1 / 8

Markowitz Model

Markowitz Model. For 3-stock portfolio, short selling allowed. Eg. R A = 20% R B = 10% R C = 8%  2 A =100  2 B =25  2 C =16  AB = 15  AC = 20  BC = 4. Markowitz Model. Form the Lagrangian. Markowitz Model: Solution. For R* = 15% w A = 50.214%

charles-burke
Download Presentation

Markowitz Model

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Markowitz Model For 3-stock portfolio, short selling allowed Eg. RA= 20% RB= 10% RC= 8% 2A=100 2B=25 2C=16 AB= 15 AC= 20 BC= 4

  2. Markowitz Model Form the Lagrangian

  3. Markowitz Model: Solution For R* = 15% wA = 50.214% wB = 48.715% wC = 1.075% Standard Dev = 6.22% For R* = 20% wA = 91% wB = 56% wC = -47% (short sale) Standard Dev = 9.47%

  4. Single Index Model Rt= A + BRmt + et E(Rt) = A + BE(Rmt) Cov(ei,ek)=0 E(ei)=0 Cov(ei,Rm)=0 2p=Pi[Ri - E(R)]2 by substitution 2=Pi[A + BRmt +ei -A - BE(Rm)]2 2=Pi{B[Rmi-E(Rm)] + ei}2 2=Pi{B2[Rmi-E(Rm)]2 +ei2+2B[Rmi-E(Rm)] ei} 2p= B2p 2m + 2e

  5. Single Index Model (Cont’d) 2p= B2p2m + 2ep We also know that Bp= Cov(Rp, Rm)/ 2m Bp=wjBj 2ep= wj2 2ej Hence, the portfolio variance is: 2p= (xjBj )22m + xj2 2ej

  6. Single Index Model (Cont’d) For 3-stock portfolio, short selling allowed Eg. RA= 20% RB= 10% RC= 8% 2A=20 2B=15 2C=9 A= 1.5 B= 0.75 C= 0.50

  7. Single Index Model (Cont’d) Form the Lagrangian

  8. Single Index Model Solution When R* = 15% wA = 0.57 wB = 0.08 wC = 0.35 Standard Deviation =

More Related