HI
@sumitmaan19 Three of my videos in our recent P1.T1. playlist might be helpful, esp T1-8 and T1-9. Your (1) is consistent with the definition given by Elton: "First, we have shown that, under the assumptions of the CAPM, the only portfolio of risky assets that any investor will own is the market portfolio. Recall that the market portfolio is a portfolio in which the fraction invested in any asset is equal to the market value of that asset divided by the market value of all risky assets." [Elton, Edwin J.; Gruber, Martin J.; Brown, Stephen J.; Goetzmann, William N.. Modern Portfolio Theory and Investment Analysis, 9th Edition (Page 302). Wiley. Kindle Edition.] ... but that's a description of the market portfolio in equilibrium. In practice, I think we treat its solution as an
optimization problem, knowing that we are merely
approximating because whatever is our set of investable assets is not the whole market. In the XLS for these, I actually assume a two-asset universe (ridiculously unrealistic)! How to i then define the market portfolio? I solve for the portfolio with the highest Sharpe ratio consistent with your #3 (because the assumptions are returns, volatilities and correlations -- prices do not enter this optimization approach, as opposed to the price-based description under equilibrium); this can be done for a large matrix of n assets. So, in my ridiculously unrealistic 2-asset world the mathematical solution to the market portfolio is a highest-Sharpe-ratio optimization problem, for which I recently found the analytical solution (via Mathematica), see here
https://www.bionicturtle.com/forum/threads/market-portfolio-and-derivative-of-weight.9919/post-45560 I hope that's a bit of clarity!
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