(This article was first published on

**Speaking Statistically**, and kindly contributed to R-bloggers)

__(Obligatory Warning: This post should not be considered investment advice. The author(s) of this blog are not certified financial analysts. Any analysis presented here is meant only as an opinion. Following our opinion could end up losing you a lot of money.)__None of what I said in the last post in this series should come as a surprise to anyone that is familiar with finance. Indeed, we did that exercise just to validate our data and make sure we were on the right path.

For our main results, we choose efficient frontier portfolios based on data from 1990-2005 and then hold the portfolios from 2005-2010 and plot the returns and variances of these efficient portfolios. We also simulate random portfolios by taking a random weight of stocks from the universe and hold them for the testing period.

Efficient Portfolios vs. Simulated Portfolios and Individual Stocks (Training 1990-2005, Testing 2005-2010). |

From the figure we see that:

- Efficient Portfolios from higher rate of returns initially tend to do poorly in the testing period. This is probably because those portfolios have very high weights of some stocks that have done exceptionally well in the training period. Unfortunately, these stocks then don’t do well in the testing period.
- Random portfolios (blue cloud in the figure) beat efficient frontiers in terms of return vs. variance for higher returns. For lower returns, it seems that efficient frontier portfolios have very low variance compared to random portfolios and individual stocks.

**Different Holdout and Training Periods**

We tested different training periods and holdout periods as well as different rebalancing frequencies with no meaningful difference in results. We also did some tests to avoid the 2008-2010 time period (and the associated financial crisis). Our results hold in that circumstance as well.

**Conclusions:**

- Choosing efficient frontier portfolios don’t help if you want high returns. If you’re a cautious investor (think people nearing retirement, some institutional investors, etc.), however, it makes sense to choose efficient frontier portfolios with lower required rate of returns. These portfolios have lower variance compared to random portfolios and individual stocks with the same rate of return.
- Perhaps incorporating some reversion to the mean or mandating a diverse selection for the high returns could produce more sensible optimal portfolios at the higher levels.

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