I am working with mean variance optimization (MVO) and as such after "training" my model I test the results on a test dataset. Markowitz states that the return of a portfolio is the "Sum of weighted average returns". Let's now show an example on how this is not true on a real world scenario.
- Asset A has a weight of 10% and an annual geometric return of 100%
- Asset B has a weight of 90% and an annual geometric return of 10%
According to markowitz the return of the portfolio should be (0.1 * 100) + (0.9 * 10) = 19%.
Now, let's do a simulation on the value gained with the portfolio. Total value to invest in the portfolio is 100. Timeframe is 5 years. Compound annualy.
- Markowitz: Start value is 100. Rate is 19%. End value is 238.64. (Investment websites used to get this value)
- "Real" return: Start value is 100. Asset A start value is 10, and Asset B start value is 90. Asset A grows from 10 to 320. Asset B grows from 90 to 144.95. In total the end value is 464.95. The return necessary to get this end value, starting with 100 (combining assets) is 35.98%.
Right now I have a training model with multiple input parameters, and as such I am trying to find the best combination by averaging the performance on the test dataset. So my question is which return is "more correct" and which one should I used to compare strategies.
A quick end note is that not only are the returns different when comparing "real" vs markowitz but also volatility is different (unless multiplying the weights with the respective returns every period), so I am bit confused on which pair of values I should use.