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Portfolio Optimization – Finding the Efficient Frontier

Portfolio Optimization – Finding the Efficient Frontier. Theory, and a Practical Example. Concept of Beta. Source: Value Line , March 2005. Security Market Line Equation. Required Return = Risk Free + Risk Premium on Stock i Rate on Stock i

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Portfolio Optimization – Finding the Efficient Frontier

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

  2. Concept of Beta Stodder, Efficient Frontier

  3. Source: Value Line, March 2005 Stodder, Efficient Frontier

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

  5. Beta of the Market = 1 βi= (Ri– Rrf)/(Rm - Rrf) So if Ri = Rm, βi = βm then βm = (Rm– Rrf)/(Rm - Rrf) = 1 Stodder, Efficient Frontier

  6. The Efficient Frontier Non-Diversifiable Risk Stodder, Efficient Frontier

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

  8. Run Simulation • From Financial Models Using Simulation and Optimization by Wayne Winston: Ch. 16, “Portfolio Optimization” Stodder, Efficient Frontier

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