FSA Exam 3

What is a “numerator” effect on valuation? What is a “denominator” effect? How is risk accounted for in the basic valuation model (DCF model – income approach)?

• Numerator effect: Adjusts cash flows to reflect risk.

• Denominator effect: Adjusts discount rate (cost of capital) to reflect risk.

• Risk adjustment: Typically done via the discount rate for simplicity.

What is the cost of equity capital? How can you intuitively explain the cost of capital?

Definition: Return investors demand to compensate for risk in equity investment.

Intuition: It's the opportunity cost—what you need to earn to justify the risk of owning the stock.

What is risk? Explain volatility, relative volatility, volatility of returns vs. fundamentals, and estimation risk. How does the story of Mr. Market apply to risk as volatility?

Risk: The chance that financial outcomes differ from expectations.

Volatility: Standard deviation of returns.

Relative volatility: Compared to a benchmark (e.g., beta).

Returns vs. fundamentals: Market returns show perception; fundamentals show actual performance.

Estimation risk: Uncertainty in forecasting future cash flows.

Mr. Market: Illustrates market volatility often doesn’t reflect true value.

How does diversification reduce risk?

Diversification: Spreads investments to reduce firm-specific (unsystematic) risk.

Does not eliminate: Market (systematic) risk remains.

What are mutual funds, index funds, hedge funds, and ETFs? Does buying an index fund reduce or eliminate risk?

Mutual funds: Pooled investment actively managed.

Index funds: Track market indexes; low-cost diversification.

Hedge funds: Active, often riskier strategies for accredited investors.

ETFs: Trade like stocks, often mimic index funds.

Index funds reduce risk through diversification but do not eliminate risk.

What is the risk-free rate and where can you find it? What is an equity risk premium and how is it calculated?

Risk-free rate: Return on default-free securities (e.g., 10-year Treasury).

Equity risk premium (ERP): Extra return over risk-free rate to compensate for equity risk.

ERP = Market return – Risk-free rate.

How do you use the CAPM model to calculate the cost of equity capital? What is beta and how is it calculated?

CAPM: COEC = Risk-free rate + Beta × ERP.

Beta: Measures stock’s sensitivity to market returns.

Beta calculation: Regression of stock returns vs. market returns (usually 5 years of monthly data).

How do you implement the size model and the CAPM + size model? What are their limitations?

Size model: Adds a size-based premium to COEC (smaller firms = higher risk).

Combined model: COEC = Risk-free rate + (Beta × ERP) + Size premium.

Limitations: Relies on historical data; may not predict future accurately.

What are the four risk factors in finance and why are they considered risk factors?

Beta (market risk)

Size (small firms = riskier)

Book-to-market ratio (value firms = riskier)

Momentum (recent past returns)

What does the volatility of a company’s fundamentals tell you about risk? How is this different from beta?

Fundamental volatility: Shows business uncertainty, possibly manipulated by managers.

Beta: Reflects market perception of risk, not actual business risk.

Both offer different perspectives on a firm's risk profile.

What is an implied cost of capital? How is it determined and interpreted? What does it imply about market efficiency, current stock price, and future cash flows?

Definition: The discount rate that equates forecasted cash flows with current market price.

Interpretation: Shows market's expected return; assumes efficient pricing and correct forecasts.

Higher implied COEC: Indicates riskier or undervalued firm (if forecasts are accurate).

What is the Sharpe ratio and how can we compare two portfolios using it?

Formula: (Portfolio Return – Risk-Free Rate) / Std. Dev. of Returns.

Use: Compare investments’ risk-adjusted performance—higher is better.

What is the Sortino ratio and why might it be preferred over the Sharpe ratio?

Formula: (Portfolio Return – Benchmark) / Downside Std. Dev.

Advantage: Focuses only on harmful volatility (downside risk), not total volatility.

Why better: More accurate for investors who only care about losses, not gains.

What are the three GAAP valuation approaches? Describe each using the example of valuing a house.

Market approach: Use recent sales of comparable homes, adjust for differences.

Income approach: Discount expected future rental income from the house.

Cost approach: Estimate cost to rebuild the same house today.

What inputs are needed for the market approach? What adjustments are made?

Identical or comparable asset

Liquid or active market

Quoted prices

(Then adjust for differences—e.g., extra bedrooms, size)

How do you choose and find comparable companies? What attributes and sources are important?

Critical attributes:

Industry

Size (market cap, revenue)

Growth stage

Profitability

Risk profile

Sources:

• Zacks.com, S&P NetAdvantage

• SEC EDGAR using SIC codes

• Industry and sector reports

How can you use segment information in the market approach? Where do you find it and when is it valuable?

Found in footnotes of company financial statements (10-K)

Valuable when a company has diverse business segments

Value each segment separately, then sum them

What are SIC and NAICS codes? What do the digits mean?

SIC (Standard Industrial Classification): 4-digit code

1st 2 digits = division

3rd = industry group

4th = specialization

NAICS: Newer government classification system (since 1997)

What is a valuation ratio? What elements does it combine? Why do investors use them?

Combine:

• Market value (numerator)

• Fundamental measure (denominator)

Purpose:

• Allow comparisons across companies

• Used to estimate firm value

How do you interpret the P/E and M/B ratios?

P/E (Price/Earnings): How much investors pay per dollar of earnings

M/B (Market-to-Book): Market value compared to accounting book value

• Higher = more growth expectations or intangible value

What is the 'E' in P/E? What are forward and ttm P/Es? Why use non-GAAP earnings? What is the Shiller PE10? What is the best 'E'?

Earnings (GAAP or Non-GAAP)

Forward P/E: Uses forecasted earnings (next 12 months)

Trailing P/E (ttm): Uses past 12 months of earnings

Shiller PE10 (CAPE): Avg. inflation-adjusted earnings over past 10 yrs

Best “E” = forward-looking, normalized, sustainable earnings

What are the pros and cons of the market approach vs. a DCF model?

Pros:

Quick and intuitive

Useful for private firms or IPOs

Cons:

Relies on finding good comparables

Doesn’t model long-term cash flows

How do you use market multiples to value a firm? Include steps and adjustments.

Select appropriate comparable firm/industry

Choose the valuation ratio (e.g., P/E)

Calculate the comparable firm’s ratio

Adjust for differences (if needed)

Multiply your firm’s fundamental by the adjusted multiple

What does the market approach imply about efficiency? What is the best setting for it?

Implies markets are somewhat efficient (prices reflect value)

Best used when:

Markets are liquid

Good comparables exist

No reliable cash flow forecasts are available (e.g., private firms)

How can segment info and future earnings be used in a multiples approach? How do you estimate rate of return from it?

Apply relevant multiples to each segment based on industry comps

Add segment valuations together for total firm value

(Useful in diverse/multinational firms)

• Estimate future EPS

• Estimate future P/E multiple

• Multiply to get expected future stock price

• Use RATE() or FV/PV formulas to calculate expected return

  • Include EPS growth, multiple expansion/contraction, and dividend yield

How do you create a trading strategy? What are good signals and how do you develop them?

• Identify a signal that predicts returns or fundamentals.

• Ensure there's a solid theory behind why it should work.

• Good signals predict both returns and fundamentals.

What is data mining in trading? Why can it be risky?

• Searching through data for patterns without theory.

• Bad if it finds random patterns that don’t generalize (false positives).

What is predictive value? What does it mean if signals predict fundamentals or returns—but not both?

• A signal has predictive value if it forecasts:

  1. Future fundamentals (earnings, cash flows).

  2. Future returns.

• Predicts fundamentals but not returns: market is efficient.

• Predicts returns but not fundamentals: signal may lack theory.

• Best: predicts both.

What are fundamental signals like Piotroski and PEAD?

• Based on accounting/financial data.

• Examples:

  • Piotroski Score (B/M + financial health)

  • Accruals (Sloan 1996)

  • Non-GAAP exclusions

  • Frankel & Lee intrinsic value model

  • PEAD (Post Earnings Announcement Drift)

What are technical signals like momentum and mean reversion? What is a moving average?

• Based on stock price patterns.

• Examples:

  • Momentum: recent gains → future gains (e.g., price > 50-day avg).

  • Mean reversion: extremes revert to mean (e.g., Dogs of the Dow).

What is a back test? Why do we do it and how?

• Retrospective test of a strategy’s performance.

• Key steps:

  • Select firms

  • Define time horizon

  • Rank firms by signal

  • Measure future returns/fundamentals

  • Run regressions or compare deciles

How do you select firms for a back test? Why apply liquidity constraints?

• Use investable firms: liquid, tradable

• Impose liquidity constraints (market cap, volume)

How do you choose the back test time period? Pros and cons of short vs. long periods?

• Short: current, but may be unreliable.

• Long: more reliable, but may be outdated.

• Often use ~10 years.

What is survivorship bias and how does it affect results? How can we fix it?

• Ignoring failed/delisted firms.

• Inflates returns.

• Fix: assign 0% return or delisting-adjusted return.

What is look ahead bias and why is it a problem?

• Using info not available at the time of trading.

• Makes strategy appear better than it is.

What are abnormal/market-adjusted returns? Difference between equal and value weighted returns? What about dividends?

• Return in excess of a benchmark (e.g., S&P 500).

• Equal-weighted: each stock counts the same.

• Value-weighted: weights by market cap.

• Dividends should be included.

How do you know if a trading strategy is successful? What are hedge returns? What does it mean to be long or short?

• Portfolio return: avg. return of top-decile firms.

• Hedge return: top decile – bottom decile.

• Long: buy/hold stock.

• Short: sell borrowed stock, hoping it drops.

What is statistical vs. economic significance in evaluating trading results?

• Statistical: t-statistic, p-value (is result reliable?).

• Economic: is the return large enough to matter?

How do you counter the risk explanation for strategy returns? How can you control for risk?

• Your signal might just reflect risk.

• Control using:

  • Beta

  • Size

  • B/M

  • Momentum

• Use in regressions or matched samples.

How do you counter the argument that your strategy was just lucky?

• Have a strong theory.

• Look for monotonic decile patterns.

• Test consistency over time.

• Use a hold-out sample.

What are limitations of trading strategies (e.g., luck, costs, sustainability, efficiency)?

• Might reflect luck or risk.

• May not be implementable (costs, illiquidity).

• Past success doesn’t guarantee future results.

• Strategies get arbitraged away.

What is the difference between arithmetic and geometric means? How are they calculated? Which is better for investments?

• Arithmetic: simple average.

• Geometric: includes compounding:
  (Π(1+ri))1/n−1(Π(1+r_i))^{1/n} - 1(Π(1+ri​))1/n−1

• Geometric is more accurate for actual investment results.

• Fund managers usually report arithmetic.

What is information content in accounting? How can we measure it? What is ERC?

• Whether the market reacts to new info.

• Use |returns| or volume to measure.

• Use absolute returns to detect reaction strength (not direction).

• ERC = (magnitude of return) / (earnings change)

What is PEAD? Is it momentum or mean reversion? How was it tested and what did we find?

• Post Earnings Announcement Drift = prices keep drifting after earnings news.

• It’s a momentum strategy.

• In P12-5:

  • Sorted firms by earnings surprise.

  • Top surprise firms had positive drift.

• Criticisms:

  • Might be data mining

  • Hard to short

  • Market may be slow, not irrational

What is the "market approach", "income approach", and "cost approach" to valuation?

• Market approach: using comparable firms and/or a valuation multiple (e.g., P/E ratio) to estimate price. Useful for firms that lack fundamental information.

• Income approach: using fundamental analysis to estimate future financial statements, and ultimately, future income/cash flows

• Cost approach: valuing something based on how much it would cost to create today

What is a momentum trading strategy, and how is it different from a mean reversion trading strategy?

• Momentum: "the trend is your friend." In other words, recent positive returns will predict future positive returns. This is generally a short-term strategy.

• Mean reversion: "what goes up must come down (and vice versa)." In other words, on average firms performing very well will struggle in the future, and firms performing poorly will improve in the future. This is generally a longer-term strategy.

What factors influence the estimation of a cost of equity capital for a company? What effect do they have on COEC?

While many factors could be considered, we focused on risk-free rate, equity-risk premium, beta, and size. All else equal, (1) a higher risk-free rate results in a higher COEC, (2) a higher equity-risk premium results in a higher COEC, (3) higher beta results in a higher COEC, and (4) larger size results in a higher COEC.

What is the difference between "value stocks" and "glamour stocks"?

Value stocks are generally those stocks with low P/E or M/B ratios (or a high B/M ratio). Such shares are price lower relative to their fundamentals, potentially due to risk (since they may be financially distressed), low growth expectations, or misvaluation. "Glamor stocks" are the opposite: those stocks with high P/E or M/B ratios (or a low B/M ratio).

What are some things you should consider / be careful with when backtesting and/or validating a trading strategy?

1. Choosing the right window for testing (not too long to avoid irrelevance, but not too short to ensure reliability)

2. Making sure that you can actually make the trades you test (Is the share traded/available? Will you move the price by trading? Are there additional trading costs to consider?)

3. Avoiding survivorship and "look-ahead" bias (you can't simply drop companies that leave the sample (e.g., due to delisting). You must make an assumption about the delisting return (e.g., 0% or market average). You also must be sure your trading signal was available when the trade initiation occurs!

4. You need to select an appropriate trading window (is it a day-trading strategy, or a more long-term strategy?)

5. You must measure "success" while controlling for other factors. For example, you can use abnormal (e.g., market-adjusted) returns, or you can incorporate control variables for other explanations, such as risk, luck, and other known trading strategies (e.g., accruals).

Describe Piotroski's general approach to creating a trading signal (and why it was effective).

Piotroski took a known trading strategy (investing in high B/M companies) and tried to determine which specific stocks with high B/M provide the best return. His theory was that those high B/M companies with the best financial indicators/ratios would be the most likely to recover and "revert to the mean" with improved performance. He used a series of nine indicators to give a score for each stock, organized by decile, and showed that deciles with the highest scores performed best, while those with the lowest scores performed worst (including "hedge returns"). He used an ideal signal (predicting fundamentals and price) grounded in theory, and he showed through extensive backtesting that his model worked.

What are valuation ratios? How are they calculated?

Valuation ratios are "measures comparing a market valuation with a fundamental measure of value." Examples include P/E, M/B, PEG, P/Sales, etc. The ratio must contain both a market measure (e.g., price) and a fundamental accounting measure (e.g., earnings, book value, sales, etc.)

What is an implied cost of equity capital? How is it calculated?

The implied cost of equity capital is the cost of capital implied given the market's expectations for future cash flows and the current market price. In other words, if you create cash flow forecasts in a valuation workbook and assume the market shares those expectations, then the implied cost of equity capital is whatever cost of equity capital forces the intrinsic value of the share to equal the exact current market price. All else equal, if the market price increases, the implied COEC goes down (holding cash flow forecasts constant).

What is an earnings response coefficient? How is it interpreted?

An earnings response coefficient (ERC) is the stock price reaction for every cent of surprise at the time of the earnings announcement. In other words, the ERC shows (1) whether the market reacts in the same direction as the earnings surprise, and (2) to what extent the market reacts to the surprise. A positive ERC would indicate the market reacts in the same direction, and the larger the ERC, the larger the price reaction per cent of EPS surprise.

What is a hedge return? When should it be used?

A hedge return is created when you buy the stocks your signal suggests will have the highest return and sell the stocks your signal suggests will have the lowest return. For example, Piotroski created a score for all high B/M stocks ranging from zero to nine. He then shows the raw and abnormal returns that would be earned when buying high-score stocks (8 and 9) and selling low-score stocks (0 and 1). Hedge returns are commonly used to test whether a trading signal/strategy is effective.

What is an abnormal return, and how is it calculated? How is it different from a raw return?

Raw returns represent the actual return for a given stock/portfolio. In contrast, abnormal returns represent the returns earned compared to some benchmark, such as average market returns, average returns for similarly sized stocks, etc. Thus, abnormal returns show the value of a trading strategy compared to other potential strategies (such as investing in the entire market).

What is post-earnings announcement drift (PEAD)? How did we test for it during class?

Post-earnings announcement drift (PEAD) is the identified relation between earnings surprise and future returns. In theory, the market should fully react to earnings news on the day it occurs. In practice, returns "drift" in the same direction as the earnings surprise for a period of time. Thus, a positive earnings surprise today predicts positive market returns for a period of time after the announcement (as long as 6 months). We tested for it in class looking at whether the earnings surprise on day "0" predicts vs. the price response on day "+1". If the market is efficient, the price should fully react on day "0", and the ERC should have no effect on day "+1", but we identified drift, i.e., market reaction in the same direction as the surprise the following day.

When would researchers want to use "signed returns" vs. "unsigned (absolute value) returns" to test a research question?

We use "unsigned (absolute value) returns" when we want to know if the market reacts to the release of information, i.e., if information matters (has "information content"). In contrast, we use "signed returns" when we want to show the direction of the market's response, i.e., if the market reacts the way we expect given the signal. The ERC is an example of using "signed returns".

Describe conceptually what the Sharpe and Sortino ratios reveal about portfolio performance.

The Sharpe ratio reveals the average return per unit of risk (i.e., volatility) for a share or portfolio of shares. In other words, "average risk-adjusted returns." Risk (in the denominator) is measured as the standard deviation of returns over time. The Sortino ratio is similar, but the risk measure (in the denominator) is adjusted to remove "upside volatility". In other words, to avoid penalizing volatility coming from price increases, all returns above the (either for the portfolio or for the market in general) is adjusted to equal the mean, and then the standard deviation is recalculated.

What are some of the factors investors should consider when identifying a "comparable firm" for valuation?

Some of the factors we discussed to identify a comparable firm include (1) industry, (2) size, (3) growth, (4) profitability, (5) and risk.

What is the difference between a "trailing P/E" valuation vs. a "forward P/E" valuation?

Valuation using a trailing P/E approach uses historical EPS information (often trailing 12 months, or ttm) compared to current price, in the P/E ratio. In contrast, a "forward P/E" approach uses projected EPS (e.g., the consensus analyst forecast for the current year) compared to current price, in the P/E ratio.

What are the characteristics of an ideal trading signal to be used in a trading strategy?

The ideal trading signal predicts both an accounting fundamental (e.g., earnings) and market returns. This indicates that the there is a theoretical reason for the signal to work (by better predicting a fundamental) and that the market does not understand (is not efficient to) the signal.

What is a margin of safety? How is it calculated?

The margin of safety is the difference between estimated intrinsic value and the current market price. The more the intrinsic value exceeds the current market price, the "safer" the investment is, because there is room for the intrinsic value to be overestimated. The margin is often calculated in percentage terms, as follows:

Margin of Safety = 1 - (current stock price / intrinsic value)

For example, if the current stock price is $40 and you estimate intrinsic value equal to $50, the margin of safety equals:

1-(40/50) = 20%