# MPT Efficient portfolio /Asset allocation

When finding the optimal allocation using markovitz, the model will return '0' weights for assets that are "inefficient". What is the standard way for dealing with these weights if all assets have to be included in the portfolio and a simple minimum is not an option? Also when introducing the CML the textbook says one should add a risk free asset to produce the optimal portfolio but i cant seem to find a formula to calculate the weight of the risk free asset. I understand the optimal portfolio should be a point on the CML but how can i find it?

You want the CML to be as steep as possible (greater reward for lesser risk), so find the corresponding point, $$T$$, from all of those on the frontier that satisfies:
$$\max_{T} \quad \nabla = \frac{R_T - R_f}{\sigma_T}$$
• The point about it being a line is that if your investment decision is solely Sharpe Ratio based then you are indifferent at any point on the line. So weights of $(R_T, R_f) = (1,0) = (0,1) = (0.5, 0.5)$ are all equivalent, but each comes with a different risk and different return so further criteria is required to sub-select. Leverage can even be obtained if you can borrow at risk free rate, i.e. $(2,-1)$ – Attack68 Oct 3 '18 at 6:55