Portfolio Construction - Data: (Uniform Number of Observations Problem) HELP!

Hello there,

I'm currently setting out on doing an assignment for a portfolio theory class.

We have been allocated 15 stocks listed on the ISEQ (Irish Stock Exchange) and a choice of indices to choose from - the overall index, financial sub-index and 'other'/general sub-index.

The period of monthly observations of return data we have been given stretches back from 2016 to 1986 (~400 observations). However, I am like a rabbit caught in the headlights from the get-go for the following reason:

Most of the stocks I have been allocated do not have observations listed for the full period 1986-2016 since they have been listed at different times over the past twenty years. One stock in particular only has 60 observations and is extremely 'blocky' in its returns characteristics.

How do I therefore, with such little data/observations for some stocks, proceed? How does industry get around this problem?

I see this being a problem when calculating covariances - should I use the full array (~400 of observations) of one stock (for variance calculations) against the 60 observations of this problematic stock when calculating the variance co-variance matrix.

My logic is telling me I must compare like with like and cut my observations across my stock selection to 60 observations - but am I not sacrificing descriptive power in my outputs if I do this?

Any portfolio managers out there who knows how to deal with this problem - I'd love to hear from you!

My humblest thanks and best wishes,

Squeezebox.