# How can I compose a graph of historic data of some arbitrary benchmark?

My company provides pension saving plans through the Great-West Life. They have all bunch of mutual funds and all bunch of PDFs with all bunch of data, including a comparison chart with a so called benchmark.

A benchmark could be just `S&P/TSX Composite Index` or it could be a mix of, for example:

• 53.6% S&P/TSX Composite Index
• 35.7% MSCI World Index
• 10.7% DEX Universe Index

Now, I would like to be able to build this benchmark graph myself and compare it with, `100% S&P/TSX Composite Index`, for example.

Is there a way to do so?

Using the sample benchmark you described, you would need the monthly return rates for the 3 indexes. You would also need the monthly weightings for the 3 indexes (assuming these weights vary over time). Then calculate the weighted average return for each month.

e.g. weighted average ROR = (1% ROR * 0.536) + (2% ROR * 0.357) + (1.5% ROR * 0.107).

It's not entirely accurate because in reality the weightings will vary each day, but should be close enough.

I picked 'by month' arbitrarily - you might be happy to do it yearly. But yearly will be less accurate because the weightings will vary more over the year.

The data points for your graph will not be the weighted average RORs, but instead the CUMULATIVE weighted average RORs. e.g.

Starting point to graph = 100.

Month 1: ROR = 1.02, Cumulative ROR = 100 * 1.02 = 102

Month 2: ROR = 1.03, Cumulative ROR = 102 * 1.03 = 105.06

Month 3: ROR = 1.025, Cumulative ROR = 105.06 * 1.025 = 106.085

etc.

This 'cumulative' graph will show you how an investment of \$100 grows each month.