Systematic versus Non-Systematic Risk
With respect to any given securities market there exists Sytematic Risk and Non-Systematic Risk.
Systematic Risk
Systematic risk is the general ebb and flow of the market as a whole - or the tendency for all stocks to increase or decrease in value at the same time with a certain degree of positive correlation. For example, ‘Black Monday’ on October 19th, 1987 was a Systematic event in that almost all stocks fell in value on that single day. Macro-economic events and stimuli can be expected to have broad systematic effects on capital markets - positive or negative - on an on-going basis such as interest rate levels, political events, war, etc. It is important to note that systematic risk cannot be diversified away. In other words, you could have a portfolio that is diversified with 1000 different stocks from a given market and there will always be a base level of return variance (shown as the asymptote in the figure below).
Non-Systematic Risk
Non-Systematic risk is the element of price risk than can be largely eliminated through sufficient diversification within a particular asset class. The best way to describe it is to build an analogy. Let us assume you owned one stock - if that company went bankrupt you will have lost 100% of your portfolio. If you owned one hundred stocks, and one company went bankrupt you would have lost 1% of your portfolio. Conversely, what if that one company doubled in value? You either doubled your money or only gained 1% if you held 1 stock or 100, respectively. Non-Systematic risk is the individual business risk associated with the underlying stock - if this company goes bankrupt - this is a non-systematic risk event and generally has very little to do with the general ebb and flow of the overall markets.
(You can click on the graph for a larger view)
It is generally debated as to how many securities one needs to hold to eliminate non-systematic risk. Research has shown that between thirty and forty securities are enough to eliminate non-systematic risk.
A rational investor would be expected to take measures to eliminate non-systematic risk from one’s portfolio by increasing the number of holdings within each distinct asset class - a task that is easily accomplished through asset class indexing products which may routinely hold hundreds of asset class constituents.

