I once tried to follow a client's system for tracking share and mutual fund data in their Simply Accounting G/L. It did work, but it was a lot of work and the results weren't great - a bit like cutting plywood with a ball peen hammer. 

I suppose one could try using the Inventory module to keep track of the stocks purchased and sold as inventory items:

Since an invoiced purchase is recorded into inventory dollar for dollar, and the cost of a sale is based on historical cost:

 - Purchases would show as the asset value, 
 - Sales would reduce 'inventory' stock on hand value by the exact calculated cost.

If you wanted to 'use up' the oldest stocks at their historical cost, you would use FIFO. If you wanted to 'use up' the stock at average cost, you would use Average Cost.    
 
You could update selling prices in the 'price list', and see an overview of  your portfolio in the Inventory Summary report. (cost, (regular) price, and Margin %
 
It would be a little smoother - maybe like switching to cutting plywood with an axe, so less 'sanding off rough edges'.

BUT... Even though I've used Sage 50 since it ran off a floppy diskette, I use 'Quicken.' for my personal finance because my time is limited.