Question

You are contemplating investments in the stock of Clorox and in the S&P 500 index (a collection of stocks approximately representing the overall market). The Clorox required return (calculated using the capital asset pricing model or CAPM) is 18%, the Clorox beta is .95, and its bonds are rated A. The standard deviation of returns for Clorox stock is 14%. Its payout ratio is 65% and its sales are expected to grow by 7% during the next year. The S&P 500 has a standard deviation of 15%. The A-rated bond yield is 5.1% and the expected return of risk-free securities is 8%. Calculate the standard deviation of a portfolio consisting of 40% invested in Clorox stock and 60% invested in the S&P 500.

Answer 1

To calculate standard deviation of Portfolio consisting Clorox stock and S&P 500 (Market) we need following information -

Weight of Clorox stock in Portfolio = 40%

Weight of Market in Portfolio = 60%

Standard deviation of Clorox = 14%

Standard deviation of Market = 15%

Covariance(Market,Clorox) = ?

Thus, we need to find Covariance (market,clorox) first. We can find Covariance of Market and Clorox through Clorox Beta.

The equation for Beta is given below -

Where,

M = Market

C = Clorox

= Standard deviation of market

Beta of Clorox = 0.95

Putting the values in Beta equation to calculate Covariance -

Now, we have all information required to calculate Standard Deviation of Portfolio. We can following equation to calculate the standard deviation of portfolio -

Where,

Wm = weight of market

Wc = weight of clorox

= Standard deviation of market

= Standard deviation of Clorox

Cov(M,C) = Covariance (M,C)

Putting the values-

Standard Deviation of Portfolio (M,C) = 14.66%

Hope this will help, please do comment if you need any further explanation. Your feedback would be appreciated.