# Can simple risk management outperform portfolio optimization like this, or is there most likely an error?

I am using a simulation approach to compare the performances achievable by simple risk management and portfolio optimization for portfolio selection. My problem is that my results indicate that simple risk management outperforms portfolio optimization. Is this possible or is there most likely an error in my simulation?

My simulation approach is as follows. Assume there are N different assets in the universe, each of which is assigned to one of K groups, based on some properties. For each of these assets I have daily returns data for a two-year period. Each iteration in the simulation randomly selects one asset from each of the groups. I.e., K assets are selected and will be assigned a weight in $$[0, 1]$$ Then, each asset is assigned a weight. The mean-variance approach calculates the optimal weights based on the daily returns data. The naive approach simply assigns the weight $$1/M$$ to each of the assets in the portfolio. This gives the portfolio returns, from which I calculate annualized portfolio volatility. The results are shown in the table below. Could these results be feasible or could it be that I made a mistake somewhere (e.g., mixed up the column names, incorrectly multiplied returns with weights, etc.)?

Edit: the optimal portfolio is the one with minimal variance over all returns.

• What is your optimal portfolio, exactly? Is it supposed to be the minimal variance portfolio over all possible returns? If so, the only explanation left besides an error is estimation error. Your naive method doesn't require any estimation, but a mean-variance optimization requires a covariance matrix which can be poorly estimated... With K assets, you're talking about K first moments plus K(K+1)/2 second moments, so it can quickly be A LOT to demand from data. But, then again, I have no idea what you're doing in your simulation. – Stéphane May 25 at 23:16
• yes, I use the minimal variance portfolio over all possible returns as the optimal portfolio – Ali Mustafa May 26 at 4:48
• Are you comparing the sample in-sample or out-of-sample? In-sample it might be due to the estimation errors, out-of-sample i would bet Naive diversification would beat mean-variance most of the times, refer to this study papers.ssrn.com/sol3/papers.cfm?abstract_id=2713501 – Dhruv Mahajan May 26 at 8:30
• Year 1 is in-sample, while year 2 is out-of-sample. – Ali Mustafa May 26 at 15:57
• Are the vols in the table in %? It looks a bit suspicious that out-of-sample vols are larger than in-sample vols. What is the size of N and K in your simulation? – Pontus Hultkrantz May 26 at 19:44