Incorporating Risk and Expected Returns: Solving for Portfolio Curve and Range

[johnaphun]

Homework Statement

A risky portfolio P is to be formed from securities S1 and S2 where the expected returns
are E(R1) = 0:05 and E(R2) = 0:1, the variances are s₁₂² = 1 and s₂² = 2 and S1 and S2 are uncorrelated. Suppose no short selling is allowed so that

P= x₁S1 + x₂S2, x₁ + x² = 1 x1,x1>0

Show that all portfolios P lie on the curve

s_p² =1200E(Rp )² - 160E(Rp ) + 6

state the range of E(Rp)

Homework Equations

s_p² = x₁²s₁² +x₂²s₂²

The Attempt at a Solution

As S1 and S2 are uncorrelated the covariance is equal to 0

So far I've subbed x₂ = (1 - x₂) into the above equation and solved but I'm unsure what to do from here

 

[Stephen Tashi]

I'm not a portfolio theorist, but my guess is that you must use the fact that the variance of a random variable is related to it's mean. The variance of $X$ is the expected value of $X^2$ minus the square of the mean of $X$.