Portfolio Optimization – Finding the Efficient Frontier

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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

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 iRate on Stock i

Required Return=Risk Free + βi(Market Risk)

Ri = Rrf + βi(Rm - Rrf)

Stodder, Efficient Frontier, July

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

Non-Diversifiable

Risk

Stodder, Efficient Frontier, July

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
• From Financial Models Using Simulation and Optimization

by Wayne Winston.

Stodder, Efficient Frontier, July