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An investor divides her portfolio into four parts, with 1/3 in Treasury bills, 1/3 in a...

An investor divides her portfolio into four parts, with 1/3 in Treasury bills, 1/3 in a market index, 1/3 in an asset with beta of 1.5. What is the beta of the investor's overall portfolio?

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Answer #1
Total Portfolio value = Value of T bill + Value of Market + Value of Asset
=0.3333+0.3333+0.3333
=0.9999
Weight of T bill = Value of T bill/Total Portfolio Value
= 0.3333/0.9999
=0.3333
Weight of Market = Value of Market/Total Portfolio Value
= 0.3333/0.9999
=0.3333
Weight of Asset = Value of Asset/Total Portfolio Value
= 0.3333/0.9999
=0.3333
Beta of Portfolio = Weight of T bill*Beta of T bill+Weight of Market*Beta of Market+Weight of Asset*Beta of Asset
Beta of Portfolio = 0*0.3333+1*0.3333+1.5*0.3333
Beta of Portfolio = 0.8333
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