Rebalancing is when an investor decides to “rebuild” their portfolio. This is done through buying additional amounts of stocks currently in your portfolio, adding new stocks into your portfolio and/or selling off some your currently held stocks. This means the weights assigned to an asset, as previously discussed, will likely change. Rebalancing can be done for a number of reasons. Maybe an investor has decided their portfolio is doing well and wants to sell some of their stock, but wants to know how much of each stock they should still keep. Alternatively, maybe after holding a stock for a long period of time, they no long expect the stock to continue to perform as well in the future, and want to decrease the weight.
Regardless of reason, the rebalancing process is very commonly done at pre-defined intervals, such as every six months or every year. Larger quant trading or algorithmic trading firms commonly rebalance at least every day, if not more frequently. In the case of these firms, if they are expecting a stock price to go down, even just for a short period of time, they will sell off that stock, and put the money into other assets.
When rebalancing is considered in our model, the weights placed on assets are now subject to change throughout the simulation. At the most simple level we can treat each rebalancing period as a separate optimization problem. For example, if we are rebalancing every six months in a two year simulation, we could solve an optimization sub-problem that only uses predictions for the first 6 months. Then we solve another optimization problem using predictions for months 7-12, and so on. Once we have solved optimization problems for the entire two year simulation period, we can combine the results of the four smaller optimization sub-problems. The total portfolio risk can be taken as the square-root of the sum of the variances of portfolios from the sub-problems. The total portfolio return can be calculated as the sum of portfolio returns from the sub-problems.