Stodder, Efficient Frontier, July Portfolio Optimization – Finding the Efficient Frontier Theory, and a Practical Example.

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Presentation transcript:

Stodder, Efficient Frontier, July Portfolio Optimization – Finding the Efficient Frontier Theory, and a Practical Example

Stodder, Efficient Frontier, July Concept of Beta

Stodder, Efficient Frontier, July Source: Value Line, March 2005

Stodder, Efficient Frontier, July Security Market Line Equation Required Return = Risk Free + Risk Premium on Stock i Rate on Stock i on Stock i Rate on Stock i Required Return = Risk Free + βi( Market Risk ) on Stock i Rate Premium on Stock i Rate Premium Ri = Rrf + β i (Rm - Rrf)

Stodder, Efficient Frontier, July Beta of the Market must be = 1 Beta of the Market must be = 1 Ri = Rrf + βi(Rm - Rrf) if Ri = Rm, βi = βm then Rm = Rrf + βm(Rm - Rrf) => Rm - Rrf = βm(Rm - Rrf) => βm = 1 βm = 1

Stodder, Efficient Frontier, July The Efficient Frontier Non-Diversifiable Risk

Stodder, Efficient Frontier, July How do We Find the Efficient Frontier? Basic Strategy: Find the Standard Deviation ( σ i ) and Mean Return ( μ i ) of every stock Stock i. Find the Standard Deviation ( σ i ) and Mean Return ( μ i ) of every stock Stock i. For any given rate of return, find the minimal standard deviation portfolio that can achieve that return. For any given rate of return, find the minimal standard deviation portfolio that can achieve that return.

Stodder, Efficient Frontier, July Run Simulation From Financial Models Using Simulation and Optimization From Financial Models Using Simulation and Optimization by Wayne Winston.