Your portfolio is comprised of 40 percent of stock X, 15 percent of stock Y, and 45 percent of stock Z. Stock X has a beta of 1.24, stock Y has a beta of 1.49, and stock Z has a beta of 0.41. What is the beta of your portfolio?

Portfolio beta = 0.904

Explanation:

The portfolio beta is the weighted average of all the beta associated with each of the different stock making up the portfolio. The betas are weighted using the probability associated with each of the stock.  

Portfolio beta = WaRa + Wb+Rb + Wn+Rn  

W- weight of the beta, R- Stock beta -  

W- Probability of the beta, R- stock beta

Note that the sum of the probability of different outcomes should equal to one. Hence, the probability of economy being normal is

Portfolio beta = (0.4 × 1.24)  + (0.15 × 1.49) +  ( 0.45 ×0.41) =0.904

Portfolio beta = 0.904

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