I would appreciate help with how to compute the expected return of a market portfolio in the question (Exercise 3.14) below:
In the question it says that we shall use the data given in Exercise 3.10 so I will present that question below as well so you will be able to see the three securities and its values:
In the solution, they have provided the correct answers as $w=[0.438 , 0.012 , 0.550]$ and $\mu_m=0.183$, where $\mu_m$ is the expected return for the market portfolio, (they also gave the solution of the standard deviation but that is not necessary for my question here). I know how they compute the weights so this solution we can ignore, however I do not manage to understand how they get the expected return of the market portfolio.
In my course literature it says that the expected return of a portfolio is given by the formula $$\mu_v=wm^T$$ where w=row matrix of the weights and $\mu_v$=row matrix of the expected returns for each asset/security. So I figured that the expected return of the market portfolio in our case would be given by $$\mu_m=w_mm^T=[0.438 , 0.012 , 0.550]\cdot [0.08 , 0.1 , 0.06]^T$$ since in Exercise 3.10 it is said that $m=[0.08 , 0.1 , 0.06]$, but this does not give the correct solutions and I can't figure out why?
Edit: When this did not work I thought it was because one might need to find the expected returns of each asset for the weights of the market portfolio and not use the given $m=[0.08 , 0.1 , 0.06]$ in Exercise 3.10 when calculating. But I did not manage to find a way to bring out new values of m and do not even know if this would have been a correct solution..