I need to see intermediate steps and formulas.
Analyzing a Portfolio
You have $100,000 to invest in a portfolio containing Stock X, Stock Y and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 13.5% and that has only 53% of the risk of the overall market. If X has an expected return of 31% and a Beta of 1.8, Y has an expected return of 20% and a Beta of 1.3, and the risk-free rate is 7%, how much money will you invest in Stock X?
The question implies that the portfolio return should be 13.5% and the portfolio beta should be 0.53 (since it has 53% of the risk of market and market beta is 1). Let wx be the weight of X and wy be the ...
The solution explains how to estimate the amount to be allocated to various assets in the portfolio given the expected return and risk of the portfolio.