Inverse Volatility Portfolio
Each asset is weighted in inverse proportion to its volatility and then all assets are rescaled to sum up to 1. Therefore, lower weights are given to high volatility assets and higher weights to low volatility securities. Misleadingly, this concept is often being mixed-up with the risk parity approach, since they are quite similar. Nevertheless, since the overall portfolio volatility is not an additive function of the underlying volatilities, each asset class is not contributing exactly the same amount of risk to the overall portfolio.
Let's see how this would work with our 5 asset classes from the Mean-Variance Optimization segment and having the only constraints that our portfolio is long-only and fully-invested at all times.
Remember the standard deviations of our 5 asset classes:
The inverse volatility portfolio simply divides 1 by each standard deviation, from which we get the following picture:
Now, the only thing left to do is to rescale the allocations to 1, which we do by dividing each allocation by the sum (106.4433), so that we get the following allocation picture:
Voilà, you've just created your first inverse volatility portfolio!