Question

An investor divides her portfolio into three equal parts, with one part in Treasury bills, one...

An investor divides her portfolio into three equal parts, with one part in Treasury bills, one part in a market index, and one part in a mutual fund with beta of 1.50. What is the beta of the investor's overall portfolio? Please show work with formulas.

Hint: Beta of a portfolio is the weighted average of individual assets' betas.

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Answer #1

An investor divides her portfolio into three equal parts, with one part in Treasury bills, one part in a market index, and one part in a mutual fund with beta of 1.50

So, weight in risk free asset, Wf = 1/3

Beta of risk free assets, Bf = 0

Weight of market, Wm = 1/3

Beta of market, Bm = 1

Weight of mutual fund Wr = 1/3

Beta of mutual fund, Br = 1.50

So, beta of overall portfolio is weighted average of individual assets' betas.

So, beta of portfolio = Wf*Bf + Wm*Bm + Wr*Br

=> Beta = (1/3)*0 + (1/3)*1 + (1/3)*1.5 = 0.83

So, beta of investor's overall portfolio is 0.83

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