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?

The post-purchase expected return of the portfolio is the weighted average return of Syngine stock and pre-purchase return of the portfolio, calculated as below:

Post-purchase portfolio return = (Market value of Synhine stock purchase/Total market value of post-purchase portfolio)x Syngine stock return + (Market value of pre-purchase porfolio/Total market value of post-purchase portfolio) 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% = 11.2%

Using the same concept, beta of the post-purchase is calculated as below:

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 = 1.23