• Internal Code :
  • Subject Code : EFB335
  • University : Queensland University of Technology
  • Subject Name : Accounting and Finance

Question 4: Efficient Frontier (EF) of The Portfolios

1. The weights of the selected stock for determining the Efficient Frontier have been calculated by assigning random weights to some of the stocks and the weights for the remaining stocks have been calculated using the formula W5=1- sum(W1+ W2+ W3+ W4+ W5 )

2. The expected return and standard deviation of the portfolios have been calculated using the below formula

Expected return of portfolio = w1E(R1) + w2E(R2)+ w3 (R3)+ w4(R4)+ w5(R5)

Standard Deviation of portfolio= w21Var(R1) + w22Var(R2) + w23Var(R3)+ w24Var(R4) + w25Var(R5) 2w1w2Cov(R1, R2)+ 2w2w3Cov(R2, R3)+ 2w3w4Cov(R3, R4)………………………… And so on

3. The Efficient frontier has been drawn by using a scatter chart. The values for the said scatter chart have been arranged such that Standard Deviation is on X Axis and Expected returns are placed on Y Axis.

Question 5: Construction of Tangency Portfolio

1. The weights of the five selected stocks in the tangency portfolio have been determined by calculating the Sharpe ratio. The formula that has been used for calculation of Sharp ratio is

(p−f)/ σ

In this formula,

 P = expected return of the portfolio

F= Risk free rate

Σ = Standard Deviation of portfolio

The portfolio that has the highest sharpe ratio is the tangency portfolio which is Portfolio 10 and its weights are shown below:
















2. The expected return and standard deviation of the tangency portfolio have been calculated using the below formula:

Expected Return of Tangency portfolio = E(Rc) = wpE(Rp) + (1 − wp)Rf

Standard Deviation of Tangency portfolio = wpσ(Rp)

4. The Sharpe ratio of the tangency portfolio is 1.077.

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