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CFA Level I Quantitative Methods Calculation Practice with Answers

Practice 50 CFA Level I Quantitative Methods calculation questions with answers and detailed explanations. Test your skills, review step-by-step solutions, and strengthen your understanding of key quantitative concepts for the CFA exam.

Question 1
Assume that Security A has a standard deviation of 4.1% and Security B has a standard deviation of 9.3%. If the covariance of the returns is 19.37, then the correlation coefficient between the two securities is:
Question 2
William purchased an investment for $600. He kept the investment for 5 years before selling it If the internal rate of return for the 5-year period was 9%, the final selling price is:
Question 3
Alpha Corporation’s investment of $3.4 million produces the following cash flows:
Year 1: $2.1 million
Year 2: $2.2 million
Year 3: $1.6 million
If the discount rate is 7%, the investment's net present value (NPV) is:
Question 4
A security has a coefficient of variation of 1.27 and a standard deviation of 13%. The expected return of the security is:
Question 5
Jane has been investing $2,000 at the end of each year for the past 11 years. Assuming she has earned 8% compounded annually on her investments, she has accumulated:
Question 6
Beta Investment Company quotes an annual interest rate of 6.00%. If that rate is equal to an effective annual rate of 6.17%, then the investment company is compounding interest:
Question 7
Sam purchased an investment for $30,000. He expects it will increase in value at a rate of 12% compounded annually for the next 4 years. If his expectations are correct, at the end of the fourth year his investment will be worth:
Question 8
Delta Corporation manufactured 6.86 million units of product in 2016. Four years earlier, the company manufactured 7.33 million units. The compound annual growth rate of units manufactured from 2012 to 2016 is:
Question 9
Beth wants to accumulate $95,000 in 7.5 years to purchase a rental property. She expects to earn an annual rate of 9.5% compounded quarterly. To achieve her goal, the amount that she needs to invest today is:
Question 10
Steven’s portfolio has a mean return of 15%, a standard deviation of 7%, and a beta of 2.0. If the risk-free rate of return is 4%, the portfolio’s Sharpe ratio is:
Question 11
Gamma Corporation loans money at a quoted annual interest rate of 5.00%. If interest is compounded daily, the effective annual rate is:
Question 12
A leading trade publication reports that Epsilon stock has a short interest of 5,869,121 shares, with an average daily trading volume of 4,018,472. The average declining volume is 2,102,554. The short interest ratio for Epsilon stock is:
Question 13
Rose sued her former employer and won a judgment that provides her $2,000 at the end of each 6-month period for the next 5 years. If the account that holds her settlement earns an average annual rate of 7% compounded semiannually, the employer was initially required to pay Rose:
Question 14
The average annual return and the standard deviation for three investments is provided in the following table:
| Investment | Average Annual Return (%) | Standard Deviation of Return (%) |
| — | — | — |
| Security A | 6.8 | 2.2 |
| Security B | 2.1 | 1.3 |
| Security C | 4.4 | 1.2 |
Based on the coefficient of variation, the riskiest investment is:
Question 15
Michael purchased an investment for $315,000, which earned a return of-2% in the most recent year. In the previous three years, the investment returns were 5%, -1%, and 6%, respectively. Assuming all income has been reinvested, the standard deviation of the rates of return for the investment over the last four years is:
Question 16
Evelyn expects to receive $150,000 from an irrevocable trust in 7 years. If the trust is earning an annual rate of 10% compounded quarterly, its current value is:
Question 17
Brett, an analyst, has identified four stocks that meet his criteria for inclusion in his portfolio. Of those stocks, he will purchase only three this year. The number of different groups of three stocks that are possible is:
Question 18
Katrina’s portfolio has a Sharpe ratio of 0.55, and a mean return of 4.6%, If the 30-day T-bill rate is 2.0%, the standard deviation of return on Katrina's portfolio is:
Question 19
In a normal distribution, the percent of observations that lie between plus and minus one standard deviation from the mean, plus and minus two standard deviations from the mean, and plus and minus three standard deviations from the mean, respectively, is:
Question 20
Karl has been investing $2,000 at the end of each 6-month period to accumulate funds for his daughter's college tuition. The funds are earning an annual rate of 6% compounded semiannually. When Karl’s daughter begins college in 7 years, the account will be worth:
Question 21
Renee purchases a share of Zeta stock for $39.10 and receives a dividend of $1.05 one year later. If the share of stock is sold for $42.30 immediately following the dividend payment, the holding period return is:
Question 22
John has a T-bill with a face value of $100,000 that is currently selling for $96,500. If the T-bill has 270 days until maturity, the bank discount yield is:
Question 23
Catherine purchased an investment with a 250-day holding period yield (HPY) of 5.5%. The effective annual yield (EAY) on her investment is:
Question 24
If Raymond’s security pays $450 per year in perpetuity, and his required rate of return is 6%, then the present value of the security is:
Question 25
Pamela deposits $4,000 into her IRA. Each year, for the next 10 years, she is able to deposit an additional $2,000. If her IRA earn 8% annually, then the value of her account at the end of 10 years will be:
Question 26
The Delta Fund has recorded the following investment returns since inception:
2012: +9.1%
2013: -1.3%
2014: +2.1%
2015: +10.1%
2016: +13.1%
The geometric mean for the Delta Fund is:
Question 27
Alice has established certain criteria that stocks must meet for inclusion in her portfolio. If 8% of the stocks that meet her criteria are in the energy industry, and international energy stocks are 4% of the total number of stocks meeting her selection criteria, then the probability that a stock is international, given that it is an energy stock that has met her selection criteria is:
Question 28
Robert would like to give his nephew $15,000 to take a trip around the world in 8 years If his investments earn an annual rate of 5% compounded annually, then the amoun he should invest today is:
Question 29
The Theta Fund has recorded the following investment returns for the past seven years: -3%, +4%, +5%, -3%, +2%, +6%, -1%. The mean, median, and mode of the returns, respectively, is:
Question 30
Assume that Security A has a standard deviation of 6.5% and Security B has a standard deviation of 12.4%. If the correlation coefficient between the two securities is 0.30, then the covariance of the returns is:
Question 31
Keith invested $10,000 in a security that earns a 7% annual rate of return compounded monthly. The value of Keith's account at the end of 9 years will be:
Question 32
For a sample size of 49, with a mean of 24 taken from a normally distributed population with a variance of 441, a 99% confidence interval for the population mean will have an upper limit equal
Question 33
Jordan is researching two securities for possible inclusion in his portfolio. Security A has an expected return of 9% and a standard deviation of 10%. Security B has an expected return of 5% and a standard deviation of 8%. If Jordan is a risk-averse investor, he would select:
Question 34
Linda, an investment manager, uses the following four criteria to find potential stocks to add to her investment portfolio:
| Criteria | Fraction of S&P 100 Stocks Meeting Criteria |
| — | — |
| High Sharpe ratio | 0.45 |
| High Treynor ratio | 0.40 |
| High alpha | 0.25 |
| Low coefficient of variation | 0.50 |
If the criteria are independent, the number of stocks that will pass Linda’s screen is:
Question 35
A sample mean is calculated from a population with a variance of 3.19. If the sample size is 33, then the standard error of the sample mean is:
Question 36
Irene, a business owner, has a balloon payment of $50,000 due in 6 years. The loan is discounted at a rate of 8% compounded semiannually. If Irene can make a lump-sum payment today, the amount she should offer to satisfy the loan is:
Question 37
In an inverted head and shoulders pattern, if the neckline is at $220.33, the shoulders at $200.50, and the head at $175.45, the price target is:
Question 38
Christopher, an investment manager, estimates that a stock he is researching will pay a dividend between $3.10 and $4.05 within the next month. Assuming that all outcomes for dividends between these two values is equally likely, the probability that the dividend will be less than or equal to $3.40 is:
Question 39
Christine invests $6,000 today with the promise that she will receive $11,000 in 4 years. If interest is compounded weekly, the average annual rate of return that Christine will earn is:
Question 40
James, an investment analyst, provides the following data for the NYSE.
| Metric | Value |
| — | — |
| Number of advancing issues | 310 |
| Number of declining issues | 412 |
| Volume of advancing issues | 44,383,384 |
| Volume of declining issues | 87,194,109 |
Given the information provided, the TRIN value of the NYSE is:
Question 41
An analyst is reviewing Kappa Corporation's earnings per share (EPS) and has recorded the following probability distribution for the upcoming fiscal year:
| Probability | EPS ($) |
| — | — |
| 0.25 | 3.00 |
| 0.25 | 3.10 |
| 0.50 | 3.20 |
The expected value of Kappa Corporation’s EPS is:
Question 42
In a head and shoulders pattern, if the neckline is at $48.37, the shoulders at $51.02, and the head at $55.12, the price target is:
Question 43
Ken, a business owner, wants to purchase new equipment in three years. He expects to spend $15,000 for the equipment If he earns an annual compound rate of return of 8% on his investments, the amount he should invest today to achieve his goal is:
Question 44
In 2016, an investor allocated her portfolio in the following asset classes:
| Asset Class | Asset Allocation (%) | Asset Class Return (%) |
| — | — | — |
| Domestic equities | 40.0 | +10.0 |
| International equities | 20.0 | –4.0 |
| Corporate bonds | 30.0 | +6.0 |
| Money market funds | 10.0 | +2.0 |
The portfolio’s weighted average return for 2016 is:
Question 45
Greg purchased an investment for $700. He kept the investment for 4 years and then sold it for $1,200. The internal rate of return (IRR) that Greg earned was:
Question 46
In a double-top pattern, Omega stock’s price peaked at $116.44 before declining to $115.39. The price then rose again to $116.40 and then started to decline. The price target of Omega stock is:
Question 47
If $980 today is the equivalent of $1,000 in one year, then the required compensation stated as a rate of return is:
Question 48
Gina is an investor with a threshold return of 3%. She is reviewing two portfolios. Portfolio 1 has an expected return of 9% and a standard deviation of 12%. Portfolio 2 has an expected return of 11% and a standard deviation of 13%. The safety-first ratio (SFRatio) of Portfolio 1 and Portfolio 2, respectively, is:
Question 49
An investment manager analyzing Lambda Corporation’s earnings per share (EPS) has discovered that in 62% of recent quarters, Lambda’s EPS has increased sequentially. In 38% of recent quarters, the EPS has either decreased or remained unchanged. The probability that EPS will increase in each of the next three quarters is:
Question 50
Patricia owns a bond with a holding period yield (HPY) of 3.55%. If the face value of the bond is $1,000, the present value is: