# Risk and Return

The management of Ark Industries wants to analyze the performance of the company’s stock in the stock market. They want to compare the stock performance with Apex Inc, a strong competitor in the industry, and the market index. The following data is available for managerial finance analysis.

 Ark Industries Apex Incorporated Market Index Year Capital gain/loss Dividend Purchased Price Capital gain/loss Dividend Purchased price Rate of Return 2020 \$6.79 \$2.23 \$23.53 \$5.80 \$3.52 \$79.32 51.8% 2019 -\$5.08 \$2.65 \$28.61 \$5.00 \$3.65 \$74.32 1.30% 2018 \$13.40 \$2.73 \$15.21 -\$12.80 \$3.45 \$87.12 11.90% 2017 \$2.58 \$2.57 \$12.63 -\$8.00 \$3.47 \$95.12 13.90% 2016 -\$0.58 \$2.23 \$13.21 \$10.88 \$3.55 \$84.25 15.80%

*Capital gain = difference between ending price and beginning price

1. Use the data given to calculate the annual returns for Ark Industries, and Apex Inc during the 5-year period.
2. Calculate the historical average returns for Ark Industries, Apex Inc., and the market index during the 5-year period.
3. Calculate the standard deviation of the returns for Ark Industries.
4. Ark Industries Inc. wants to estimate its beta. The following information is available:
 Risk-free rate 5.0% Market rate of return 10.0% Expected rate of return 12.0%
1. Calculate the beta for Ark Industries.
2. If Ark Industries’ beta were 2.0, then what would be its new required rate of return?
3. 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?
4. 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.

1. 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 Portfolio weight Expected 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%

1. Calculate the portfolio beta.
2. Calculate the portfolio’s required rate of return.
1. Efficient Markets Hypothesis (EMH) holds that security prices adjust quickly to new intrinsic value as soon as new information becomes available. Distinguish among the threeforms of the EMH.
2. 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
3.    herding
1. 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%.

1. using the model, predict the stock’s return for the month of May 1.
2. if the actual return of the stock is 17.5% on May 1, calculate the unexplained return of the stock.