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How do I use the hazard rate to calculate cumulative default probability over multiple years?
The hazard rate is the conditional probability of default in a given year. Cumulative default probability equals 1 minus the survival probability, where survival is (1-h)^t for constant hazard rates. The cumulative PD is always less than h times t due to the compounding effect on survivors.
How does the tax treatment of municipal bonds work, and what is the tax-equivalent yield?
Municipal bonds are generally exempt from federal income tax, and if issued in your state, from state taxes too. The tax-equivalent yield formula (muni yield divided by one minus the marginal tax rate) allows comparison with taxable bonds.
How do you derive a justified EV/Sales multiple, and when is it more useful than EV/EBITDA?
The justified EV/Sales multiple equals the FCFF-to-Sales margin divided by the WACC-growth spread. Profit margin is the primary driver, explaining why high-margin software companies can trade at 10x+ sales while thin-margin retailers trade below 0.5x.
Why do stock prices move when they're added to or removed from a major index?
When a stock is added to a major index, passive funds tracking that index must buy shares, creating a predictable demand shock. Stocks added to major indices historically see 3-7% abnormal returns, though roughly half reverses within weeks.
How do corporate spin-offs create shareholder value, and what is the conglomerate discount?
Spin-offs create value by eliminating the conglomerate discount, allowing each entity to be valued at appropriate industry multiples with focused management, better analyst coverage, and aligned incentives. Most spin-offs are tax-free to shareholders.
What are the GIPS requirements for reporting private equity fund performance?
GIPS requires private equity funds to report since-inception IRR as the primary return metric, classified by vintage year. Firms must also present capital multiples including DPI, RVPI, and TVPI alongside committed and paid-in capital figures.
What is a box spread, and how does it create a risk-free arbitrage opportunity?
A box spread combines a bull call spread with a bear put spread at the same strikes, creating a guaranteed payoff of K2 minus K1 at expiration. If the box market price differs from the present value of this payoff, a risk-free arbitrage exists.
How do I use the coefficient of variation to compare investments with different expected returns?
The coefficient of variation measures risk per unit of expected return, making it a standardized way to compare investments when their return levels are very different. Lower CV means a more efficient risk-return tradeoff.
How does the Nelson-Siegel model describe the yield curve, and what do its parameters represent?
The Nelson-Siegel model uses three components: a level factor (β0) setting the long-term yield, a slope factor (β1) controlling the short-to-long spread, and a curvature factor (β2) creating a hump at medium maturities. The decay parameter λ controls where the hump occurs.
How is Credit VaR calculated for a bond portfolio and what does it represent?
Credit VaR is the unexpected credit loss at a specified confidence level, calculated as the difference between the worst-case loss at that percentile and the expected loss. Expected loss is priced into spreads; Credit VaR represents the capital buffer needed.
How do you calculate the inflation breakeven rate from TIPS and nominal Treasury yields?
The breakeven inflation rate equals the nominal Treasury yield minus the TIPS real yield. If you expect inflation above the breakeven, buy TIPS. If below, buy nominals. The breakeven is not a pure forecast because it includes risk and liquidity premiums.
What are Treasury STRIPS and how are they created from regular Treasury bonds?
Treasury STRIPS are zero-coupon securities created by separating a Treasury bond's coupon and principal payments into individual tradeable instruments. They eliminate reinvestment risk and are ideal for liability matching.
Why does WACC calculation become circular when using market value weights, and how do I solve it?
WACC becomes circular because market value equity weights depend on the DCF output, which depends on WACC. Solutions include iterating until convergence, using target capital structure weights (most common on the CFA exam), or enabling Excel circular references.
Why should the terminal growth rate in a DCF never exceed long-run GDP growth?
The terminal growth rate should never exceed long-run GDP growth because the Gordon growth model assumes perpetual growth. A company growing faster than the economy forever would eventually become larger than the entire economy, which is impossible.
What is the GICS classification system and how is it used in equity analysis?
GICS is a four-tiered industry classification system developed by MSCI and S&P Dow Jones. It has 11 sectors, 25 industry groups, 74 industries, and 163 sub-industries. Companies are classified based on their primary revenue source.
Why do equal-weighted indexes have higher rebalancing costs than cap-weighted indexes?
Equal-weighted indexes require periodic rebalancing because stock prices diverge, pushing weights away from equality. This creates higher turnover, increased small-cap trading in illiquid names, and tax inefficiency from selling winners regularly.
How does preferred stock of a subsidiary affect consolidation and noncontrolling interest?
Subsidiary preferred stock held by outsiders is part of noncontrolling interest. When allocating subsidiary income, first deduct preferred dividends from net income, then split the remaining common income between parent and NCI based on common ownership percentages. Cumulative preferred dividends must be deducted even if not declared.
What are the key differences between perpetual and periodic inventory systems?
Perpetual inventory systems update records continuously with each purchase and sale, while periodic systems only update at period-end. Under FIFO both produce identical results, but under LIFO and weighted average, the two systems can produce different COGS and ending inventory because cost calculations are performed at different times.
What is the Phillips curve and does the inflation-unemployment tradeoff still hold today?
The Phillips curve shows an inverse relationship between inflation and unemployment in the short run. The modern expectations-augmented version explains that the tradeoff is temporary, and in the long run, unemployment returns to its natural rate regardless of inflation.
How do you calculate the settlement amount for a forward rate agreement (FRA)?
FRA settlement occurs at the start of the notional borrowing period, so the interest differential must be discounted back. The settlement amount equals the interest differential divided by one plus the reference rate times the day count fraction.
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