Question

Use the following information to calculate the expected return and standard deviation of a portfolio that is 50 percent invested in 3 Doors, Inc., and 50 percent invested in Down Co.: (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

		3 Doors, Inc.			Down Co.
Expected return, E(R)		14	%		10	%
Standard deviation, σ		42			31
Correlation				0.10

Answer 1

Solution:

Calculation of Expected Return of a portfolio:

The formula for calculation of Expected Return of a portfolio is

ER = ( R_A * W_A )+ ( R_B * W_B )

Where

E(R_P) = Expected return on a portfolio

R_A = Return of 3 Doors Inc.    W_A = Weight of Investment in 3 Doors Inc.

R_B = Return of Down Inc.    W_B = Weight of Investment in Down Inc.

As per the information given in the question we have

R_A = 14 %   ; W_A = 50 % = 0.5    ;   R_B = 10 %    ;    W_B = 50 % = 0.5

Applying the values in the formula we have

= ( 14 % * 0.5 ) + ( 10 % * 0.5 )

= 7 % + 5 % = 12 %

Thus the expected return of the Portfolio = 12.00 %

Calculation of Standard Deviation of a portfolio:

The formula for calculation of Standard Deviation of a portfolio is

σ_P =[ ( σ_A² * W_A² ) + ( σ_B² * W_B² ) + 2 * (σ_A² * W_A² * σ_B² * W_B² * ρ _AB ) ] ^{( 1 / 2 )}

Where

σ_A = Standard Deviation of 3 Doors Inc.    ;     W_A = Weight of investment in 3 Doors Inc.

σ_B = Standard Deviation of Down Co.   ;     W_B = Weight of investment in Down Co.

ρ _{AB =} Correlation between two stocks i.e., 3 Doors Inc. and Down Co.

As per the Information given we have:

σ_A    = 42 %    ;    W_A   = 50 % = 0.50         ;     σ_B = 31 %   ;       W_B = 50 % = 0.50 ;     ρ _AB = 0.10

Applying the above values in the formula we have:

= [ (( 42 )² * (0.50)² ) + (( 31 )² * (0.50)² ) + ( 2 * 42 * 0.50 * 31 * 0.50 * 0.10 ) ] ^{(1 / 2 )}

= [ ( 1764 * 0.25) + ( 961 * 0.25 ) + 65.10 ] ^{(1 / 2 )}

= ( 441 + 240.25 + 65.10 ) ^{(1 / 2 )}

= ( 746.35 ) ^{(1 / 2 )}

= 27.3194

Thus the Standard Deviation of the portfolio is = 27.3194 %

=27.32 % ( when rounded off to two decimal places )