It is a pity that all textbooks now (2020-04-30) are WRONG on CAPM. Cause there is a Misunderstanding of the market portfolio: The portfolio separation of Tobin (1958) brings the market portfolio front and center. Although investors have different wealth and preferences, investors with mean-variance preferences all hold the same portfolio of risky assets. However, there is a precondition for this assertion in his paper, Tobin (1958) assumes that the mean vector and variance matrix of the returns of risky securities are given.
However, the returns are endogenous in CAPM. It is the result of the equilibrium of the entire market according to the mean-variance criterion.
"Initial wealth and risk aversion" will affected the equilibrium. Supposing that some investor double her initial wealth, or alter her risk aversion, such that she put more fund in risky assets, then the total value of market portfolio will be increased, and the rate of market return will be changed (the total future payoff is fixed). The market portfolio must be affected! For more on CAPM, see CAPM: Absolute Pricing, or Relative Pricing? or Arbitrage Opportunity, Impossible Frontier, and Logical Circularity in CAPM Equilibrium
Edit (2020-05-26): dislikes are anticipated. Young scientist seeks for new truths, old-fashioned scientist defends old ideas
For any investor's wealth and preference (simple trade-off coefficient) in
Example 4.1 Abad (2020): If the only change is an increase in wealth of the first
investor, such that $W_{1}=150$, then $\mu_{M}^{\,}=\frac{R_{0}D}{R_{0}%
x+D}=\frac{2820\,783}{2411\,900}=1.1695$. If the only change is an increase in preference parameter of the last investor, such that $G_{4}=\frac{158}{13}$,
then $\mu_{M}^{\,}=\frac{2586\,801}{2189\,060}=1.1817$. If the only changes
are parameters $W_{1}=150$ and $G_{4}=\frac{158}{13}$, and all other
parameters remain unchanged, then $\mu_{M}^{\,}=\frac{1857}{1580}=1.1753$.
Which restores the original expected market return, because of these two
parameters have opposite effect and are offset completely. For these three
cases, the weight vectors of the market portfolio are
$$
\frac{1}{120\,595}
\begin{bmatrix}
15\,214\\
6100\\
99\,281
\end{bmatrix}
,\quad\frac{1}{109\,453}
\begin{bmatrix}
13\,906\\
5548\\
89\,999
\end{bmatrix}
,\text{ and }\frac{1}{79}
\begin{bmatrix}
10\\
4\\
65
\end{bmatrix}
$$
respectively.