Business Statistical Question?

Question

An investor can choose to invest $100,000 between two different stock investments, a utility stock with an expected return of 5.6% and a standard deviation of returns of 3%, or a growth stock with an expected return of 9.5% and a standard deviation of returns of 9.9%. Returns of the two stocks have a correlation of zero.




What is the standard deviation of returns of an equally weighted portfolio of the two stocks?
Portfolio standard deviation?

Answer 1

Here are the formulas that you need:

Rp = WaRa+(1-Wa)Rb

where
Rp is the expected return of the portfolio
Ra is the expected return of Investment A
Rb is the expected return of Investment B
Wa is the percent of the portfolio invested in A
(1-Wa) is the percent of the portfolio invested in B

To get the standard deviarion (also called volatility), you have to remember that the Std Dev squared is equal to the Cariance. The relationship you need is:

Vp^2 = Wa^2*Va^2 + 2*Wa*(1-Wa)Cov(A,B) + (1-Wa)^2*Vb^2

Here
Vp = the volatility of the portfolio (std dev)
Va = the volatility of Security A (std dev)
Vb = the volatility of Security B (std dev)
Cov(A,B) is the covariance between the returns of asset A and asset B -- which is also equal to Va*Vb*Correlation. In your case, this is zero.

So -- the expected return is

Rp = 0.5*5.6% + 0.5*9.5

Variance = 0.5^2*0.03^2 + 0.5^2*0.099^2
Pp is the square root of this.

Answer 2

The answer is zero (0) I came along and took all his money.