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Portfolio Scenario Model

Problem: How to Demonstrate the differences when minimising three different measures of risk.

There are a variety of ways to measure the risk of a portfolio. In this model, you need to observe the changes in the optimal investment allocations resulting from the minimisation of risk as measured in three different ways and determine the best measure of risk for your lifestyle.

Once again there are three assets, this time with twelve equally likely expected return scenarios. Scenarios are outcomes of events with an influence on your analysis: China goes capitalist, China stays communist, China engulfs Japan, etc.. This model calculates three different measures of risk: variance, semi-variance, and downside risk. You can minimise each of the three and get different levels of each asset that achieve your target return of 15% - each offers the "lowest risk", depending on which of the three measures you select.

Variance is a measure of the fluctuation of the expected return. However, this measure of risk considers a scenario that returns 5% above the target to be as desirable as a scenario that returns 5% below the target. You're probably only worried about the risk that the return will be below your target return.

Both Semi-variance and downside risk look only at the risk that your return will be below the target. Downside risk minimises the difference between the target and returns below the target. The semi-variance minimises the difference between the target and the square of the returns below the target. Therefore, it puts a higher weight on larger differences below the target.

The objective is to determine the percent to invest in each asset while minimising the risk of the entire portfolio using the risk measure that is most important to you.

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