Mean-Variance Analysis (From AllenResources in Youtube)

This video has 3 parts.

The first part lists the assumptions behind the mean-variance analysis:

1. Investors are risk-averse (is that true? Look at behavioral finance for loss aversion)
2. Expectation values, variances and co-variances of all assets are known
3. Assume pure Gaussian (no need to know skewness and kurtosis)
4. No transaction costs and tax

The second part introduces the concept of having negative or >1 portfolio weight. This is an interesting part.

If you borrow money to invest in a particular asset, the portfolio weight of that asset can be larger than one because

                 Wi = (total value of the asset) / your investment

                     = (your investment + money borrowed) / your investment

                     > 1

Of course, we have to add another asset j, which becomes the money you borrowed and this is <0:

Wj = – money borrowed / your investment

Again Wi + Wj =1 still holds.

The last part is about portfolio (with 2 assets) variance calculation which I won’t repeat here.