So far in this lesson, you’ve learned how to use optimization techniques to come up with optimal portfolio weights. Is your job done? Not really. As a portfolio manager, the next step after portfolio construction, is to constantly monitor your portfolio, and make sure it is in line with your goals. Over time, assets produce returns that can differ from those originally estimated. So, the amount of money invested in different assets, changes. Therefore, the portfolio weights, which represent the proportion of money invested in each asset, change. In order to make sure the portfolio maintains the desired set of weights, we need two rebalance. For example, say we started with a strategy in which we wanted to invest 50% of our portfolio in a solar energy company and 50% in a construction company. Let’s say the solar energy company does really well and it’s value appreciates such that the shares we’ve invested in it, now represent 70% of the value of our portfolio. If we wanted to return to the 50% in a solar energy company and 50% in the construction company, we’d sell some shares of the solar energy company, and buy some shares of the construction company to bring us back to 50-50. When you have determined your portfolio weights via optimization and later want to rebalance, you simply re-run the optimization with the same objective function and constraints, but using updated data. Before we discuss different rebalancing strategies, let’s consider the costs incurred during rebalancing. Think about it, when you rebalance, you place trades. To place trades, you generally have to pay a broker commissions. These commissions are one type of transaction costs. Transaction costs, are probably the most important costs incurred during rebalancing. But, there are others, such as taxes, like capital gains taxes and the administrative costs of time and labor. Transaction costs can be potentially significant. In the year 2000, the Texas Permanent School Fund rebalanced its portfolio of more than 2,000 securities, 40 portfolio managers, 500 million shares, and $17.5 billion were involved not including administrative costs, the transactions themselves costs $120 million. Now, you can see how crazy transaction costs can be. In general, it’s hard to model transaction costs directly. To know the transaction costs, you must know what the trade is. But the whole reason to do the optimization, is to know what the trade is. So, instead of trying to estimate transaction costs, we can make the assumption that transaction costs will be proportional to the magnitude of change in the holdings. This is called portfolio turnover and it’s basically, the sum total of the changes in the weights on all the assets. To calculate turnover between two time periods, you would take the absolute value of the difference in weight between two time periods for each asset, and then sum these over assets. To get an annualized turnover, you would calculate the average turnover per rebalancing event by calculating, total turnover for all the rebalancing events in the timeframe you’re considering, and dividing by the number of rebalancing events, and then multiplying by the number of rebalancing events per year.