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Portfolio Optimization: Finding the Efficient Frontier - Theory and Practical Example

This article explores the concept of the Efficient Frontier in portfolio optimization, providing both theoretical insights and a practical example. It discusses the significance of beta in assessing required returns based on the Security Market Line. The methodology includes calculating the standard deviation and mean return for stocks, ultimately identifying the minimal standard deviation portfolio for any given rate of return. The piece references key concepts from the works of Stodder and the simulation techniques found in "Financial Models Using Simulation and Optimization" by Wayne Winston.

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Portfolio Optimization: Finding the Efficient Frontier - Theory and Practical Example

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

  2. Concept of Beta Stodder, Efficient Frontier, July

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

  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, July

  5. 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 Stodder, Efficient Frontier, July

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

  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, July

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

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