Quantitative Methods

CFA® Level I, published weight 6–9%. Returns, time value, distributions, hypothesis tests, simple regression.

What the outline covers

These 5 questions are free in the app too. Try each one before opening the answer.

An investment offers a stated annual rate of 8% compounded quarterly. The effective annual rate is closest to:

r = 8% · m = 4

A. 8.00%
B. 8.24%
C. 8.30%
D. 8.33%

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B. EAR = (1 + 0.08/4)⁴ − 1 = 1.02⁴ − 1 = 8.243%. More frequent compounding always raises the effective rate above the stated rate.

Reading: Quantitative Methods — Rates and Returns, LOS 1.b

A researcher rejects the null hypothesis at the 5% significance level when the null is in fact true. This is best described as:

A. A Type I error
B. A Type II error
C. A power failure
D. A specification error

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A. Rejecting a true null is a Type I error, and its probability equals the significance level chosen. Failing to reject a false null is Type II.

Reading: Quantitative Methods — Hypothesis Testing, LOS 8.a

A sample of 25 monthly returns has a mean of 1.2% and a standard deviation of 3.0%. The standard error of the sample mean is closest to:

x̄ = 1.2% · s = 3.0% · n = 25

A. 0.12%
B. 0.60%
C. 3.00%
D. 1.20%

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B. The standard error is s/√n = 3.0%/5 = 0.60%. It falls with the square root of sample size, not with sample size itself.

Reading: Quantitative Methods — Estimation and Inference, LOS 7.c

In a simple linear regression the coefficient of determination is 0.64. The correlation between the dependent and independent variable is:

R² = 0.64

A. 0.41
B. 0.64
C. 0.80 in absolute value
D. 1.28

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C. In simple linear regression R² is the squared correlation, so

= √0.64 = 0.80. The sign follows the sign of the slope coefficient.

Reading: Quantitative Methods — Simple Linear Regression, LOS 10.d

Which measure of central tendency is most appropriate for describing a compound annual growth rate over multiple periods?

A. Arithmetic mean
B. Geometric mean
C. Harmonic mean
D. Mode

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B. The geometric mean accounts for compounding and gives the constant rate that reproduces the ending value. It is always ≤ the arithmetic mean.

Reading: Quantitative Methods — Rates and Returns, LOS 1.d

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