Risk reduction through Diversification

If we are buying shares in the same market (i.e. the same stock exchange) then although the systematic risk in each share will be different, in cannot be diversified away because all shares in that market move up and down together. However, if you can create a portfolio of shares in different markets then in theory it might be possible to diversify the systematic risk away, because different markets might move in different ways. But, because of increasing globalisation (e.g. companies like Apple trading world wide) the markets in different countries tend more and more to move in the same way - this makes international diversification of systematic risk less likely.