Assume the single-factor apt model applies and a portfolio exists such that half of the funds are invested in risky security q and the rest in the risk-free asset. security q has a beta of 1.8. the portfolio has a factor beta of:

The portfolio has a factor beta of 0.9

Explanation:

The computation of portfolio has a factor beta is shown below:

= Beta × half of funds in security Q + Beta × half in the risk-free asset

where,

Beta is 1.8

Half of funds in security Q = 1 ÷ 2

Beta of risk free assets is not given so we assume 0

And, the half in the risk-free asset = 1 ÷ 2

Now, put these values to the above formula

So, the value would be equal to

= 1.8 × (1 ÷ 2) + 0 × (1 ÷ 2)

= 0.9 + 0

= 0.9

Hence, The portfolio has a factor beta of 0.9

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