What is the beta of a portfolio consisting of multiple stocks?
What is the beta of a portfolio which consists of the following stocks: Security $ invested beta A $2,000 1.38 B $5,000 0.47 C $9,000 1.70 D $4,000 1.08?
The beta of a portfolio consisting of the stocks is 1.2365. Beta is a measure of the systematic risk of a stock. A well-diversified portfolio had a mix of high-beta and low-beta stocks. High-beta stocks ensure that returns are maximized when markets move higher and low-beta stocks ensure that capital is preserved when market trends lower. As a first step, we need to calculate the weight of each stock in the portfolio. Weight of Stock A = 2000 / ( 2000 + 5000 + 9000 + 4000 ) = 0.1 Weight of Stock B = 5000 / ( 2000 + 5000 + 9000 + 4000 ) = 0.25 Weight of Stock C = 9000 / ( 2000 + 5000 + 9000 + 4000 ) = 0.45 Weight of Stock D = 4000 / ( 2000 + 5000 + 9000 + 4000 ) = 0.2 Once we have the weight of the stocks, the portfolio beta can be calculated as follows - Portfolio Beta = ( Weight of Stock A * Beta of A ) + ( Weight of Stock B * Beta of B ) + ( Weight of Stock C * Beta of C ) + ( Weight of Stock D * Beta of D ) Portfolio Beta = ( 0.1 * 1.38 ) + ( 0.25 * 0.47 ) + ( 0.45 * 1.70 ) + (0.2*1.08) Portfolio Beta = 0.138 + 0.1175 + 0.765 + 0.216 = 1.2365