Week 4 - Optimal Diversification (2) (COMPUTING EFFICIENT PORTFOLIO/FRONTIER) Flashcards
What is the value for A
R bar transposed x sigma to the power of -1 x R bar
What is the value for B
R bar transposed x Sigma to the power of -1 x -1
What is the value for C
1 transposed x sigma to the power of -1 x 1
How do you calculate λ
C x r bar portfolio - B / AC - B squared
How do you calculate μ
A - B r bar portfolio / AC - B squared
How do you calculate the weights?
w = sigma -1 (Rbar x λ + 1μ)
How do you calculate the efficient portfolio?
- Calculate A,B and C
- Calculate μ and λ
- Calculate weight of portfolio
- Calculate the variance of the portfolio
SEE EXAMPLE IN NOTES (VERY IMPORTANT TO KNOW AS WELL AS THE IMPLICATION OF THIS) -> 9% AND 14% IS PRACTISE QUESTION
How do you calculate the weight of a minimum variance portfolio? (where investor just want to reduce risk regardless of return)
Sigma to the power of -1 x 1 / C
How do you calculate the return of return and variance of the minimum variance portfolio?
Return on Min (Rbar min) = B/C
VAR (Rbar min) = 1/ 1 transposed x sigma to the power of minus 1 x 1
How do you calculate the weight of a two fund separation?
Wsep = Sigma to the power of -1 R bar/B
How can we find any portfolio on the min variance frontier?
As a linear combo of W min and W sep
What does the Optimisation problem change with the introduction of a risk free asset?
Min (wn) = 1/2 W transposed x sum of W
With constraints being placed on Weight and Return on portfolio
Weight = W transposed ( rbar - rf)= Rbar p to the power of E
How do you calculate the weights at the tangency portfolio?
Wtp = Sigma to the power of -1 x Rbar to the power of e/ 1 transposed x Sigma to the power of -1 x Rbar to the power of E
SEE EXAMPLE IN NOTES
How do you do matricies multiplication?
See in notes
