If you hold a portfolio made up of the following stocks: Investment Value Beta S
ID: 2631996 • Letter: I
Question
If you hold a portfolio made up of the following stocks:
Investment Value Beta
Stock X $4,000 1.5
Stock Y $5,000 1.0
Stock Z $1,000 .5
What is the beta of the portfolio?
You must add one of two investments to an already well- diversified portfolio.
Security A Security B
Expected Return = 14% Expected Return = 14%
Standard Deviation of Standard Deviation of
Returns = 15.8% Returns = 19.7%
Beta = 1.8 Beta = 1.5
If you are a risk averse investor, which one is the better choice?
Explanation / Answer
Beta of Portfolio:-
Weight for stock X= 4000/(4000+5000+1000) =0.4
Weighted beta for Stock X=0.4*1.5 =0.6
Beta of Portfolio=0.6+0.5+0.05=1.15
A risk Averse investor tries to minimize the Risk.
Standard Deviation (Measure of Total risk)= Systematic risk+ Unsystematic risk
(Standard deviation of Portfolio)2 =(Beta*Standard Deviation of market return)2 + (Unsystematic risk) 2
Where, (Beta*Standard Deviation of market return)2 = Systematic Risk
That is Beta measures the Systematic risk.
Unsystematic risk can be reduced through diversification, So the investors should be concerned about the systematic risk(Beta). Thus a risk averse investor will choose security B over security A as security B has lower beta or lower systematic risk than security A. Also the expected returns of both the security is same.
Underlying Invetment value weight= Invetment/Total investement Beta Weighted Beta= weight*Beta Stock X 4000 0.4 1.5 0.6 Stock Y 5000 0.5 1 0.5 Stock Z 1000 0.1 0.5 0.05 Average beta 1.15Related Questions
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