1. In-sample vs. out-of-sample evaluation
I've got some good news and some bad news for you.
2. Bad news: estimation error
The bad news is that the efficient frontier you just obtained is too good to be true. It is based on optimizing the estimated variance under a constraint on the estimated expected return.
3. Bad news: estimation error
Ideally, it should, however, be based on the true portfolio variance and the true portfolio expected return. Because of the errors in the estimation of the mean and variance, there is also an estimation error in terms
4. Bad news: estimation error
of the optimized weights. Depending on the magnitude of the errors, the optimized portfolio weights could thus be far from being optimal.
5. Good news: opportunities
The good news is that this makes portfolio management challenging, and by doing the right data analysis, you can beat the other more naive investors who are ignoring the estimation error.
In this last video, I will teach you to use split-sample analysis to evaluate in an objective way what the future performance of the optimized portfolio could be.
As you probably can guess, the split-sample analysis consists of splitting the sample of historical returns in two parts.
6. Good news: opportunities
The first part is called the estimation sample and will be used
7. Good news: opportunities
to estimate the mean returns and the covariance matrix, used to optimize the portfolio.
8. Good news: opportunities
The second part is the out-of-sample evaluation sample. It is the sample of returns that is used to evaluate the performance of the optimized portfolios.
When doing the split sample, we mimic the investor who, at the end of the estimation sample, decides to invest and to use the weights optimized using the data in the estimation sample.
By separating the estimation sample and the evaluation sample, we thus give a realistic assessment of the performance of the portfolio.
9. No look-ahead bias in optimized weights
It is crucial that there is no overlap between the estimation sample and the evaluation sample. Otherwise, there is a look-ahead bias. This means that we are optimizing the portfolio using more information than we actually
10. No look-ahead bias in optimized weights
have at the time of the investment decision. Such a look ahead bias leads to a too optimistic view on how good the optimized portfolio performs in real-life. In R, split-sample analysis is made simple with the function window in the package xts. Let’s find out how that works in practice.
11. Let's practice!