Quantitative Methods test - Chartered Financial Analyst Level 1 questions

Question 1

A financial analyst is studying the average daily returns of a stock index. They randomly select a sample of 40 trading days and calculate the sample mean return to be 0.2% with a sample standard deviation of 1.2%. The analyst wants to construct a 99% confidence interval for the true population mean daily return. Assuming the daily returns are approximately normally distributed, what is the most appropriate z-score (critical value) to use for this confidence interval?

1.645 (this is the z-score for a 90% confidence interval, but the analyst wants a 99% confidence interval) 1.960 (this is the z-score for a 95% confidence interval, but the question specifically asks for a 99% confidence interval, so a higher z-score is needed to achieve the desired level of confidence) 2.576

Correct Answer: 2.576

The correct answer is 2.576. This is because for a 99% confidence interval, the corresponding z-score (critical value) is 2.576. To determine the appropriate z-score, we need to consider the desired confidence level. The confidence level tells us the probability that the true population parameter falls within the confidence interval. The higher the confidence level, the wider the interval, and the larger the z-score. Here are the commonly used z-scores for different confidence levels: - 90% confidence level: z-score = 1.645 - 95% confidence level: z-score = 1.960 - 99% confidence level: z-score = 2.576 Since the analyst specifically wants to construct a 99% confidence interval, the most appropriate z-score to use is 2.576.

Question 2

A company's monthly sales data is known to follow a normal distribution with a mean of $500,000 and a standard deviation of $100,000. The management wants to determine the probability that the monthly sales will exceed $650,000. What is the z-score that corresponds to a monthly sales figure of $650,000?

1.25 1.5 1.65

Correct Answer: 1.5

The correct answer is 1.5. To find the z-score, we use the formula: z = (x - μ) / σ Where: x = the value we're interested in (in this case, $650,000) μ = the mean of the distribution ($500,000) σ = the standard deviation ($100,000) Plugging in the values: z = (650,000 - 500,000) / 100,000 z = 150,000 / 100,000 z = 1.5 So, a monthly sales figure of $650,000 corresponds to a z-score of 1.5 in this distribution.

Question 3

An investor is considering an investment that requires an initial outlay of $20,000 and is expected to generate annual cash inflows of $6,000 for the next 4 years. If the investor's required rate of return is 12% per annum, what is the internal rate of return (IRR) of this investment?

The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of the investment equal to zero. The internal rate of return (IRR) is determined by adding the present values of all cash inflows and comparing the result to the initial investment amount. The internal rate of return (IRR) is calculated by dividing the total cash inflows by the initial investment amount and expressing the result as a percentage.

Correct Answer: The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of the investment equal to zero.

The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of an investment equal to zero. To calculate the IRR, we need to find the discount rate that satisfies the following equation: -20,000 + 6,000/(1+IRR)^1 + 6,000/(1+IRR)^2 + 6,000/(1+IRR)^3 + 6,000/(1+IRR)^4 = 0 This equation cannot be solved analytically and requires an iterative process or a financial calculator to find the IRR. The other two answer options are incorrect because: - Dividing the total cash inflows by the initial investment does not give the IRR. This would give a simple average return, not considering the time value of money. - Adding the present values of cash inflows and comparing it to the initial investment is the method for calculating NPV, not IRR.

Quantitative Methods

CFA Level 1 - Quantitative Methods Example Questions

Question 1

Question 2

Question 3

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