FINA 441 Investments Practice Exam 2 PDF

**FINA 441 INVESTMENTS -- PRACTICE EXAM 2 - SOLUTIONS** [Multiple Choice]. Circle the best/most correct answer. (3 points each) 1\. An investment earns 2.5% per quarter. What is the effective annual rate (EAR)? 2\. Which return type below takes the timing of investment cashflows into account when...

**FINA 441 INVESTMENTS -- PRACTICE EXAM 2 - SOLUTIONS** [Multiple Choice]. Circle the best/most correct answer. (3 points each) 1\. An investment earns 2.5% per quarter. What is the effective annual rate (EAR)? 2\. Which return type below takes the timing of investment cashflows into account when aggregating holding period returns over multiple periods? 3\. An investor will mix a risky asset with the risk-free asset to form her\_\_\_\_\_\_\_\_\_\_\_\_ based on her degree of risk aversion d\. efficient portfolio 4\. The Capital Allocation Line which uses the market index as the risky asset is called \_\_\_\_\_\_\_\_\_\_ 5\. The standard deviation of a portfolio formed with two risky assets will be highest when the correlation coefficient between the two assets is \_\_\_\_\_\_\_\_\_\_\_ **a. 1** b\. 0.5 c\. 0 d\. -1 6\. 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 \_\_\_\_\_\_\_. d\. greater than 0 7. Suppose investors can only choose to invest in one of the 5 stocks in the below graph. Every risk averse investor would prefer: a. Only stock C b. Only stock A c. Only stock B d. Either stock A or stock C e. Either stock A or Stock E f. **Either Stock A or Stock B or Stock C** 8. Compare Portfolio A and Portfolio B in the below investment opportunity set. Which of the following is [not] true?  a\. Portfolio A and Portfolio B have the same volatility b\. Portfolio A has a higher expected return compared to Portfolio B c\. Risk averse investors will prefer Portfolio A to Portfolio B. **d. Portfolio A is dominated by Portfolio B** 9\. If we run a regression where the dependent variable is AAPL's excess returns and the independent variable is market excess returns, [1 - R^2^] of the regression will be a\. The systematic portion of APPL's variance **b. The firm-specific portion of APPL's variance** c\. The systematic portion of APPL's volatility d\. The firm-specific portion of APPL's volatility 10\. Which of the following is [not] an implication of CAPM? a\. Every investor will choose the market portfolio as the optimal risky portfolio **b. Every investor will put 100% of her investment in the market portfolio** c\. Market risk premium = average risk aversion \* market variance d\. Individual security risk premium = beta \* market risk premium 11\. Among securities with identical betas, a security with a ­\_\_\_\_\_\_\_\_\_\_\_ alpha is underpriced and will offer higher expected return, whereas a security with a \_\_\_\_\_\_\_\_\_\_\_ alpha is overpriced and will yield lower expected returns. 12\. Which of the following criticisms of CAPM is [not] addressed by the Fama-French three factor model? [\ Short Answer]. Give a concise but complete answer. (5 points each) 13\. 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.** 14\. 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.** [Numerical Problems]. Show your work, as partial credit is available here. Points as specified. 15\. You bought 10 shares of stock at \$40 per share in 2016. In 2017, you received a \$1 dividend per share on the shares you already owned and then bought an additional 2 shares at \$45 per share. In 2018, you received a \$1.25 dividend per share and then sold six shares for \$44 per share. In 2019, you received no dividend and sold all remaining shares for \$47 per share. a\. Calculate the net cash flows of your investment for each year. (6 points) b\. What is the dollar-weighted return of your investment? (5 points) 16\. Stock A has an expected return of 18% and a standard deviation of 30%. Stock B has an expected return of 12% and a standard deviation of 20%. The correlation between stock A and B is -0.30. The risk-free rate is 4%. a. Find the weights of the portfolio formed by stocks A and B that has the least possible risk. (5 points) b. Find the expected return and standard deviation of this portfolio (5 points) \ [**σ**~**P**~^**2**^**=** **(w**~**A**~**σ**~**A**~**)**^**2**^**+** **(w**~**B**~**σ**~**B**~**)**^**2**^ **+** **2w**~**A**~**σ**~**A**~**w**~**B**~**σ**~**B**~**ρ**~AB~]{.math.display}\ c. 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? (4 points) **= (14.10% - 4%) / (6 \* 14.05%\^2) = 85.27%** d. What will be the final weights of Stock A, Stock B and risk-free asset in your complete portfolio? (5 points) **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%** 17. Assume CAPM holds. You know that Portfolio A has an expected return of 8% and a beta of 0.6. Portfolio B has an expected return of 14% and a beta of 1.4. The risk free-rate is 3.5% a. Find the slope of the security market line (5 points) b. What is the beta of a portfolio with an expected return of 8.5%? (5 points) **Beta= (Expected return -- risk-free rate) / MRP = (8.5%-3.5%)/ 7.5%= 0.67** 18\. Given the information below, determine whether or not an arbitrage opportunity exists. (5 points) If so, please describe the arbitrage opportunity, including the positions (weights in each) you would take (5 points) and the return you would generate. (4points) Asset Expected Return Beta ------------- ----------------- ------ Portfolio A 14% 1.6 Portfolio B 2% -.2 Risk-free 4% \ [**0=** **w**~**A**~**β**~**A**~**+** **(1−** **w**~**A**~**)β**~**B**~]{.math.display}\ \ [**0=** **1.6w**~**A**~**+**  **−** **0.2(1−** **w**~**A**~**)**]{.math.display}\ \ [**0=** **1.6w**~**A**~**+**  **−** **0.2** **+** **0.2** **w**~**A**~**)**]{.math.display}\ \ [**0.2=** **1.8w**~**A**~]{.math.display}\ [**w**~**A**~**=** **0.11111**]{.math.inline} [**w**~**B**~ **=** **0.88889**]{.math.inline}