Question

Assume you are considering a portfolio containing two​ assets, L and M. Asset L will represent 40 % of the dollar value of the​ portfolio, and asset M will account for the other 60 % . The projected returns over the next 6​ years, 2018 dash2023 ​, for each of these assets are summarized in the following​ table: LOADING... . a. Calculate the projected portfolio​ return, r overbar Subscript p ​, for each of the 6 years. b. Calculate the average expected portfolio​ return, r overbar Subscript p ​, over the​ 6-year period. c. Calculate the standard deviation of expected portfolio​ returns, s Subscript p ​, over the​ 6-year period. d. How would you characterize the correlation of returns of the two assets L and​ M? e. Discuss any benefits of diversification achieved through creation of the portfolio.

Year            Asset L               Asset M

2018            13%                     19%

2019            13%                     19%

2020            17% 15%

2021    17% 14%

2022    18% 13%

2023    18% 10%   

Answer 1

a) Expected Return of Portfolio :-

(i) in Year 2018 = 0.4*13%+0.6*19% =5.2%+11.4% =16.6%

(ii) in Year 2019 =0.4*13%+0.6*19% =5.2%+11.4% =16.6%

(iii) in Year 2020 =0.4*17%+0.6*15% =6.8%+9% =15.8%

(iv) in Year 2021 =0.4*17%+0.6*14% =6.8%+8.4% =15.2%

(v) in Year 2022 =0.4*18%+0.6*13% =7.2%+7.8% =15.0%

(vi) in Year 2023 =0.4*18%+0.6*10% =7.2%+6.0% =13.2%

b) Average Expected Portfolio Return :- sum of expected returns in all periods/number of periods

= (16.6+16.6++15.8+15.2+15+13.2)/5

=18.48%

c) To calcualte standard deviation of Portfolio we need to calculate variance and Co-varince of two portfolio:

Avg return of Asset L :- (13+13+17+17+18+18)/6

=96/6 =16%

Avg return of Asset M :- (19+19+15+14+13+10)/6

=96/5 =15%

Variance of Asset M=  sum of the squared differences between each return and avg return

={(0.19-0.15)²+(0.19-0.15)²+(0.15-0.15)²+(0.14-0.15)²+(0.13-0.15)²+(0.10-0.15)²}/6

=(0.0016+0.0016+0.000+0.0001+0.0004+0.0025)/6

=0.001033

Variance of Asset L=  sum of the squared differences between each return and avg return

=(0.0009+0.0009+0.0001+0.0001+0.0004+0.0004)/6

=0.0004667

Covariance = [(0.13-0.16)*(0.19-0.15)]+[(0.13-0.16)*(0.19-0.15)]+[(0.17-0.16)*(0.15-0.15)]+[(0.17-0.16)*(0.14- 0.15)]+[(0.18-0.16)*(0.13-0.15)]+[(0.18-0.16)*(0.10-0.15)]/(6-1)

=[(-0.03*0.04)+(-0.03*0.04)+(0.01*0)+(0.01*-0.01)+(0.02*-0.02)+(0.02*-0.05)]/5

=(-0.0012-0.0012-0.0001-0.0004-0.001)/5

=-0.00078

Variance of Portfolio =(Weight of Portfolio L)²*Variance of Portfolio L+(Weight of Portfolio M)²*Variance of portfolio M+2*Weight of L*Weight of M*Covariance

=(0.4)²  *0.0004667+(0.6)² * 0.001033 +2*0.4*0.6*-0.00078

=0.0000747+0.00037188-0.0003744

=0.00007218

Standard Deviation of Portfolio = Square root of variance

=0.008495

=0.85%

d) Co relation b/w portfolio = Covariance/varian of asset L* variance of asset M

=-0.00078/(0.001033*0.0004667)

We can see the corelation is negaive and that implies the two assets L & M move in opposite directions from each other.