Problem Set 6 (1)

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1 Problem Set 6 NAME: Shardul Mullur Managerial Finance (BADM-534-M20) - Full Term Due date- 2-18-2024

2 1. Use the data given to calculate the annual returns for Ark Industries, and Apex Inc during the 5-year period. The annual returns for Ark Industries and Apex Inc are as follows:  Ark Industries:  2020: 38.33%  2019: -8.49%  2018: 106.05%  2017: 40.78%  2016: 12.49%  Apex Inc:  2020: 11.75%  2019: 11.64%  2018: -10.73%  2017: -4.76%  2016: 17.13% These figures represent the annual returns over the specified years for each respective company. 2. Calculate the historical average returns for Ark Industries, Apex Inc., and the market index during the 5-year period. The historical average returns for Ark Industries and Apex Inc. over the past five years, compared to the market index, are as follows:  Ark Industries: 37.83%  Apex Inc.: 5%  Market index: 18.94%

3 These values represent the average returns calculated by summing the yearly returns over the five-year period and dividing by the total number of years. The market index provides a benchmark for comparison against the performance of Ark Industries and Apex Inc. 3. Calculate the standard deviation of the returns for Ark Industries. The standard deviation of Ark Industries' returns is 43.16%. This metric measures the dispersion of Ark Industries' annual returns around their mean value, providing insight into the volatility or variability of the company's performance over the specified time period. 4. An individual investor, James Bond needs an extra return of 6.0% before he will take on the stock market's risk to invest in Ark Industries. If the risk-free rate on long-term Treasury bonds is 5.0%. what would be the required return on the market? The required market return = 11%. 5.James Bond wants to determine the required rate of return on two stocks (stock A and stock B) that he just added to his portfolio. The following information is available: Market rate of return = 11.0% Risk free rate =5.0% Beta for stock A= 0.77 Beta for stock B = 0.99 Use the Security Market Line (SML) equation to calculate the required rate of return for stock A and stock B. The Return on Investment (ROI) for Stock A is as follows:  2019: 9.62%  2020: 10.94% The Net Capital Gain of Ark Industries is detailed below:  2020: $6.79 million - $5.80 million = $0.99 million  2019: -$5.80 million + $5.00 million = -$0.80 million

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4  2018: $13.40 million - $12.80 million = $0.60 million  2017: $2.58 million - $8.00 million = -$5.42 million  2016: -$0.58 million + $10.88 million = $10.3 million These figures represent the financial gains or losses for Ark Industries over the specified years. 7. Richard Morgan, another individual investor wants to purchase four stocks for his portfolio. The expected return, portfolio weights, and the betas of the stocks are given below: Stocks Beta Portfoli o weight Expecte d return Goodman Industries 0.7 30% 9.20% Renfro Inc. 0.79 20% 9.74% Heath Inc. 1.1 30% 11.60% Lincoln Inc. 1.44 20% 13.64% i. Calculate the portfolio beta. Portfolio beta = 1. ii. Calculate the portfolio’s required rate of return. Portfolio's expected return = 10.92%. The estimated value per share of Goodman Industries stock is $107.14. This valuation is calculated based on the expected dividend payment of $4.50 per share at the end of the year (D1 = $4.50), with a growth rate of 5% per year and a required rate of return (rs) of 9.2%.

5 1. #8 Three forms of Efficient market Hypothesis are: 1. Weak-form efficiency: Weak- form efficiency asserts that the current market price already integrates all information from past price movements, indicating that recent trends in stock prices provide no advantage when making investment decisions. 2. Semi-strong-form efficiency contends that current market prices embody all publicly available information, rendering annual reports and other published data irrelevant for investment decisions, as stock prices would have already adjusted accordingly. 3. Strong-form efficiency posits that current market prices incorporate all relevant information, whether publicly available or privately held. This suggests that even insiders would be unable to consistently generate returns on a stock, as all pertinent information is already reflected in the stock price. 9. A new body of evidence is emerging in the field of behavioral finance which shows that investors often behave irrationally, but in predictable ways. Explain the following biases that affect the rationality of people’s decision-making process: 1. Overconfidence : This bias refers to the tendency of individuals to overestimate their own abilities, knowledge, or judgment. In investment contexts, overconfident investors may believe they have superior skills in predicting market movements or selecting winning stocks. As a result, they may trade more frequently, take on excessive risks, or disregard advice from others. Overconfidence can lead to suboptimal investment decisions, increased trading costs, and lower returns. 2. Self-attribution Bias : This bias occurs when individuals attribute their successes to their own abilities or skill while attributing failures to external factors beyond their control, such as luck or market conditions. In the context of investing, investors affected by self-attribution bias may take credit for successful investment decisions but blame external factors for losses. This bias can lead to an inflated sense of

6 confidence, overestimation of one's investment abilities, and reluctance to learn from mistakes, potentially resulting in repeated poor investment choices. 3. Herding : Herding bias refers to the tendency of individuals to follow the actions or decisions of the crowd, even if those actions may not be rational or well-informed. In investment markets, herding behavior often manifests when investors mimic the trading activities of others, particularly during times of uncertainty or market volatility. This behavior can amplify market movements, lead to asset bubbles or crashes, and result in inefficient market outcomes. Herding can also prevent investors from critically evaluating information or making independent decisions, as they may fear missing out on potential gains or avoiding losses. 10. The Fama-French three-factor model predicts stock’s return given the return of the market, the SMB portfolio, and the HML portfolio. The model is given as: Predicted return = ai + bi (r M,t) + ci (r SMB,t) + di (r HML,t). You have estimated that ai = 0, bi = 1.2, ci = -0.4, and di =1.3. On May 1, the market return (rM,t), was 10%, the return on the SMB portfolio (rSMB) was 3.2%, and the return on the HML portfolio (rHML) was 4.8%. i. using the model, predict the stock’s return for the month of May 1. ii. if the actual return of the stock is 17.5% on May 1, calculate the unexplained return of the stock. (i) By utilizing the provided equation, we can compute the predicted return as follows: Predicted return = 0 + 1.2 * 0.10 - 0.4 * 0.032 + 1.3 * 0.048 = 0.12 - 0.0128 + 0.0624 = 0.1696 or 16.96% (ii) If the actual return is 17.5%, then the unexplained return is calculated as:

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7 Unexplained return = Actual return - Predicted return = 17.5% - 16.96% = 0.54% References: Ehrhardt, M. C., & Brigham, E. F. (2023). Corporate Finance. ISBN: 9780357714638. Published on March 15, 2023.