The expected return and standard deviation of a portfolio that is 70 percent inv

Question

The expected return and standard deviation of a portfolio that is 70 percent invested in 3 Doors, Inc., and 30 percent invested in Down Co. are the following:

What is the standard deviation if the correlation is +1? 0? ?1? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

The expected return and standard deviation of a portfolio that is 70 percent invested in 3 Doors, Inc., and 30 percent invested in Down Co. are the following:

Explanation / Answer

Let Doors Inc be X and Down Co be Y
Correlation can be given by the following formula:
=[Covariance (X,Y)] / [(Standard deviation of X) * (Standard deviation of Y)]
Standard deviation of :
X= 50% and Y= 39%
Thus, if Correlation is:
1) +1, hence Covariance (X,Y) = Correlation * (Standard deviation of X) * (Standard deviation of Y)
= +1 * 50 * 39= 1950
2) 0, hence Covariance (X,Y) = Correlation * (Standard deviation of X) * (Standard deviation of Y)
= 0 * 50 * 39 = 0
3) -1, hence Covariance (X,Y) = Correlation * (Standard deviation of X) * (Standard deviation of Y)
= -1 * 50 * 39= -1950

In the said portfolio:
Weight of X= 70%= 0.70
Weight of Y= 30%= 0.30

Standard deviation of the portfolio can be given by the following formula:
{Square root of [(Square of weight of X * Square of Standard Deviation of X) + (Square of weight of Y * Square of Standard Deviation of Y) + (2 * Weight of X * Weight of Y * Covariance (X,Y)]}

1) If correlation is +1
Standard Deviation of the Portfolio= {Square root of [(0.70*0.70*50*50) + (0.30*0.30*39*39) + (2*0.70*0.30*1950)]}
= Square root of 2180.89 = 46.7

2) If correlation is 0
Standard Deviation of the Portfolio= {Square root of [(0.70*0.70*50*50) + (0.30*0.30*39*39) + (2*0.70*0.30*0)]}
= Square root of 1361.89 = 36.90

3) If correlation is -1
Standard Deviation of the Portfolio= {Square root of [(0.70*0.70*50*50) + (0.30*0.30*39*39) + (2*0.70*0.30*-1950)]}
= Square root of 542.89 = 23.3

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