Exam IFM Sample Questions and Solutions Finance and …

SOCIETY OF ACTUARIES

EXAM IFM INVESTMENT AND FINANCIAL MARKETS

EXAM IFM SAMPLE QUESTIONS AND SOLUTIONS

FINANCE AND INVESTMENT

These questions and solutions are based on material from the Corporate Finance textbook by Berk/DeMarzo (Learning Outcomes 1-5 of the Exam IFM syllabus) and two study notes, IFM-21-18 and IFM-22-18. Questions 1-33 are from Corporate Finance and Questions 34?43 are from the study notes.

They are representative of the types of questions that might be asked of candidates sitting for Exam IFM. These questions are intended to represent the depth of understanding required of candidates. The distribution of questions by topic is not intended to represent the distribution of questions on future exams.

March 2018 update: 3: Typo in solution corrected 5: Typo in question corrected 8: Changed E(X) to E(Rx) in solution 11: Deleted correlation input, and now require correlation to be derived from the given table. 12: Changed answer C, which could have interpreted as correct 40: Arithmetic error in solution corrected 41: "Only" deleted from answer choice D

June 2018 update: Edits have been made to questions/solutions 3, 7, 8, 9, 10, 14, 15, 16, 18, 28, 34, 42. These changes improve clarity and remove some possible ambiguities. Question 44 has been added.

November 2019 update: 31: Answer E changed 37: A clarification that p(t) and c(t) are payoffs

Copyright 2018 by the Society of Actuaries

IFM-02-18

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Finance and Investment Questions 1) You are given the following information about an asset.

i) Using 36 years of data, the average annual asset return is 10%. ii) The volatility of the asset's return, over the same time period, was

estimated to be 27%. iii) The distributions of each year's returns are identically distributed and

independent from each other year's returns.

Calculate the lower bound of the 95% confidence interval for the asset's annual expected return, using the approximation formula given in Corporate Finance.

(A) 1.0% (B) 2.6% (C) 4.5% (D) 5.5% (E) 8.5%

IFM-02-18

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Key: A Because there are 36 years' worth of data points and the distributions are IID, the standard error is given by S=E S= D 0.= 27 0.045

n 36 Berk/DeMarzo equation 10.9 for the 95% confidence interval is Historical Average Return ? (2?Standard Error). Thus, the lower bound of the 95% confidence interval is 0.10 - 2? 0.04=5 0.10 - 0.0=9 0.0=1 1%. Reference: Berk/DeMarzo, Section 10.3

IFM-02-18

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2) You are given the following information about a portfolio with four assets.

Asset

I II III IV

Market Value of Asset 40,000 20,000 10,000 30,000

Covariance of asset's return with the portfolio return 0.15 -0.10 0.20 -0.05

Calculate the standard deviation of the portfolio return.

(A) 4.50% (B) 13.2% (C) 20.0% (D) 21.2% (E) 44.7%

IFM-02-18

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Key: D

Solution: Formula 11.10 in Berk/DeMarzo gives the equation for the variance of a portfolio in terms of assets and covariance with the entire portfolio (where xi is the proportion of the portfolio invested in asset i):

Var(RP ) = xiCov(Ri , RP ) . i

The standard deviation is the square root of the variance. Therefore, the standard deviation of the portfolio in the problem is:

SD = 40, 000 ? (.15) + 20, 000 ? (-.10) + 10, 000 ? (.20) + 30, 000 ? (-.05) = 21.2%

100, 000

100, 000

100, 000

100, 000

.

Reference: Berk/DeMarzo, Section 11.3

IFM-02-18

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3) You are given the following information about the annual returns of two stocks, X and Y: i) The expected returns of X and Y are E[RX] = 10% and E[RY] = 15%. ii) The volatilities of the returns are VX = 18% and VY = 20% . iii) The correlation coefficient of the returns for these two stocks is 0.25. iv) The expected return for a certain portfolio, consisting only of stocks X and Y, is 12%.

Calculate the volatility of the portfolio return.

(A) 10.88% (B) 12.56% (C) 13.55% (D) 14.96% (E) 16.91%

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Key: D Let w be the weight of stock X and so 1 ? w is the weight of stock Y. Then, the expected return of the portfolio is: 0.12 = [ + (1 - )] 0.12 = [] + (1 - )[] = (0.10) + (1 - )(0.15) = 0.15 - 0.05 0.05 = 0.03

= 0.6

The variance of the return of the portfolio is: [0.6 + 0.4] = 0.62[] + 0.42[] + 2(0.6)(0.4)[, ] = 0.62(0.182) + 0.42(0.202) + 2(0.6)(0.4)(0.25)(0.18)(0.20) = 0.022384

The volatility of the return of the portfolio is: 0.022384 = 0.1496 Reference: Berk/DeMarzo, Section 11.2

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4) You are given the following information about a portfolio consisting of stocks X, Y, and Z:

Stock X Y Z

Investment Expected Return

10,000

8%

15,000

12%

25,000

16%

Calculate the expected return of the portfolio.

(A) 10.8% (B) 11.4% (C) 12.0% (D) 12.6% (E) 13.2%

IFM-02-18

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