Quantitative Portfolio Optimisation and Efficient Portfolios

Abstract

In the previous chapter we demonstrated that there exist natural and automatic diversification effects from adding ever more stocks to a portfolio. Because the returns on assets are only very infrequently perfectly correlated, including several assets in a portfolio will tend to reduce overall portfolio risk: and generally speaking, the more stocks are included, the lower the portfolio risk. There is, however, an obvious downside to this approach. A very large number of stocks in a portfolio will entail larger transaction costs, particularly if the portfolio is expected to be turned over a few times during a year. In addition, the more stocks the portfolio manager includes in the portfolio, the more difficult it will be for him to ‘tilt’ it purposefully towards certain factors or characteristics that he deems might perform better than average in the future. In other words, the ability to precisely control the characteristics of the portfolio, and thereby its expected cash flow, is degraded as the number of stocks in the portfolio becomes very large. Finally, it can become quite a task for a portfolio manager to have to keep a close eye on a large number of stocks, so it is obvious that the risk of adverse performance from a single stock increases with a large number of stocks.KeywordsEfficient FrontierSharpe RatioAsset AllocationPortfolio ReturnAsset ClassThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.