Tom O'Brien has a 2-stock portfolio with a total value of $100,000. $47,500 is invested in Stock A with a beta of 0.75 and the remainder is invested in Stock B with a beta of 1.42. What is his portfolio's beta? Do not round your intermediate calculations. Round your final answer to 2 decimal places.
Answered on
To find the portfolio's beta, you can use a weighted average based on the beta of each stock in the portfolio.
Given:
Investment in Stock A = $47,500
Investment in Stock B = Total value - Investment in Stock A = $100,000 - $47,500 = $52,500
Beta of Stock A = 0.75
Beta of Stock B = 1.42
Now, calculate the weighted average of the betas:
Portfolio Beta = ( Weight of Stock A × Beta of Stock A ) + ( Weight of Stock B × Beta of Stock B )
Portfolio Beta = ( Investment in Stock A / Total Portfolio Value × Beta of Stock A ) + ( Investment in Stock B / Total Portfolio Value × Beta of Stock B )
Portfolio Beta = (47,500 /1,00,000 x 0.75 ) + (52,00,000 / 1,00,000 x 1.42 )
Portfolio Beta = ( 0.475 × 0.75 ) + ( 0.525 × 1.42 )
Portfolio Beta = 0.35625 + 0.7455
Portfolio Beta=1.10175
Rounded to two decimal places, Tom O'Brien's portfolio beta is 1.10.