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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

Portfolio Optimization – Finding the Efficient Frontier

Theory, and

a Practical Example

Stodder, Efficient Frontier, July


Concept of beta
Concept of Beta

Stodder, Efficient Frontier, July


Source value line march 2005
Source: Value Line, March 2005

Stodder, Efficient Frontier, July


Security market line equation
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


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

Stodder, Efficient Frontier, July


The efficient frontier
The Efficient Frontier

Non-Diversifiable

Risk

Stodder, Efficient Frontier, July


How do we find the efficient frontier
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


Run simulation
Run Simulation

  • From Financial Models Using Simulation and Optimization

    by Wayne Winston.

Stodder, Efficient Frontier, July


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