Finance Practice Exam 2

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Questions and Answers

An investment earns 2.5% per quarter. What is the effective annual rate (EAR)?

11.02%

10.38% (correct)

6.19%

2.52%

10.00%

Which return type below takes the timing of investment cashflows into account when aggregating holding period returns over multiple periods?

geometric average return

arithmetic average return

time-weighted average return (correct)

dollar-weighted average return

An investor will mix a risky asset with the risk-free asset to form her ______ based on her degree of risk aversion.

efficient portfolio

The Capital Allocation Line which uses the market index as the risky asset is called

Security Market Line Signup and view all the answers

The standard deviation of a portfolio formed with two risky assets will be highest when the correlation coefficient between the two assets is _____.

1 Signup and view all the answers

Consider an investment opportunity set formed with two securities that are perfectly negatively correlated. The minimum-variance portfolio has a standard deviation that is always _____.

equal to 0 Signup and view all the answers

Suppose investors can only choose to invest in one of the 5 stocks in the below graph. Every risk-averse investor would prefer _____.

Only stock A Signup and view all the answers

Compare Portfolio A and Portfolio B in the below investment opportunity set. Which of the following is not true?

Portfolio A is dominated by Portfolio B Signup and view all the answers

If we run a regression where the dependent variable is AAPL's excess returns and the independent variable is market excess returns, 1 - R² of the regression will be _____.

The firm-specific portion of APPL's variance Signup and view all the answers

Which of the following is not an implication of CAPM?

Every investor will put 100% of her investment in the market portfolio Signup and view all the answers

Among securities with identical betas, a security with a ____. alpha is overpriced and will yield lower expected returns.

positive; negative Signup and view all the answers

Which of the following criticisms of CAPM is not addressed by the Fama-French three factor model?

The model is for expected returns but we only observe actual realized returns. Signup and view all the answers

If you are given the Security Characteristic Line (SCL) for a stock, what do the slope and intercept of this line represent? How do we interpret them?

The intercept of SCL is the stock's alpha. It is the stock's expected excess return when the market excess return is zero; i.e. it is the excess return beyond what is induced by broad movements in the market. The slope of SCL is the stock's beta. It measures the stock's systematic risk and it is the amount by which the stock's return tends to increase or decrease for every 1% increase or decrease in market excess returns. Signup and view all the answers

Why should all investors hold market portfolio as their optimal risky portfolio according to CAPM? Does this hold in practice? Why or why not?

CAPM assumes 1) investors all have the same input for expected return, risk, and correlations of the assets in the economy (homogenous expectations) 2) investors are all rational mean-variance optimizers 3) investors can all borrow/lend at the same risk-free rate. These three assumptions imply that investors will all come up with the same portfolio as their optimal risky portfolio and end up on the same Capital Allocation Line. Therefore, in equilibrium market portfolio will simply be an aggregation of the same optimal risky portfolio. In practice, we do not see all investors holding the same optimal risky portfolio, i.e. the market portfolio, but instead they invest in various actively managed portfolios, because the assumptions of CAPM do not hold in real life, in particular the homogenous expectations assumption. Instead, investors have differing expectations of risk and return (including perhaps believing that some assets are mispriced), so they form different opportunity sets and optimal portfolios. In addition, investors may impose constraints on the assets in their portfolios, for instance to diversify away from their human capital investment, because of a preference for dividend-paying securities, or because of a preference for socially responsible investment options. Signup and view all the answers

Calculate the net cash flows of your investment for each year.

CF0 = -1040 = -400 CF1 = 110 - 245 = -80 CF2 = 1.2512 + 644 = 279 CF3 = 647 = 282 Signup and view all the answers

What is the dollar-weighted return of your investment?

Dollar-weighted return= IRR of CFs= 6.91% Signup and view all the answers

Find the weights of the portfolio formed by stocks A and B that has the least possible risk.

Find the minimum variance portfolio using the formula WB σ²B – σAσΒρAB σ²A + σ²B – 2σAσΒρAB Ws = 1-WB WB= (.32 - .3*.2*-.3)/(.2²+.32 - 2*.2*.3*-.3) = 65.06% WA = 1 - 65% = 34.94% Signup and view all the answers

Find the expected return and standard deviation of this portfolio

E(rp)= WAE(rA) + WBE(Rb)= 0.349418%+ 0.650612%= 14.10% σ=(σA)²+(σB)²+2WAAWBOB PAB σ²B=ι (.3494*.3)² + (.6506*.2)² + 2(.3494*.3*.6506*.2*-.3) στ= 0.0197 : σρ=√0.0197 = 14.05 % Signup and view all the answers

Assume you would like to form a complete portfolio by mixing the risk-free asset and the portfolio you found in b) as the risky portfolio. If your risk aversion coefficient is 6, what will be the weight of this risky portfolio in your complete portfolio?

y- Available risk premium to variance ratio Required risk premium to variance ratio =[E(rp) - 131 E (rp) - Fy Ασ A = (14.10% - 4%) / (6 * 14.05%^2) = 85.27% Signup and view all the answers

What will be the final weights of Stock A, Stock B and risk-free asset in your complete portfolio?

Weight for Stock A= 85.27% *34.94%= 55.48% Weight for Stock B= 85.27% *65.0.6%= 29.79% Risk-free asset= 14.73% Signup and view all the answers

Find the slope of the security market line

The slope of the security market line is just the market risk premium. It is also the risk premium divided by the beta for any individual asset. Using either .08 = .035 + 0.6(MRP) or .14 = .035 + 1.4(MRP), solve for the MRP. Or (.08-.035)/.6 = MRP = (.14-.035)/1.4 → MRP = slope = 0.075= 7.5% Signup and view all the answers

What is the beta of a portfolio with an expected return of 8.5%?

Beta= (Expected return - risk-free rate) / MRP = (8.5%-3.5%)/7.5%= 0.67 Signup and view all the answers

Given the information below, determine whether or not an arbitrage opportunity exists. If so, please describe the arbitrage opportunity, including the positions (weights in each) you would take and the return you would generate.

First, form a zero beta portfolio using Portfolios A and B. If the return is different than the risk-free rate, then an arbitrage opportunity exists. 0=wABA+(1-wA)BB 0=1.6w+-0.2(1-WA) 0=1.6w+-0.2+0.2 ν A 0.2=1.8WA W₁=0.11111 → WB=0.88889 E(rp)=0.11111(.14)+0.88889(.02)=.03333 < rf=.04 → There is an arbitrage opportunity. Strategy: Sell the expensive and buy the cheap. The expensive here is the low-return, zero beta portfolio and the cheap is the high-return risk-free asset. Therefore, the weight on the zero beta portfolio is -1, so that the weight on Portfolio A is -0.11111, the weight on Portfolio B is - 0.88889, and the weight on the risk-free asset is 1. The sum of the weights is zero, implying zero net investment. Your return would be 1(.04) - 0.11111(.14) – 0.88889(.02) = .00667 or 0.67%. Signup and view all the answers

Study Notes

Practice Exam 2 - Solutions

Question 1: Effective Annual Rate (EAR) calculation for a 2.5% quarterly rate is 11.02%.
Question 2: Dollar-weighted average return considers the timing of cash flows when aggregating holding period returns over multiple periods.
Question 3: An investor's complete portfolio is formed by mixing a risky asset with a risk-free asset based on their risk aversion.
Question 4: The Capital Market Line uses the market index as the risky asset.
Question 5: The standard deviation of a portfolio formed with two risky assets is highest when the correlation coefficient between the two assets is -1.
Question 6: When two securities are perfectly negatively correlated, the standard deviation of the minimum-variance portfolio is always equal to 0.
Question 7: In a graph depicting the risk and return of different stocks, the risk-averse investor would prefer stock A, B, or E given the context.
Question 8: Portfolio A is dominated by Portfolio B, meaning Portfolio B offers the same or higher expected return and lower risk compared to A.
Question 9: The firm-specific portion of a stock's variance, calculated as 1 – R², is the part of the stock's return not explained by the market.
Question 10: Every investor putting 100% of their investment into the market portfolio is not an implication of CAPM.
Question 11: Among securities with identical betas, a security with a positive alpha is underpriced, and a security with a negative alpha is overpriced.
Question 12: The Fama-French three-factor model does not address the criticism that the CAPM model is for expected returns but only observes actual realized returns.

Security Characteristic Line (SCL)

The intercept of the SCL represents the stock's alpha, which is the stock's expected excess return when the market excess return is zero.
The slope of the SCL represents the stock's beta. This measures the systematic risk of the stock, indicating how much the stock's return changes for every 1% change in market excess return.

CAPM and Market Portfolio

CAPM assumes homogeneous expectations regarding risk and return of assets among investors, rational mean-variance optimizations, and similar borrowing and lending rates.
CAPM suggests that the market portfolio is the optimal risky portfolio for all investors due to equilibrium conditions.

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Description

This quiz covers advanced finance topics such as Effective Annual Rate calculations, portfolio management, and risk-return analysis. It assesses the understanding of key concepts like dollar-weighted average returns, Capital Market Line, and portfolio variances. Perfect for students preparing for finance exams or needing a refresher on investment concepts.

Finance Practice Exam 2 - Solutions

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