Question

You are planning to make some investment during the down market like we have now. You are not confident about the overall stock market, so you decide to hold 80% of your wealth as cash and only invest 20% of your wealth in an individual stock that you have strong faith in. The stock's beta is 1.4000000000000001 and its standard deviation is 3.6%. What is the beta of your entire wealth?

what is the standard deviation of your entire wealth? (What %)

Answer 1

1. Beta of Cash is zero. market movements have theoritically no effect on Cash

Beta of his stock = 1.4000000000000001

Beta of portfolio = Wa X Betaa + Wb x Betab

where Wa & Wb are weights of a & b in portfolio

Betaa & Betab are beta of a & b respectively

Beta of portfolio with 80% cash & 20% in the stock

= 80% x 0 + 20% x 1.4000000000000001

=  0.28000000000000002

2. Standard deviation of portfolio

= (Wa^2 x σa^2 + Wb^2 x σb^2 + 2 Wa x Wb X Covab) ^(1/2)

The standard deviation of cash =0 and covariance of Cash with any stock = 0

Standard devbiation of portfolio with 80% cash & 20% in stciok which has 3.6% standard deviation

= (80%^2 x 0^2 + 20%^2 x 3.60%^2 + 2 x 80% x 20% X 0)^(1/2)

= (0 + 20%^2 x 3.60%^2 + 0)^0.5

= (20% x 3.60%) ^ (2 x 0.5)

= 20% x 3.60%

= 0.72%