Question

You just finished the first quarter managing a portfolio for a client. The initial investment was $175,000 and at the end of the quarter the value was $168,665. Your performance is judged against a combination of U.S. and Non-U.S. equity indices. The U.S. index is the S&P 500 and has a weight of 75%. The Non-U.S. index is the ACWI and has a weight of 25%. For the quarter, the S&P 500 Index lost 2.93% and the ACWI lost 5.13%. Which of the following best describes how you did against the benchmark? (recurring content question) Your alpha is −41 basis points Your alpha is +28 basis points Your alpha is −41 basis points Your alpha is 3.62% Your alpha is-96 basis point

Answer 1

Step-by-step explanation:

To determine how you performed against the benchmark, we need to calculate the benchmark return and compare it to your portfolio return.

The benchmark return can be calculated by weighting the returns of the S&P 500 and ACWI indices based on their respective weights:

Benchmark return = (Weight of S&P 500 × Return of S&P 500) + (Weight of ACWI × Return of ACWI)

Weight of S&P 500 = 75%

Return of S&P 500 = -2.93%

Weight of ACWI = 25%

Return of ACWI = -5.13%

Benchmark return = (0.75 × (-2.93%)) + (0.25 × (-5.13%))

Benchmark return = (-2.1975%) + (-1.2825%)

Benchmark return = -3.48%

Now, let's calculate your portfolio return:

Portfolio return = (Ending value - Initial investment) / Initial investment

Portfolio return = (168,665 - 175,000) / 175,000

Portfolio return = -0.036257 (-3.63%)

Finally, to calculate the alpha, we subtract the benchmark return from your portfolio return:

Alpha = Portfolio return - Benchmark return

Alpha = -3.63% - (-3.48%)

Alpha = -0.15% (-15 basis points)

Therefore, the closest option that describes your performance against the benchmark is: "Your alpha is -15 basis points."