Question

Assume a portfolio is worth $70,000, consisting of X, Y, and cash. Also assume you invested $35,000 in X, $14,000 in Y and the rest in cash, and that X and Y have betas of 1.45 and 0.80 respectively. Calculate the portfolio beta. (Provide numerical answer to 3 decimal places.)

Answer 1

0.885

Step-by-step explanation:

Beta measures systemic risk. The higher beta is, the higher the systemic risk and the higher the compensation demanded for by investors

The portfolio's beta can be determined by adding together the weighted beta of each stock in the portfolio

weighed beta of a stock = percentage of the stock in the portfolio x beta of the stock

Percentage of x = $35,000 / 70,000 = 0.5 = 50%

Percentage of y = $14,000 / 70,000 = 0.2 = 20%

Percentage of cash = 100 - (50 + 20) = 30%

Cash usually have a beta of zero

portfolio beta = (0.5 x 1.45) + (0.2 x 0.8) + (0.3 x 0) =

0.725 + 0.16 + 0 = 0.885

0.725

0.16