Modern portfolio theory
Asset Class Analysis
The analysis is mechanical. The historical performance of all investment options is collected. Statistical techniques are used to sort the investments into groups that have behaved the same over time; these are called Asset Classes. Investment options that cannot be grouped into large pools are discarded.
Statistical techniques are then used to determine the correlation of performance between the Asset Classes over time. If some Asset Classes show non-linear or highly varying correlation, they are discarded.
The remaining Asset Classes are used in a linear algebra model to construct an Efficient Frontier. Essentially, all potential investment allocation mixes of all Asset Classes are considered for their risk and return over time. The allocation mix with the lowest historical risk (variation) for a given return is considered the most efficient portfolio for that level of return - it becomes one point on the Efficient Frontier.
The Efficient Frontier is usually depicted as a graph with risk on the x-axis and return on the y-axis. It has the shape of an inverted exponential decay, although the exact shape is determined by the data.
Modern Portfolio Management
In Modern Portfolio Management, the Asset Classes are combined with other economic measures, such as inflation. The correlation between each Asset Class return and each economic measure is calculated. Portfolio management software will conduct a Monte Carlo Simulation that varies these economic measures within some predetermined limits. Each investment allocation mix is considered in the face of these varying economic assumptions and again, allocation mixes with the least risk for a given return are selected for use.
As an example, conventional wisdom holds that the portfolio with the least risk is one made up entirely of Treasury Notes. However, Modern Portfolio Theory showed that the least risky portfolio was actually a mix of 92% Treasury Notes and 8% equity (stocks). The small percentage investment in stocks provided a buffer against the very real possibility of mild inflation over the life of the portfolio.