Quantitative Methods — CFA Level I practice questions

Beta of 1.5 means:

1. Lower systematic risk than the market
2. Stock moves 1.5 times the market on average
3. The stock is uncorrelated with the market
4. The stock has negative correlation with market

Answer: B — Stock moves 1.5 times the market on average

A) Beta < 1 would indicate lower systematic risk. B) Correct — beta = 1.5 amplifies market moves by 1.5x. C) Beta near 0 would suggest low correlation. D) Beta < 0 (rare) would indicate inverse movement.

Blockchain differs from a generic distributed ledger primarily because a blockchain has which of the following defining data-structure features?

1. It is necessarily public and open to all participants, without any permissioned or private variants existing in current practice
2. It organizes data into cryptographically linked, time-stamped blocks arranged in an append-only chain of transaction blocks
3. It uses no cryptography at all, relying instead on ordinary legal contracts to ensure the integrity of the network's records

Answer: B — It organizes data into cryptographically linked, time-stamped blocks arranged in an append-only chain of transaction blocks

A) Both public and private (permissioned) blockchains exist. B) Correct — blockchain is a specific chained data structure on DLT. C) Cryptography is central to blockchain.

An investor deposits $5,000 today and $5,000 at the end of each year for 4 more years. With a 6% annual rate, the future value at the end of year 4 is closest to:

1. $26,872 total value
2. $25,000 total value
3. $28,185 total value
4. $30,470 total value

Answer: C — $28,185 total value

A) Uses wrong compounding of the initial deposit. B) Ignores time value entirely. C) Correct — 5000(1.06)^4 + 5000×[((1.06)^4−1)/0.06] ≈ 6,312 + 21,873 ≈ 28,185. D) Adds an extra period of growth.

Return is normally distributed with mean 8% and SD 12%. P(return < −16%) is approximately:

1. 16% because that matches the one standard deviation tail
2. 5% by conflating the two-tail and one-tail probability
3. 2.5% since −16% is two SDs below the eight percent mean
4. 0.5% because that matches the three standard deviations tail

Answer: C — 2.5% since −16% is two SDs below the eight percent mean

A) 16% is roughly the one-SD tail (below −4%), not the two-SD tail. B) 5% would be the two-tailed sum near ±1.96 SD. C) Correct — (−16 − 8)/12 = −2, and P(Z < −2) ≈ 2.5%. D) 0.5% is roughly the three-SD tail, deeper than −16%.

Monte Carlo simulation in finance is most commonly used to accomplish which of the following analytical objectives when closed-form solutions are unavailable?

1. Replace deterministic optimization routines with direct closed-form analytical solutions in essentially every relevant portfolio-management setting
2. Model uncertainty by repeatedly drawing random samples in order to estimate the distribution of portfolio, ruin probability, or option-price outcomes
3. Eliminate model risk entirely by exhausting all possible parameter values in a deterministic grid search over each of the relevant model inputs

Answer: B — Model uncertainty by repeatedly drawing random samples in order to estimate the distribution of portfolio, ruin probability, or option-price outcomes

A) Monte Carlo does not deliver closed-form solutions. B) Correct — Monte Carlo is sampling-based estimation of outcome distributions. C) Simulation cannot eliminate model risk.

A correlation coefficient of −0.85 between two assets implies which of the following about the co-movement of the two asset returns?

1. A strong negative linear relationship between the two return series, so that combining them can substantially reduce portfolio variance
2. The two asset return series are statistically unrelated to each other over the historical sample period from which the coefficient is drawn
3. The two asset return series move together in the same direction, showing very high positive linear co-movement across the sample period

Answer: A — A strong negative linear relationship between the two return series, so that combining them can substantially reduce portfolio variance

A) Correct — −0.85 signals strong inverse linear co-movement, ideal for diversification. B) A magnitude of 0.85 rules out independence. C) Positive co-movement would require a positive coefficient.

Alternative data used in investment analysis most commonly includes which of the following categories of non-traditional data sources?

1. Audited quarterly financial statements filed by publicly listed issuers with securities regulators on the standard reporting cycle
2. Satellite imagery, credit-card transaction data, web traffic, mobile app usage, geolocation, and social-media sentiment signals
3. Formal sell-side broker research reports published by regulated investment banks on the covered universe of listed corporate issuers

Answer: B — Satellite imagery, credit-card transaction data, web traffic, mobile app usage, geolocation, and social-media sentiment signals

A) Audited financials are traditional, not alternative, data. B) Correct — non-traditional high-frequency sources define alternative data. C) Broker research is traditional sell-side data.

For a normal distribution, approximately what percentage of observations fall within ±2 standard deviations of the mean?

1. 68 percent, the empirical-rule interval bounded by roughly ±1 standard deviation on either side
2. 50 percent, the interquartile range bounded by roughly ±0.67 standard deviations from center
3. 99.7 percent, the empirical-rule interval bounded by roughly ±3 standard deviations either side
4. 95 percent, the empirical-rule interval bounded by roughly ±2 standard deviations on each side

Answer: D — 95 percent, the empirical-rule interval bounded by roughly ±2 standard deviations on each side

A) That figure describes the ±1σ interval, not ±2σ. B) The 50% figure describes the interquartile range instead. C) That figure describes the ±3σ interval. D) Correct — the 68/95/99.7 empirical rule places 95.4% within ±2σ.

A time series is considered (weakly) stationary when it satisfies which of the following defining conditions on its statistical moments over time?

1. Its unconditional mean is exactly zero at every point across the entire observed sample period without any residual drift over calendar time
2. Its plotted level line has no visible trend, although the variance or the autocorrelation is allowed to fluctuate freely across the sample period
3. Its statistical properties (mean, variance, and autocovariance structure) do not change through calendar time over the entire relevant sample period

Answer: C — Its statistical properties (mean, variance, and autocovariance structure) do not change through calendar time over the entire relevant sample period

A) Zero mean is neither necessary nor sufficient. B) Trend absence is one aspect; other moments must also be constant. C) Correct — constant moments and autocovariance define stationarity.

A 95% confidence interval for the mean of a normally distributed variable, computed with known population standard deviation, is BEST given by:

1. mean plus or minus 2.33 × standard error
2. mean plus or minus 1.65 × standard error
3. mean plus or minus 2.58 × standard error
4. mean plus or minus 1.96 × standard error

Answer: D — mean plus or minus 1.96 × standard error

A) 2.33 is a one-tailed 99% critical value. B) 1.65 corresponds to a 90% two-tailed CI. C) 2.58 corresponds to a 99% two-tailed CI. D) Correct — 95% two-tailed critical z is 1.96.

What is the correlation coefficient?

Measures linear relationship between two assets (−1 to +1). Negative correlation reduces portfolio risk. +1 offers no diversification.

What is skewness?

A measure of distribution asymmetry. Positive skew: long right tail (mean > median). Negative skew: long left tail (mean < median).

What is the money-weighted return?

The IRR of an investment, considering the timing and amounts of cash flows. Affected by the timing of contributions and withdrawals.

Population vs. sample?

Population includes all members of a defined group. Sample is a subset used for analysis. Sample statistics estimate population parameters.