Question

The following table contains annual returns for the stocks of ABC Corp. (ABC​) and Company B (B​). The returns are calculated using​ end-of-year prices​ (adjusted for dividends and stock​ splits). Use the information for ABC Corp. ​(ABC​) and Company B ​(B) to create an Excel spreadsheet that calculates the average returns over the​ 10-year period for portfolios comprised of ABC and B using the​ following, respective,​ weightings: (1.0,​ 0.0), (0.9,​ 0.1), (0.8,​ 0.2), (0.7,​ 0.3), (0.6,​ 0.4), (0.5,​ 0.5), (0.4,​ 0.6), (0.3,​ 0.7), (0.2,​ 0.8), (0.1,​ 0.9), and​ (0.0, 1.0). The average annual returns over the​ 10-year period for ABC and B are 15.03% and 12.78​% respectively.​ Also, calculate the portfolio standard deviation over the​ 10-year period associated with each portfolio composition. The standard deviation over the​ 10-year period for ABC Corp. and Company B and their correlation coefficient are 25.87%, 22.95​%, and 0.84123 respectively.

​(Hint: Review Table​ 5.2.) 

Year   ABC Corp.   Company B
2005   -5.3   17.2
2006   1.1   -8.1
2007   -32.7   -26.7
2008   -10.3   -3.4
2009   30.9   10.7
2010   24.9   9.9
2011   22.7   5.2
2012   52.1   42.3
2013   37.8   41.5
2014   29.1   39.2

Answer 1

Solution:

For two asset portofolio if

• r1 = the return of the ABC Company
• r2 = the return of Company B
• w1 = the portfolio weight of the ABC Company
• w2 = the portfolio weight of the Company B
• σ1= the standard deviation of ABC Companyt
• σ2 = the standard deviation of Company B
• p(1,2) = is the correlation coefficient between the Company ABC and Company

Then the portfolio standard deviation =

The porfolio return rp = w1 * r1 + w2 * r2

In the following table, i have computed the Average return using the Excel functions of AVERAGE and STDEV.S and also using the above formula.

As you can see both the answers match. Last column shows the formauls used.

-x-