Question

The variance of a 2-asset portfolio has been calculated to be .0225, meaning its standard deviation is .15 (or 15%). Its expected return is 10%. This portfolio also has a covariance of .01 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 asset(s), if any, would lower the SYSTEMATIC risk of your portfolio. (Assume equally-weighted portfolios in all cases, e.g. w1=w1= ½ for the first portfolio and if you add a third asset, w1=w2=w3= 1/3).

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 = 0.80

Asset GHI: Expected Return = 6%, standard deviation = 22%, Beta with the market = 0.80

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 = 1.00

A- Assets DEF and GHI

B- Assets ABC and DEF

C- All of the assets

D- Assets ABC and JKL

E- Assets GHJ and JKL

F- None of the assets

Answer 1

covariance = 0.01

variance of market = 0.10^2 =0.01

beta of current portfolio = covariance/variance of market = 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 : Assets DEF anf GHI [Thumbs up please]