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
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 : A : Assets DEF anf GHI [Thumbs up please]
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