Question

Risk and Return using EXCEL

Use the following data to explore the return-risk relation and the concept of beta for Apple stock, JPMorgan Chase & Co stock, and the S&P 500 market index:

Year | Apple Stock Price | JPMorgan Chase & Co Stock Price | S&P 500 Market Index Value

2017 | $149.04 | $93.85 | 2,425.17

2016 | $95.89 | $59.60 | 2,102.94

2015 | $124.50 | $68.25 | 2,076.79

2014 | $94.03 | $57.05 | 1,960.96

2013 | $60.93 | $56.49 | 1,606.28

2012 | $55.78 | $37.12 | 1,325.66

Part 1: Risk and Beta

A) Calculate the return each year for Apple, JPMorgan Chase & Co, and the S&P 500 market index using the following equation:

Value t - Value t-1

Return = -------------------------------------

Value t-1

In addition, use the Excel function to find the average for each corporation. (8 Points)

B) Calculate the standard deviation of returns for Apple, JPMorgan Chase & Co, and the S&P 500 market index using the Excel function. (8 Points)

C) Make a scatter plot of stock returns (y-axis) against market returns (x-axis) for both Apple and JPMorgan Chase & Co stock in one plot. Add a linear trendline to the scatter plot for each stock and include the equation on the chart. Identify the slope for each stock from the trendline equation. Label the y-axis, x-axis, legend, and chart title. (8 Points)

AAPL	JPM
Slope from Linear trendline	Slope from linear trendline

D) For each stock, use the Excel function to calculate the correlation between the stock returns and market returns. Furthermore, copy the standard deviations (from part B) and calculate the beta for each stock. (8 Points)

Standard Deviation stock

Beta = ---------------------------------------------- ( Correlation between stock and market )

Standard Deviation market

	Correlation	Stock Standard Deviation (decimal)	Market Standard Deviation (decimal)	Beta
AAPL
JPM

Part 2: Required Return

E) Assume a market risk premium of 5.40% and a risk free-free rate of 1.31%. Calculate the expected return on the market. Also calculate the required return for Apple and JPMorgan Chase & Co according to the CAPM. (8 Points)

F) If you formed a portfolio that consisted of 50% Apple stock and 50% JPMorgan Chase & Co stock, what would be its beta and its required return? (8 Points)

	Beta	Portfolio Weight
AAPL
JPM

Porfolio Beta
Portfolio Required Return

G) Suppose an investor wants to include Apple stock in their portfolio. Stocks A, B, and C are currently in the portfolio, and their betas are 0.68, 0.98, and 1.43, respectively. Calculate the new portfolio's beta and required return if it consists of 25% of Apple, 15% of Stock A, 40% of Stock B, and 20% of Stock C. (8 Points)

	Beta	Portfolio Weight
Apple
Stock A
Stock B
Stock C

Portfolio Beta

Risk-free Rate	Market Risk Premium	Portfolio Beta	Required Return on Portfolio

Answer 1

Part 1 - Risk and Beta

a)

Years	Apple	JPM	S&P	Returns - Apple	Returns - JPM	Market Returns (S&P)
2017	149.04	93.85	2425.17	0.554280947	0.57466443	0.153228337
2016	95.89	59.6	2102.94	-0.229799197	-0.126739927	0.012591548
2015	124.5	68.25	2076.79	0.324045517	0.196319018	0.089057977
2014	94.03	57.05	1906.96	0.543246348	0.009913259	0.187190278
2013	60.93	56.49	1606.28	0.092326999	0.521821121	0.211683237
2012	55.78	37.12	1325.66
	Average Return			0.256820123	0.23519558	0.130750275

b) Standard Deviation

Apple	JPM	S&P
0.331247	0.308486	0.080530451

d) use Correl function to calculate correlation between stock and market (values required for array 1 and array 2 which would be market returns)

	Correlation	Stock Standard Deviation (decimal)	Market Standard Deviation (decimal)	Beta
AAPL	0.602003	0.331247	0.080530451	2.47622713
JPM	0.62896	0.308486	0.080530451	2.40934146

Part 2 - Required Return

e)

CAPM - Risk free rate + Beta *(Market return - Risk free return)

Apple - 1.31 + 2.48*(5.40) - 14.70

JPM - 1.31 + 2.41*(5.40) - 14.324

Expected return on market - 6.71 (1.31 + 1*5.40) beta will always be one for the market.

f)

Portfolio Beta - 2.445 (weighted average of the beta of individual stocks) - 0.50*2.48+0.5*2.41

Portfolio Expected Return - 14.512 (weighted average of the expected returns of the stocks calculated in previous step) - 0.5*14.7+0.5*14.324

g) Portfolio beta - 1.4 (0.25*2.48+0.15*0.68+0.40*0.98+0.25*1.43)

assuming risk free rate - 1.31 equity risk premium - 5.4

required portfolio returns - 1.31 + 1.4* 5.4 = 8.87