Portfolio Optimization Finding the Efficient Frontier

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Portfolio Optimization Finding the Efficient
Frontier

• Theory, and
• a Practical Example

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Concept of Beta
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Source Value Line, March 2005
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Security Market Line Equation

• Required Return Risk Free Risk Premium
• on Stock i Rate on
  Stock i
• Required Return Risk Free ßi(Market Risk)
• on Stock i Rate Premium

Ri Rrf ßi(Rm - Rrf)
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Beta of the Market 1

• ßi (Ri Rrf)/(Rm - Rrf)
• So if Ri Rm, ßi ßm then
• ßm (Rm Rrf)/(Rm - Rrf) 1

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The Efficient Frontier
Non-Diversifiable Risk
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How do We Find the Efficient Frontier?

• Basic Strategy
• Find the Standard Deviation (si) 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.

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Run Simulation

• From Financial Models Using Simulation and
  Optimization
• by Wayne Winston
• Ch. 16, Portfolio Optimization