The following equation is known as the Capital Asset Pricing Model (CAPM) and defines the expected return of an asset i, E(r), as a function of the risk-free rate,ry, the expected return of the market portfolio, E(rm), and the ratio = B. (where om denotes the covariance of OM returns of the asset i with the market portfolio, and of stands for the variance of returns of the market portfolio). E(n) = r, + (ECM) - ) OM on 1.1 Assume a portfolio P, where an amount wi is invested in a risky asset i, and WM = (1 - w.) in the market portfolio and derive the above equation (CAPM). Present all your steps in detail. (25%) 1.2 Show that the CAPM B. is linearly additive. Present all your calculations analytically and explain every step. (10%) 1.3 Prove that the CAPM formula holds true for any combination of assets, and confirm that the beta of the market portfolio, BM, equals to 1. Provide an economic interpretation of your findings. (15%)