Ivan Knobel holds a well-diversified portfolio that has an expected return of 11.0% and a beta of 1.20. He is in the process of buying 1,000 shares of Syngine Corp at $10 a share and adding it to his portfolio. Syngine has an expected return of 13.0% and a beta of 1.50. The total value of Ivan's current portfolio is $90,000. What will the expected return and beta on the portfolio be after the purchase of the Syngine stock?

Expected return = 11.2%

Beta = 1.23  

Solution:

The estimated post-purchase return on the portfolio seems to be the weighted average return on the Syngine stock as well as the pre-purchase return on the portfolio, determined as follows:

Post-purchase portfolio return

= / x Syngine stock return +

x Pre-purchase return

= [(1,000 x 10)/(1,000 x 10 + 90,000)] x 13% +  [(90,000)/(1,000 x 10 + 90,000)] x 11%

Post-purchase portfolio return  = 11.2%

Using the same equation, the post-purchase beta is estimated as follows:

Post-purchase portfolio beta = [(1,000 x 10)/(1,000 x 10 + 90,000)] x 1.5 +  [(90,000)/(1,000 x 10 + 90,000)] x 1.2

Post-purchase portfolio beta = 1.23

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