Reinvesting of profits is essential for an investment to compound. If a client does not withdraw gains from his account, the gains are eventually reinvested by increasing the size of the trades that are allocated to the client's account.
An example will clarify the reinvesting process. Let's say that a client has had a great month in a managed account program and is up 10% by month's end. This means that if his account was at $10,000 one month earlier, it would be at $11,000 one month later. Now, let's say that when the account was at $10,000, the size of trades allocated to that account were 0.2 lots (please see the education section for an explanation of "lots" and other basic concepts). This means that at the end of the month, the trade size would be bumped up to approximately 0.22 lots per trade (or 10% more than the starting size).
Please note that the prior example was simplified for clients to understand the reinvesting/compounding process clearly. In reality, the trade size might not be increased every time that a profitable trade is realized or even at the end of every month. The portfolio manager has discretion over exactly when the trade sizes should be adjusted based on the resulting gain or loss accumulated; in other words, the trade size readjustment is not necessarily implemented in a robotic way (although some fully-automated programs might use auto trade size adjustment).
Slower Growth When Profits are Withdrawn from the Account
Not every investor is the same or has the same needs or financial objectives. Some investors like to leave their accumulated profits in their accounts so they could compound, while some prefer to make periodic withdrawals of their profits (most commonly on a monthly basis). This is totally up to the discretion of the investor; but one thing remains true: if an investor withdraws profits from his account, the account will compound at a slower rate than the account of an investor who allows all profits to be reinvested. The more profits an investor withdraws from his account, the slower the overall compounding rate of his managed portfolio will be.