Question

Now you have $1,000,000 to invest. If you invest $195,000 in stock A (beta is 0.32), and invest $340,000 in stock B (beta is 0.8). Then you invest $135,000 in risk-free asset and invest the rest money in stock C. What’s the beta of stock C? You can regard investment value as expected value here.

Answer 1

Concept - Investment value and expected value will remain same only when the investment moves in the same direction and in same value as market moves.

               This is the case when portfolio beta is equal to 1.

Calculation

Investment in Asset C = 1,000,000 - 195,000 - 340,000 - 135,000

                                 = 330,000

Portfolio Beta = 1

=> [195,000/1,000,000]*0.32 + [340,000/1,000,000]*0.80 + [135,000/1,000,000]*0 + [330,000/1,000,000]* Beta C = 1

=> 0.0624 + 0.272 + 0 + 0.33 * Beta C = 1

=> Beta C = [ 1 - 0.0624 - 0.272 ] / 0.33

=> Beta C = 2.02 Answer

Hope you understand the solution.