# Understanding CAPM, CML, and efficient portfolios

I'm trying to understand the CAPM model and how we can use it to understand efficient portfolios. Specfically, I'm trying to use the CML line (mapping expected returns and standard deviations of portfolios) to value proposed portfolios.

In this scenario: risk free rate = 2%. Expected excess return on market portfolio is 8% (so, I'm assuming, the expected return on the the market portfolio is 10%). The last given value is that the standard deviation of the market portfolio is 20.

I have to analyze 3 portfolios:

A: E(r) = 8%, SD = 10% B: E(r) = 12% SD = 25% C: E(r) = 13% SD = 30%

Based on the Sharpe Ratio (ie: the slope of the CML), I deduced that portfolio A is unfeasible and C is inefficient, whereas B falls on the CML and must therefore be efficient for the level of risk.

The next question I'm posed with is "How can the expected return of the wining portfolio be achieved? Specify the amount invested in each asset/portfolio of assets?"

It is given that I have some number X to invest, but I'm not quite sure how to approach this problem. The question does not seem too clear to me.

You just need: $\alpha * .08 + (1-\alpha) * .02 = .12$. Solve for alpha and then check the standard deviation that should be .25.