2

I am trying to see how diversified a **portfolio** is, using the portfolio holdings weights and their return streams.

For example, let's say that the portfolio has $3$ stocks, so I will have the $3x1$ W (weight) matrix and $3x3$ correlation matrix C.

The following matrix multiplication $W^T * C * W$ will result in a single number that tells you how diversified the portfolio is. The bigger the number, the less diversified and vice versa.

One challenge is that the stocks may have **different time periods**. For example, stock A may have $3$ months of data, stock B may be $5$ months of data and stock C may have 1 year of data. Using the naive, standard correlation function will use the common date ranges between the stock pairs and calculate correlations.

This may be a problem if the date ranges are extremely different (e.g. stock A may be $1$ month of data, while stock B and C may have 5 years of data), which will skew the result number.

Is there a name for this phenomenon? What kinds of techniques are out there to solve this kind of problem?