Question

The following​ table, contains annual returns for the stocks of ABC Corp. ​(ABC ​) and XYZ Corp. ​(XYZ ​). The returns are calculated using​ end-of-year prices​ (adjusted for dividends and stock​ splits). Use the information for ABC Corp. ​(ABC ​) and XYZ Corp. ​(XYZ ​) to create an Excel spreadsheet that calculates the average returns over the​ 10-year period for portfolios comprised of ABC and XYZ using the​ following, respective,​ weightings: (1.0,​ 0.0), (0.9,​ 0.1). The average annual returns over the​ 10-year period for ABC and XYZ are 15.33 ​% and 13.04 ​% 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 XYZ Corp. and their correlation coefficient are 25.33 ​%, 23.42 ​%, and 0.84285 respectively. ​(Hint​: Review Table​ 5.2.) Enter the average return and standard deviation for a portfolio with​ 100% ABC Corp. and​ 0% XYZ Corp. in the table below.

Year   ABC Returns   XYZ Returns
2005   -3.5%   17.3%
2006   1.9%   -8.1%
2007   -31.6%   -26.7%
2008   -10.3%   -3.2%
2009   30.2%   9.9%
2010   26.5%   10.1%
2011   22.8%   4.8%
2012   52.4%   43.8%
2013   35.6%   42.3%
2014   29.3%   40.2%

Enter the average return and standard deviation for a portfolio with​ 100% ABC Corp. and​ 0% XYZ Corp. in the table below.  ​(Round to two decimal​ places.)
Enter the average return and standard deviation for a portfolio with​ 90% ABC Corp. and​ 10% XYZ Corp. in the table below.  ​(Round to two decimal​ places.)

Answer 1

Expected return of two-asset portfolio R_p = w₁R₁ + w₂R_2,

where R_p = expected return

w₁ = weight of Asset 1

R₁ = expected return of Asset 1 = average annual return

w₂ = weight of Asset 2

R₂ = expected return of Asset 2 = average annual return

For example, with 10% ABC and 90% XYZ,

w₁ = 0.10 and w₂ = 0.90

R₁ = 0.1533 and R₂ = 0.1304

R_p = (0.10 * 0.1533) + (0.90* 0.1304), which is 0.1327, or 13.27%

Expected variance for a two-asset portfolio σ_p² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov_1,2

where σ_p² = variance of the portfolio

w₁ = weight of Asset 1

w₂ = weight of Asset 2

σ₁² = variance of Asset 1

σ₂² = variance of Asset 2

Cov_1,2 = covariance of returns between Asset 1 and Asset 2

Cov_1,2 = ρ_1,2 * σ₁ * σ_2, where ρ_1,2 = correlation of returns between Asset 1 and Asset 2

In this case, Cov_1,2 = 0.84285 * 0.2533 * 0.2342 = 0.05

σ_p² = (0.10)²(0.2533)² + (0.90)²(0.2342)² + (2)(0.10)(0.90)(0.5), which is 0.05485

σ_p = square root of (0.05485), which is 0.2342, or 23.42%

In this way, we calculate the expected return and standard deviation for each portfolio