Question

Suppose Johnson​ & Johnson and Walgreen Boots Alliance have expected returns and volatilities shown​ here the table below ​,with a correlation of 20%.Calculate the expected return and the volatility​ (standard deviation) of a portfolio consisting of Johnson​ & Johnson's and​ Walgreens' stocks using a wide range of portfolio weights. Plot the expected portfolio return as a function of the portfolio volatility. Using your​ graph, identify the range of Johnson​ & Johnson's portfolio weights that yield efficient combinations of the two stocks.

Expected Return		Standard Deviation
Johnson​ & Johnson	9​%		18​%
Walgreens Boots Alliance	10​%		21%

Find the expected return and volatility of the portfolio consisting of 50​% of Johnson​ & Johnson's stock and 50 ​% of​ Walgreens' stock.

The expected return of the portfolio is ………….​%. (Round to one decimal​ place.)

The volatility​ (standard deviation) of the portfolio is …………​%. (Round to one decimal​ place.)

Find the expected return and volatility of the portfolio consisting of 60% of Johnson​ & Johnson's stock and 40​% of​Walgreens' stock.

The expected return of the portfolio is ………….​%. (Round to one decimal​ place.)

The volatility​ (standard deviation) of the portfolio is ………​%. (Round to one decimal​ place.)

Find the expected return and volatility of the portfolio consisting of 70​% of Johnson​ & Johnson's stock and 30​% of​Walgreens' stock.

The expected return of the portfolio is ……..​%. (Round to one decimal​ place.)

The volatility​ (standard deviation) of the portfolio is ………..​%. (Round to one decimal​ place.)

Plot the expected portfolio return as a function of the portfolio volatility.

Answer 1

Portfolio return = Wa x Ra + Wb x Rb

where Wa & Wb are weights of the assets A & B in the portfolio

& Ra & Rb are rate of returns on A & B

The Standard deviation of two asset portfolio is given by

σp = (wa^2 x σa^2 + wb^2 x σb^2 + 2 x wa x wb x Cova,b)^(1/2)

where,

wa & wb are weights of the assets A & B in the portfolio

σa & σb are standard deviation of A & B respectively

Covab is the covariance between A & B

Covariance = Coefficient x SD of A x SD of B

Here

1. 50% JJ & 50% Walgreens

Covariance = 20% x 18% X 21% = 0.0076

Portfolio return(50%,JJ)  = 50% x 9% + 50% x 10% =9.50%

The Standard deviation of two asset portfolio (J&J = 50%) is given by

σp = (50%^2 x 18%^2 + 50%^2 x 21%^2 + 2 x 50% x 50% x 0.0076)^(1/2)

= 0.389

= 38.90%

2. 60% JJ & 40% Walgreens

Covariance = 20% x 18% X 21% = 0.0076

Portfolio return(60%,JJ)  = 60% x 9% + 40% x 10% = 9.40%

The Standard deviation of two asset portfolio (J&J = 60%) is given by

σp = (60%^2 x 18%^2 + 40%^2 x 21%^2 + 2 x 60% x 40% x 0.0076)^(1/2)

= 0.1495

= 14.95%

3.

70% JJ & 30% Walgreens

Covariance = 20% x 18% X 21% = 0.0076

Portfolio return(60%,JJ)  = 70% x 9% + 30% x 10% = 9.30%

The Standard deviation of two asset portfolio (J&J = 60%) is given by

σp = (70%^2 x 18%^2 + 30%^2 x 21%^2 + 2 x 70% x 30% x 0.0076)^(1/2)

= 0.1517

= 15.17%

	Weight of Johnson & Johnson	Weight 0f Wallgreens	Portfolio SD	Portfolio Return
JJ0%	0%	100.00%	21.00%	10.00%
JJ10%	10.0%	90.00%	19.34%	9.90%
JJ20%	20.0%	80.00%	17.87%	9.80%
JJ30%	30.0%	70.00%	16.64%	9.70%
JJ40%	40.0%	60.00%	15.71%	9.60%
JJ50%	50.0%	50.00%	15.13%	9.50%
JJ60%	60.0%	40.00%	14.95%	9.40%
JJ70%	70.0%	30.00%	15.17%	9.30%
JJ80%	80.0%	20.00%	15.79%	9.20%
JJ90%	90.0%	10.00%	16.75%	9.10%
JJ100%	100.0%	0.00%	18.00%	9.00%

tHE GRAPH IS AS BELOW

As is evident from the graph & table above, the minimum variance porrtfolio is at 14.95%