The following 3 minute video goes over the mathematical proof of the CAPM, taken from my lecture on Asset Pricing Theory (where you can also download the Powerpoints I'm going over, and see a much larger screen size). It is so simple you can see why 4 people independently figured it out about the same time (Mossin, Sharpe, Lintner, Treynor). Given the insights of Markowitz (the efficient frontier) and Tobin (two-fund separation theorem), it is rather trivial. You can see more videos here, related to my book Finding Alpha.
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