# Portfolio Return and Standard Deviation in Stocks

Jane is considering investing in three different stocks or creating three distinct two-stock portfolios. Jane considers herself to be a rather conversative investor. She is able to obtain forecasted returns for the three securities for the years 2010 through 2016.

Year Stock A Stock B Stock C

2010 10% 10% 12%

2011 13 11 14

2012 15 8 10

2013 14 12 11

2014 16 10 9

2015 14 15 9

2016 12 15 10

In any of the possible two-stock portfolios, the weight of each stock in the portfolio will be 50%. The three possible portfolio combinations are AB, AC, and BC.

Answer the following.

a. Calculate the expected return for each individual stock.

b. Calculate the standard deviation for each individual stock.

c. Calculate the expected returns for portfolio AB, AC, and BC.

d. Calculate the standard deviations for portfolio AB, AC, and BC.

e. Would you recommend that Jane invest in the single stock A or the portfolios consisting of stock A and B? Explain your answer from a risk-return viewpoint.

f. Would you recommend that Jane invest in the single stock B or the portfolio consisting of stocks B and C? Explain your answer from a risk-return viewpoint.

#### Solution Preview

The answers are in the attached Excel file.

Jane is considering investing in three different stocks or creating three distinct two-stock portfolios. Jane considers herself to be a rather conversative investor. She is able to obtain forecasted returns for the three securities for the years 2010 through 2016.

Year Stock A Stock B Stock C

2010 10% 10% 12% 13.43% 11.57% 10.71%

2011 13% 11% 14% 1.99% 2.64% 1.80%

2012 15% 8% 10% 0.1480 0.2279 0.1680

2013 14% 12% 11%

2014 16% 10% 9%

2015 14% 15% 9%

2016 12% 15% 10%

In any of the possible two-stock portfolios, the weight of each stock in the portfolio will be 50%. The three possible portfolio combinations are AB, AC, and BC.

Answer the following.

a. Calculate the expected return for each individual stock.

b. Calculate the standard deviation for each individual stock.

We calculate Mean (Expected) return, standard deviation of return and coefficient of variation for each of the three stocks

Stock A

Year X= X 2 =

2010 10.00% 0.01

2011 13.00% 0.0169

2012 15.00% 0.0225

2013 14.00% 0.0196

2014 16.00% 0.0256

2015 14.00% 0.0196

2016 12.00% 0.0144

Total= 94.00% 0.1286

n=no of observations= 7

Mean return= 13.43% =94.%/7 13.43%

variance={summation of X 2 - n(Mean) 2 }/(n-1)= 0.000391 =(0.1286-7*0.1343^2)/(7-1)

standard deviation of return (SD)=square root of Variance= 1.98% =square root of 0.000391 1.99%

Coefficient of variation = SD/Mean= 0.1474 =1.98% / 13.43% 0.1480

Stock B

Year X= X 2 =

2010 10.00% 0.01

2011 11.00% 0.0121

2012 8.00% 0.0064

2013 12.00% 0.0144

2014 10.00% 0.01

...

#### Solution Summary

Calculates expected return and standard deviation for individual stocks and two-stock portfolios.