Given : Investment in stock A = $50,000
Beta of stock A = 0.4
Investment in stock B = $60,000
Beta of stock B = 1.1
To Find: Portfolio Beta
Solution: Beta of a security may be defined as degree of responsiveness of security return with respect to the market return. Beta of a portfolio is the weighted average beta of the securities comprising such a portfolio.
Total investment in portfolio = $50,000 + $60,000 = $110,000
Weightage of security A in portfolio, i.e [tex]W_{1}[/tex] = [tex]\frac{50,000}{110,000}[/tex] = 0.4545
Weightage of security B in the portfolio, i.e [tex]W_{2}[/tex] = [tex]\frac{60,000}{110,000}[/tex] = 0.5455
Beta of porfolio = Beta of A × [tex]W_{1}[/tex] + Beta of B × [tex]W_{2}[/tex]
= 0.4 × 0.4545 + 1.1 × 0.5455
= 0.7818
Hence, the portfolio beta is 0.78 approx.
