If CDO's collect all the cashflows from their underlying assets and then pay them out to the CDO investors whats the need for a reinvestment period? and where is the principal that is being reinvested coming from?
Let's say a CDO invests in bonds and runs for 10 years. Not all the assets e.g. bonds it buys initially will have a lifetime of 10 years, many will have shorter durations. While the assets are paying interest that is used to pay the investors in the CDO.
At some point prior to the end of the duration of the CDO though, some of the assets will end their duration, at that point those assets repay their principal. The CDO manager must then reinvest that principal payment into other assets so that the CDOs cashflow continues to be generated.
The reinvestment period will be shorter than the entire lifetime of the CDO because at some point it won't make sense to buy assets as they will need to be shorter and shorter dated so they don't overrun the CDO lifetime.