I've been trying to work through a simple example using A Step-by-Step Guide to the Black Litterman Model, but I'm having trouble understanding implied risk aversion.
Say I have two uncorrelated assets, cash as my stand in for the risk free rate and my market capitalization weight happens to conveniently be equal weighted.
According to the paper my implied risk aversion $\lambda$ should be the portfolio excess return (5%) over the portfolio variance (0.0066)
which gives $\lambda = 0.05 / 0.0066 \approx 7.6$.
However, when I try check my work by calculating the equilibrium excess returns
I get an equity excess return (again assuming uncorrelated assets) of $$ r_e = \lambda * \sigma_e^2 * w_e = 9.7 \% $$
rather than the expected $7\%$.
Is there a reason the implied risk aversion does give implied equity excess returns? Something to do with requiring fully funded portfolios maybe? Though that doesn't seem to tie out either.