How do you determine the equation of an efficient frontier? This question relates to BUS4028F 2017 Tutorial 2 question 12 i

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How do you determine the equation of an efficient frontier? This question relates to BUS4028F 2017 Tutorial 2 question 12 i

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The efficient frontier is a relationship between \(E_P\) (expected portfolio return) and \(\sigma_P\) (portfolio standard deviation).

Suppose we invest a proportion \(\alpha\) in asset A. Then we can write down:

$$E_P = 0.05(1 + \alpha) \qquad ; \qquad \sigma_P^2 = 0.04 \alpha^2.$$

We can use these two equations to write \(E_P\) in terms of \(\sigma_P\):

$$E_P = 0.05 + 0.25 \sigma_P.$$

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