CAPM - Derivation of the Capital Asset Pricing Model
Today we derive the Capital Asset Pricing Model (CAPM), first listing the assumptions used and putting the model into context of Modern Portfolio Theory (MPT). Next, we formulate the CAPM problem mathematically and use the method of Lagrange multipliers to find the local minima of the CAPM function, subject to an investor’s expected return (equality constraint). I go through all the math here!
In the financial industry, although the CAPM has a number of questionable assumptions (and there is plenty of contention regarding its implementation), it clearly provides a means to quickly develop intuition of an assets expected return for its given level of risk compared to the overall market. For this alone, the CAPM is still used heavily!
00:00 Intro
00:25 CAPM Assumptions
01:35 MPT vs CAPM
02:25 Equilibrium Condition
03:08 Capital Market Line (CML)
03:30 Warning on Normal Distribution Assumption!
04:00 Derivation of CAPM – Problem Formulation
05:15 Derivation of CAPM – Solution Method
06:00 Derivation of CAPM – All of the math
09:25 Derivation of CAPM – Putting it all together
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