Let us consider a portfolio of homeowners and automobile insurance policies. There are 1000 homeowners policies sold, and 2000 auto policies sold by an insurer. The data on each risk and correlations is as follows:

Auto policies: Mean loss = $500, Standard deviation of losses = $700, correlation among auto risks = 0.1

Homeowners (HO) policies: Mean loss = $300, Standard deviation of losses = $400, correlation among auto risks = 0.2

The cross correlations between the Auto and HO policy = 0.005.

What is the mean loss on the entire pool of auto and HO combined (portfolio) together?

What is the standard deviation of the mean loss per policy?