Question

Anna is a Vice President at the J Corporation. The company is considering
investing in a new factory and Anna must decide whether it is a feasible
project. In order to assess the viability of the project, Anna must first calculate
the rate of return that equity holders expect from the company stock. The
annual returns for J Corp. and for a market index are given below. Currently,
the risk-free rate of return is				1.2%	and the market risk-premium is				3.1%	.
a) What is the beta of J Corp.'s stock?										Enter Answer
(1 Mark)(Round your answer to two decimal places)
b) Using the CAPM model, what is  the expected rate of return on J Corp. stock for the coming year?										Enter Answer
(Round your answer to one one-hundreth of a percent)										↑
Year	J Corp. Return (%)	Market Return (%)								Enter your Final Answer Here
1	-12.38	-6.10
2	17.44	8.81
3	24.14	12.16
4	28.14	14.16
5	-32.98	-16.40
6	31.46	15.82
7	9.26	4.72
8	25.94	13.06
9	18.02	9.10
10	19.44	9.81
11	-10.96	-5.39
12	-16.98	-8.40

Answer 1

Beta coefficient is a measure of volatility of a stock in comparison with the market. It measures how the stock price will move in comparison to the market. If beta is equal to 1, it means stock price will move parallel to the changes in the market. Beta less than 1 means stock price is less volatile in comparison to the market. Means a slight fluctuation in market will result in greater movement in the stock price. Similarly, a beta less than 1 means stock is less volatile in comparison to the market fluctuations. This means that even a bigger fluctuation in market will result in only a slight change in the stock price.

The calculation for beta of the stock is done as in the picture below:

Hence, value of beta is 0.5.​​​​​​

Now, using the Capital Asset Pricing Model(CAPM), we will calculate the expected rate of return on the stock.

As per CAPM, e(r) = r_{​​​​​​f}​​​ + β(r_{​​​​​​m} - r_f)

β is the beta of the stock.

r_{​​​​​​m} is the expected return on the market.

r_{​​​​​​f} is the risk free rate.

e(r) is the expected return on the stock

(r_{​​​​​m} - r_{​​​​​​f} ​​​​​​) is the market risk premium

Here, risk free rate is 1.2% and market risk premium is 3.1%

Also, beta of the stock is 0.5 as per above calculations.

So, e(r) = 1.2% + 0.5(3.1%)

= 0.0275 = 2.75%