The CFA Institute does not publish a specific passing score. The minimum passing score (MPS) is determined by the Board of Governors each year after the exam administration.
1. An investor is evaluating a hedge fund that uses sophisticated quantitative models to identify temporary mispricings between highly correlated securities, such as convertible bonds and their underlying equities, or pairs of stocks. The fund typically takes offsetting long and short positions to minimize market risk. This approach best describes which hedge fund strategy?
Alternative Investments
A.Relative Value Arbitrage
B.Global Macro
C.Long/Short Equity
D.Event-Driven
Show answerAnswer
A. Relative Value Arbitrage
The strategy described, which involves using quantitative models to identify temporary mispricings between highly correlated securities (e.g., convertible bonds and underlying equities, or pairs of stocks) and taking offsetting long and short positions to minimize market risk, is the hallmark of a Relative Value Arbitrage strategy.
2. A credit analyst is using a structural credit model, such as the Merton model, to assess the default probability of a company. The analyst estimates the company's asset value, asset volatility, and the face value of its debt. Which of the following assumptions is fundamental to the application of the Merton model?
Fixed Income
A.The company's asset value follows a normal distribution.
B.The company's default event is an exogenous, unpredictable shock.
C.The company's equity can be viewed as a call option on its assets.
D.The company's debt is a perpetual bond.
Show answerAnswer
C. The company's equity can be viewed as a call option on its assets.
A fundamental assumption of the Merton model is that the equity of a company can be modeled as a call option on the company's total assets, with the exercise price equal to the face value of its debt and the expiration date being the debt's maturity. Default occurs if the asset value is less than the debt value at maturity.
3. A portfolio manager is considering investing in a collateralized debt obligation (CDO) that consists of various tranches. The manager is particularly interested in a junior tranche, which offers a very attractive yield but has a lower credit rating than the senior tranches. Which of the following statements most accurately describes the risk profile of this junior tranche compared to a senior tranche in the same CDO structure?
Fixed Income
A.The junior tranche has lower credit risk and higher call protection.
B.The junior tranche offers a lower yield due to its superior credit quality.
C.The junior tranche has higher credit risk and is more sensitive to defaults in the underlying collateral.
D.The junior tranche has lower interest rate risk and higher liquidity.
Show answerAnswer
C. The junior tranche has higher credit risk and is more sensitive to defaults in the underlying collateral.
Junior tranches in a CDO absorb losses first from the underlying collateral pool. This means they bear the highest credit risk and are most sensitive to defaults occurring within the collateral. To compensate for this higher risk, they typically offer a higher yield.
4. A credit analyst is evaluating the creditworthiness of a company. The company has a high debt-to-equity ratio, declining revenue growth, and a history of volatile earnings. The analyst notes that the company's industry is highly cyclical and competitive. Which of the following factors would most likely contribute to a higher probability of default for this company?
Fixed Income
A.A tightening of credit markets, making refinancing more difficult.
B.A significant increase in the company's cash reserves.
C.A recent upgrade in the company's credit rating by a major agency.
D.A successful diversification into a less cyclical industry segment.
Show answerAnswer
A. A tightening of credit markets, making refinancing more difficult.
A tightening of credit markets increases the cost of borrowing and makes it more challenging for companies, especially those with already weak financial profiles, to refinance existing debt or secure new funding. This directly elevates the risk of default.
5. A portfolio manager is evaluating a global equity fund that has consistently outperformed its benchmark over the past five years. However, the fund's active risk (tracking error) has also been relatively high. To assess whether the manager's active returns are justified by the active risk taken, which performance measure would be most appropriate?
Portfolio Management and Wealth Planning
A.Sharpe Ratio
B.Jensen's Alpha
C.Information Ratio
D.Treynor Measure
Show answerAnswer
C. Information Ratio
The Information Ratio (IR) measures the active return (portfolio return minus benchmark return) per unit of active risk (tracking error). It is specifically designed to evaluate the skill of a portfolio manager in generating returns above a benchmark, considering the risks taken to achieve those active returns.
6. An investment firm uses a time-series model to forecast daily stock returns. The firm's analyst notices that large forecast errors tend to be followed by large forecast errors, and small errors by small errors, irrespective of the sign of the error. Which of the following models would be most appropriate to capture this characteristic?
Quantitative Methods
A.Autoregressive (AR) model
B.Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model
C.Autoregressive Conditional Heteroskedasticity (ARCH) model
D.Moving Average (MA) model
Show answerAnswer
C. Autoregressive Conditional Heteroskedasticity (ARCH) model
The described pattern of forecast errors (large errors followed by large errors, small by small, irrespective of sign) is characteristic of volatility clustering, which is captured by Autoregressive Conditional Heteroskedasticity (ARCH) models. GARCH models are a generalization of ARCH, also fitting this pattern, but ARCH is the fundamental model for this specific observation.
7. A bond analyst is evaluating a credit default swap (CDS) on a corporate bond. The bond has a notional principal of $10 million, a maturity of 5 years, and a CDS spread of 150 basis points. The recovery rate is assumed to be 40%. What is the approximate expected loss on this bond if a default occurs?
Fixed Income
A.$1.5 million
B.$4.0 million
C.$15.0 million
D.$6.0 million
Show answerAnswer
D. $6.0 million
The expected loss given default (LGD) is calculated as (1 - Recovery Rate) × Notional Principal. In this case, (1 - 0.40) × $10,000,000 = 0.60 × $10,000,000 = $6,000,000. The CDS spread and maturity are relevant for pricing the CDS, but not for calculating the expected loss if a default occurs.
8. A financial analyst is evaluating the potential impact of an increase in the domestic interest rate on a country's exchange rate, assuming all other factors remain constant. The analyst is specifically interested in the short-term effects based on the interest rate parity condition. Which of the following is the most likely immediate effect on the domestic currency?
Economics
A.No immediate change, as exchange rates are primarily driven by long-term economic fundamentals.
B.Depreciation, as foreign investors withdraw capital due to higher borrowing costs.
C.Depreciation, as the central bank would likely intervene to prevent an excessive capital inflow.
D.Appreciation, as higher domestic interest rates attract foreign capital seeking better returns.
Show answerAnswer
D. Appreciation, as higher domestic interest rates attract foreign capital seeking better returns.
According to interest rate parity, a higher domestic interest rate, all else being equal, makes domestic assets more attractive to foreign investors. This increased demand for domestic currency to invest in these assets leads to an appreciation of the domestic currency in the short term.
9. A fixed-income analyst is comparing two bonds, Bond X and Bond Y, both with a 5-year maturity and a 4% annual coupon rate. Bond X is a straight (option-free) bond, while Bond Y is a callable bond with a call price of $1,020, callable annually starting from Year 1. Assuming all other factors are equal, which of the following statements about their effective duration is most accurate if interest rates are expected to fall significantly?
Fixed Income
A.Bond X will have a lower effective duration than Bond Y.
B.Both bonds will have similar effective durations.
C.Bond Y will have a lower effective duration than Bond X.
D.The effective duration of Bond Y will be negative.
Show answerAnswer
C. Bond Y will have a lower effective duration than Bond X.
If interest rates are expected to fall significantly, the callable bond (Bond Y) is more likely to be called by the issuer. This call feature effectively shortens the bond's expected life and limits its potential price appreciation, making its price less sensitive to further decreases in interest rates. Consequently, Bond Y's effective duration will be lower than that of the option-free Bond X.
10. An analyst is evaluating a hedge fund that frequently takes long and short positions in publicly traded equities. The fund aims to profit from mispricings between related securities, often within the same industry or sector, by simultaneously buying undervalued securities and selling overvalued ones. What type of hedge fund strategy is this fund most likely employing?
Alternative Investments
A.Global Macro
B.Event-Driven
C.Long/Short Equity
D.Equity Market Neutral
Show answerAnswer
C. Long/Short Equity
The description of taking long and short positions in publicly traded equities, aiming to profit from mispricings, aligns with both Equity Market Neutral and Long/Short Equity. However, a key distinction is that Long/Short Equity aims for a net long or net short exposure, while Equity Market Neutral aims for zero net exposure. Since the question does not specify zero net exposure, 'Long/Short Equity' is the broader and more appropriate answer for a fund that 'frequently takes long and short positions' and 'aims to profit from mispricings'.
11. A portfolio manager uses a covered call strategy on a significant portion of his equity holdings to generate additional income. He writes out-of-the-money call options against his long stock positions. Which of the following best describes a key risk of this strategy?
Portfolio Management and Wealth Planning
A.Unlimited downside risk if the stock price falls significantly.
B.Significant capital outlay required to initiate the strategy.
C.Limited upside potential if the stock price rises significantly.
D.Increased exposure to unexpected interest rate changes.
Show answerAnswer
C. Limited upside potential if the stock price rises significantly.
A covered call strategy involves holding a long position in a stock and selling call options against it. While it generates premium income and offers some downside protection (up to the premium received), the key drawback is that if the stock price rises significantly above the strike price of the sold call, the investor's upside potential is capped at the strike price plus the premium received, because the stock will likely be called away. The investor forfeits any further gains above the strike price.
12. A financial advisor is preparing an Investment Policy Statement (IPS) for a young couple, both 30 years old, who are saving for retirement in 35 years. They have stable jobs, no immediate liquidity needs, and a high tolerance for risk. Which of the following investment constraints should be given the LEAST emphasis in their IPS?
Portfolio Management and Wealth Planning
A.Unique circumstances
B.Legal and regulatory factors
C.Liquidity needs
D.Time horizon
Show answerAnswer
C. Liquidity needs
Given the couple's long time horizon (35 years until retirement) and stable jobs with no immediate liquidity needs, liquidity is the constraint that requires the least emphasis. They can afford to invest in less liquid assets with potentially higher returns.
13. An investor is considering a 5-year, 6% annual coupon bond currently trading at par. The current 1-year spot rate is 4%, and the 2-year spot rate is 4.5%. According to the pure expectations theory, what is the implied 1-year forward rate for the second year (f1,1)?
Fixed Income
A.4.00%
B.4.50%
C.5.00%
D.5.01%
Show answerAnswer
D. 5.01%
According to the pure expectations theory, the long-term spot rate is a geometric average of current and expected future short-term rates. We can calculate the implied forward rate using the formula: (1 + S2)^2 = (1 + S1) * (1 + f1,1). (1 + 0.045)^2 = (1 + 0.04) * (1 + f1,1). 1.092025 = 1.04 * (1 + f1,1). (1 + f1,1) = 1.092025 / 1.04 = 1.050024. f1,1 = 0.050024 or 5.0024%, which is approximately 5.01%.
14. An economist is analyzing the optimal level of government intervention in an industry characterized by significant positive externalities, such as basic scientific research. From a social welfare perspective, what is the most appropriate policy response to address this market failure?
Economics
A.Nationalization of the industry, to ensure public control over production decisions.
B.Provision of government subsidies to producers or consumers to encourage more production/consumption.
C.Deregulation, to allow market forces to determine the optimal production level.
D.Imposition of a Pigouvian tax on the industry to internalize the external costs.
Show answerAnswer
B. Provision of government subsidies to producers or consumers to encourage more production/consumption.
Positive externalities (e.g., benefits from basic research that spill over to society) lead to underproduction from a social welfare perspective, because private agents only consider their private benefits. Government subsidies can bridge the gap between private and social benefits, encouraging more production or consumption up to the socially optimal level, thereby correcting the market failure.
15. A financial analyst is examining the relationship between a company's advertising expenditure (independent variable) and its quarterly sales (dependent variable). The analyst performs a simple linear regression and obtains the following results:
* Intercept = 500 (in thousands of dollars)
* Slope coefficient = 2.5
* R-squared = 0.75
* Standard error of the estimate = 50
If the company plans to spend $100,000 on advertising in the next quarter, what is the predicted quarterly sales (in thousands of dollars)?
Quantitative Methods
A.1250
B.500
C.750
D.250
Show answerAnswer
C. 750
The predicted quarterly sales can be calculated using the simple linear regression equation: Predicted Sales = Intercept + (Slope * Advertising Expenditure). Plugging in the given values yields the correct prediction.
16. A financial institution is evaluating a fixed-rate bond with a remaining maturity of 5 years, a coupon rate of 4.0% paid semi-annually, and a current yield to maturity of 3.5%. If the institution wants to calculate the bond's approximate modified duration, what would be the first step in this calculation?
Fixed Income
A.Calculate the bond's convexity.
B.Estimate the bond's price sensitivity to a 1% change in yield.
C.Determine the bond's effective duration.
D.Calculate the bond's Macaulay duration.
Show answerAnswer
D. Calculate the bond's Macaulay duration.
Modified duration is derived directly from Macaulay duration. The formula for modified duration is Macaulay Duration / (1 + YTM / number of coupon payments per year). Therefore, the first step to calculate modified duration is to calculate Macaulay duration.
17. A quantitative researcher is performing a backtest on a new trading strategy. The strategy involves daily rebalancing based on signals generated from fundamental data. The researcher notices that the backtest results show exceptionally high, unrealistic returns, far exceeding what would be expected in real-world trading. Upon closer inspection, it is discovered that the strategy's rebalancing decisions are made using financial statements that were published several days *after* the trading day they are used to make decisions. This is an example of which type of backtesting bias?
Quantitative Methods
A.Out-of-sample bias
B.Look-ahead bias
C.Survivorship bias
D.Data snooping bias
Show answerAnswer
B. Look-ahead bias
Look-ahead bias occurs when a backtest uses information that would not have been available to a trader at the time the decision was made. Using financial statements published after the trading day they influence is a classic example, as the strategy is 'looking ahead' into future information.
18. A global investment manager is analyzing the long-term sustainability of a developing country's economic growth. The country has a high savings rate, a young and growing population, but has historically relied heavily on raw material exports with limited diversification. The manager is concerned about the 'middle-income trap.' Which of the following factors is most critical for this country to avoid the middle-income trap and achieve sustained high-income status?
Economics
A.Focusing on attracting more foreign direct investment (FDI) into existing raw material sectors.
B.Implementing policies that foster innovation, human capital development, and total factor productivity (TFP) growth.
C.Devaluing its currency to make exports more competitive and boost trade surpluses.
D.Maintaining a high savings rate to fund continuous capital accumulation.
Show answerAnswer
B. Implementing policies that foster innovation, human capital development, and total factor productivity (TFP) growth.
The 'middle-income trap' occurs when a country's growth stalls after reaching middle-income status, failing to transition to high-income. This is often due to an inability to compete with low-wage economies in manufacturing or high-income economies in innovation. The most critical factor to escape this trap is to shift from input-driven growth (capital accumulation) to productivity-driven growth, which requires significant investments in innovation, education (human capital), and institutional reforms to boost Total Factor Productivity (TFP).
19. A financial advisor is preparing an Investment Policy Statement (IPS) for a 40-year-old client who is a successful entrepreneur. The client has significant human capital (expected future earnings) but currently holds a concentrated position in the illiquid stock of her own start-up company. She aims for aggressive growth over the next 15-20 years for retirement and her children's education, but also expresses a desire for some portfolio diversification away from her concentrated position. What is the most significant investment constraint that needs to be explicitly addressed in her IPS?
Portfolio Management and Wealth Planning
A.Taxes
B.Legal and Regulatory
C.Liquidity
D.Time Horizon
Show answerAnswer
C. Liquidity
The client holds a concentrated position in an illiquid stock. This 'illiquid stock' directly points to liquidity as a major constraint. While other constraints are present, the illiquid nature of her primary asset holding is the most pressing and significant constraint that must be addressed, as it impacts her ability to reallocate or diversify her wealth.
20. A portfolio manager is evaluating the credit risk of two corporate bonds: Bond Alpha and Bond Beta. Both bonds have the same maturity, coupon rate, and issuer. Bond Alpha is a senior secured bond, while Bond Beta is a senior unsecured bond. Which of the following statements is most accurate regarding their expected loss and recovery rates?
Fixed Income
A.Both bonds will have the same expected loss but Bond Alpha will have a higher recovery rate.
B.Bond Alpha will have a higher expected loss and a lower recovery rate than Bond Beta.
C.Both bonds will have the same recovery rate but Bond Alpha will have a lower expected loss.
D.Bond Alpha will have a lower expected loss and a higher recovery rate than Bond Beta.
Show answerAnswer
D. Bond Alpha will have a lower expected loss and a higher recovery rate than Bond Beta.
Senior secured debt has a higher priority claim on the issuer's assets in the event of default, leading to a higher recovery rate. A higher recovery rate directly translates to a lower expected loss, assuming the probability of default is the same for both bonds.
21. A bond portfolio manager uses a binomial interest rate tree to value callable bonds. The tree is calibrated to market yields. When valuing a callable bond, what is the correct approach to determine its value at each node in the tree?
Fixed Income
A.The value at each node is the higher of the call price and the value if not called.
B.The value at each node is the lower of the put price and the value if not called.
C.The value at each node is the higher of the put price and the value if not put.
D.The value at each node is the lower of the call price and the value if not called.
Show answerAnswer
D. The value at each node is the lower of the call price and the value if not called.
For a callable bond, the issuer has the right to call the bond. They will exercise this right if the bond's market value (value if not called) exceeds the call price. Therefore, the bondholder will receive no more than the call price. The bond's value at each node is the minimum of the call price and the value if not called.
22. A portfolio manager is considering adding real estate to a diversified portfolio. The manager is particularly interested in a property type that typically offers long-term, stable cash flows, is often inflation-indexed, and requires significant upfront capital expenditure. This property type also tends to be non-cyclical compared to other real estate sectors. Which of the following property types is the manager most likely considering?
Alternative Investments
A.Industrial Warehouses
B.Retail Centers
C.Infrastructure Assets
D.Office Buildings
Show answerAnswer
C. Infrastructure Assets
The description of long-term, stable, often inflation-indexed cash flows, high capital expenditure, and non-cyclical nature aligns best with infrastructure assets, which are categorized under real assets and share many characteristics with traditional real estate but are distinct.
23. A researcher is using a simple linear regression to model stock returns (dependent variable) based on the market's daily volume (independent variable). The researcher plots the residuals against the predicted values and observes a distinct fan-shaped pattern, with the spread of the residuals increasing as the predicted returns increase. What is the primary consequence of this observation for the OLS regression results?
Quantitative Methods
A.The model will suffer from multicollinearity.
B.The standard errors of the coefficients will be unreliable.
C.The R-squared value will be artificially inflated.
D.The coefficient estimates will be biased.
Show answerAnswer
B. The standard errors of the coefficients will be unreliable.
A fan-shaped pattern in residuals indicates heteroskedasticity, where the variance of the error terms is not constant. While OLS coefficient estimates remain unbiased and consistent under heteroskedasticity, their standard errors become incorrect, leading to unreliable hypothesis tests and confidence intervals.
24. A portfolio manager is constructing a portfolio of mortgage-backed securities (MBS) and is concerned about the timing of principal repayments. The manager wants to minimize the risk that borrowers pay off their mortgages faster than expected, especially when interest rates decline. Which of the following MBS tranches is best suited for this objective?
Fixed Income
A.Targeted Amortization Class (TAC) Tranche
B.Companion Tranche
C.Support Tranche
D.Planned Amortization Class (PAC) Tranche
Show answerAnswer
D. Planned Amortization Class (PAC) Tranche
A Planned Amortization Class (PAC) tranche is designed to have a more predictable cash flow schedule and prepayment risk by absorbing a certain range of prepayment speeds. It achieves this by shifting prepayment risk to companion (or support) tranches. This makes PAC tranches the most suitable for minimizing prepayment risk within a specified range.
25. A data scientist is tasked with analyzing a massive dataset of real-time trading activity, which includes millions of transactions per second. The primary challenge is not the variety of data or its trustworthiness, but rather the sheer volume and the speed at which it is generated and processed. Which characteristic of Big Data does this scenario primarily highlight?
Quantitative Methods
A.Variety
B.Volume
C.Velocity
D.Veracity
Show answerAnswer
C. Velocity
The scenario explicitly mentions 'millions of transactions per second' and emphasizes the 'speed at which it is generated and processed.' This directly points to the Velocity characteristic of Big Data, which refers to the speed at which data is generated, collected, and processed.
A hedge fund strategy that seeks to profit from temporary price discrepancies between related financial instruments, often by taking offsetting long and short positions to minimize market risk.
Exploits mispricings between related securities.
Aims for market neutrality.
Common examples: convertible arbitrage, fixed income arbitrage, equity pairs trading.
The Merton model (a structural credit model) views a company's equity as a call option on its assets and its debt as a risk-free bond minus a put option on its assets. Default occurs if asset value falls below the debt's face value at maturity.
Company assets follow a geometric Brownian motion (log-normal distribution).
Equity is a call option on assets; debt is a put option on assets.
Default is endogenous, occurring when asset value < debt value at maturity.
In a Collateralized Debt Obligation (CDO), tranches are layers of securities with different seniority levels, allocating risk and return from the underlying collateral pool. Junior tranches absorb losses first, bearing higher credit risk.
Senior tranches have the lowest credit risk and lowest yields.
Mezzanine tranches have moderate credit risk and moderate yields.
Equity/Junior tranches have the highest credit risk and highest potential yields.
Credit risk factors are variables that influence a borrower's ability or willingness to meet its financial obligations, thereby affecting the probability of default.
Financial leverage (debt-to-equity) is a key indicator.
Profitability and cash flow generation are crucial for debt servicing.
Industry cyclicality and competitive landscape impact revenue stability.
The Information Ratio (IR) measures the active return of a portfolio divided by its tracking error (active risk), indicating the consistency of a manager's outperformance.
A class of statistical models used to model time-series data with changing variance (heteroskedasticity) where the variance of the current error term is a function of the squares of the previous error terms.
Captures volatility clustering.
The conditional variance depends on past squared errors.
Used extensively in financial time series analysis.
Expected Loss Given Default (LGD) represents the proportion of a bond's principal that an investor expects to lose if the issuer defaults. It is a key component in credit risk analysis.
A no-arbitrage condition stating that the difference in interest rates between two countries is equal to the difference between the forward exchange rate and the spot exchange rate.
Suggests that investors should be indifferent to investing in either country's assets if IRP holds.
Predicts the relationship between spot and forward exchange rates.
Often holds in the short term for highly liquid currencies.
Effective duration measures the interest rate sensitivity of bonds with embedded options, accounting for how changes in interest rates affect the option's value and thus the bond's cash flows.
Callable bonds have lower effective duration than comparable option-free bonds when rates fall.
Call option limits upside price potential.
Effective duration can change significantly with interest rate levels.
A hedge fund strategy that involves taking both long and short positions in equity securities. The goal is to profit from both rising and falling stock prices, often with a net market exposure.
An options strategy involving holding a long position in a stock and simultaneously selling (writing) a call option on that same stock. It's used to generate income (from the premium) and offers limited downside protection.
Reduces volatility and generates income.
Limits upside profit potential if the stock price rises substantially.
Suitable for investors who expect moderate price movements or slight declines.
The pure expectations theory states that forward rates exclusively represent expected future spot rates, and the yield curve shape is determined by these expectations.
No liquidity premium or risk premium is assumed.
Long-term rates are geometric averages of expected short-term rates.
Implied forward rates can be derived from existing spot rates.
Simple linear regression models the relationship between a dependent variable and one independent variable using a linear equation, which can then be used to predict values.
Equation: Y_hat = b0 + b1*X
b0 is the intercept, b1 is the slope coefficient
X is the independent variable, Y_hat is the predicted dependent variable
Macaulay duration is the weighted average time until a bond's cash flows are received, while modified duration is a measure of a bond's price sensitivity to yield changes, derived from Macaulay duration.
Macaulay duration is expressed in years.
Modified duration is Macaulay duration divided by (1 + YTM/frequency).
Modified duration is used to estimate percentage price change for a given yield change.
Look-ahead bias in backtesting occurs when a trading strategy uses information that would not have been available to an investor at the time the investment decision was made, leading to inflated and unrealistic backtest performance.
Uses future data to make past decisions.
Common examples: using restated financials, using future prices, using data released with a lag.
The ease and speed with which an asset can be converted into cash at a fair market value. A lack of liquidity can restrict investment choices and rebalancing opportunities.
High liquidity needs require more cash or easily marketable assets.
Illiquid assets (e.g., private equity, real estate) reduce portfolio flexibility.
Must consider both current and future liquidity requirements.
When valuing a callable bond using a binomial interest rate tree, the bond's value at each node is capped at its call price, reflecting the issuer's option to redeem.
Start from the final maturity nodes and work backward.
At each node, calculate the value if not called (discounted expected future values).
Compare this 'if not called' value with the call price.
Long-lived assets that provide essential public services, often characterized by stable, predictable, and inflation-linked cash flows, and high barriers to entry.
Heteroskedasticity is when the variance of the error term in a regression model is not constant across observations. Its main consequence is unreliable standard errors.
OLS coefficient estimates remain unbiased and consistent.
Standard errors of coefficients are incorrect (usually underestimated).
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