EC Using Random Portfolios To Test Asset Allocation Strategies

Last month I tested random rebalancing strategies based on dates and found that searching for optimal points through time to reset asset allocation may not be terribly productive after all. Let’s continue to probe this line of analysis by reviewing the results of randomly changing asset weights for testing rebalancing strategies.

I’ll use the same 11-fund portfolio that’s globally diversified across key asset classes with a starting date of Dec. 31, 2003. The benchmark strategy is simply rebalancing the portfolio at the end of each year back to the initial weights, as defined in the table below.

Let’s assume that the benchmark strategy is someone’s best effort at portfolio design. Our fictional investor—let’s call him Ronald–has thought long and hard about asset allocation and decided that the portfolio mix above is the way to go. Ronald has back-tested the strategy with actual data with the funds listed above and thinks that the results are encouraging. A $100 investment at the start date (Dec. 31, 2003) increased to just over $200 as of Oct. 2, 2015. Ronald concludes that the portfolio’s 100% cumulative gain over the sample period is pretty good. He pats himself on the back and goes out for a celebratory dinner, confident that he’s built a winning portfolio. In other words, Ronald’s convinced that he possesses a fair amount of skill in the art/science of building and managing portfolios through time.

While Ronald’s away at the Overconfidence Café, let’s analyze his portfolio design by comparing it with random portfolios. We’ll use the same funds in the table above but randomly vary the weights for each of the portfolio’s assets. To ensure a fair test, we’ll keep the random weights within the same range in the table above—a minimum of 5% up to a maximum of 25%. Using R (you can find the code here), we’ll create 1,000 portfolios, each with a randomly selected mix of different weights for the 11 funds. To match Ronald’s portfolio, the strategies are 1) rebalanced back to the randomly selected target weights at the end of each year; 2) are always invested in each fund in some degree; 3) but no shorting or leverage is allowed. In sum, the random portfolios are identical to Ronald’s strategy with one exception: the asset weights are allowed to wander within a 5%-to-25% range.