Question

The variance of a 2-asset portfolio has been calculated to be .0225, meaning its standard deviation is .15 (for 15%) its expected return is 10%. This portfolio also has a covariance of 0.1 with the broad market. The standard deviation of the market portfolio is 10%. You are looking to add a third asset to the portfolio and are choosing amongst three assets to add. Which assets, if any, would lower the SYSTEMATIC risk of your portfolio. (Assume equally weighted portfolios) Asset ABC Expected Return- 12% Standard Deviation- 10% Beta with the market- 1.25 Asset DEF Expected Return-12% Standard Deviation-15% Beta with the market-0.8 Asset GHI Expected Return-6% Standard Deviation-22% Beta with the market-.8 Asset JKL Expected Return-6% Standard Deviation-22% Beta with the market-1.25 Asset MNO Expected Return-10% Standard Deviation-10% Beta with the market-1.0

a) Assets GHJ and JKL

b) none of the assets

c) Assets DEF and GHI

d) Assets ABC and DEF

e). All of the assets

Answer 1

beta of current portfolio = covariance/variance of market = 0.01/(0.10)^2 = 0.01/0.01 = 1

so current portfolio beta is = 1

beta measures systematic risk.

so our purpose is to reduce beta.

From given assets, DEF and GHI has beta =0.8 lower than current beta

so if we include them in current portfolio, the new beta will be less than 1, so systematic risk will reduce

new beta will be = 1/3(1) + 1/3(0.8) + 1/3(0.8) = 0.8667 =0.87

Answer : C : Assets DEF anf GHI [Thumbs up please]