options merely transfer existing shares. The exercise price determines how much cash the company receives relative to the dilution created.
How does an unrealized gain on AFS debt securities create a deferred tax liability, and where is it recognized?
An unrealized gain on AFS securities creates a DTL because the book value exceeds the tax basis. Both the unrealized gain and its deferred tax effect are recognized in OCI, maintaining matching. Upon sale, both reclassify to the income statement.
How does stock-based compensation create a deferred tax asset, and what happens when the actual tax deduction differs from the book expense?
Stock compensation creates a DTA during vesting based on grant-date fair value. At exercise, the tax deduction is based on intrinsic value, creating a windfall if the stock appreciated or a shortfall if it declined. Under current US GAAP, both flow through income tax expense.
At what exchange rate are dividends from a foreign subsidiary translated, and does it differ between the current rate and temporal methods?
Dividends from a foreign subsidiary are translated at the historical exchange rate on the declaration date under both the current rate and temporal methods. This is different from revenue and expenses which use the average rate, and is a common exam trap.
How does a net investment hedge work for a foreign subsidiary, and where are the gains/losses reported?
A net investment hedge offsets the CTA arising from translating a foreign subsidiary. The effective portion of the hedge gain/loss is recorded in OCI alongside the translation adjustment, creating a natural offset. Both are reclassified to P&L only upon disposal of the subsidiary.
What does the TED spread measure, and why is it considered a barometer of financial stress?
The TED spread measures the difference between 3-month LIBOR (interbank lending rate) and the 3-month T-bill yield, capturing the credit premium banks charge each other. Wider spreads signal banking system stress and predict broader credit market deterioration.
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