who has just been successful in an investment wants to take credit for the good decisions that created this result and to think of the result as being an almost inevitable consequence of the investor's good decisions rather than to recognize that the outcomes of investment decisions, no matter how good, are, at least in the short run, usually very much a function of luck. Consider an investor in the situation just described. Such an individual is certainly not typical. He or she has just joined the elite group of people who have experienced the closest equivalent in the business world to winning the lottery. This individual is among the lucky few with a concentrated risk position whose companies have survived, grown profitably, and at an opportune time have been sold to the public. In retrospect, the actions taken by these individuals to create their wealth-the hard work, the business acumen, and in particular the holding of a concentrated position-might seem unassailable. We might even suppose that other investors should emulate their actions and enter into one or more such illiquid concentrated positions. However, there is a bigger picture. Many small business owners have businesses that fail to create significant wealth. Just as in a lottery, the fact that there are a few big winners does not mean that a good outcome is always the result of a good investment choice. Granting that there may be many psychic benefits of being a small business owner with a highly concentrated investment in one business, it is nonetheless typically a very risky investment situation to be in. When a single business represents a significant fraction of one's investment portfolio, there is an avoidable concentration of risk. The simplest and most practical insight from modern portfolio theory is that investors should avoid concentrated sources of risk.9 Concentrated risk positions ignore the significant potential risk reduction benefit derived from diversification. While it is true that to the extent that a particular investment looks very attractive it should be given more of the overall risk budget, too much exposure can be detrimental. Portfolio theory provides a context in which one can quantify exactly how much of an overall risk budget any particular investment should consume. Now consider the investors who put all of their wealth in money market funds. There is nothing wrong with money market funds; for most investors such funds should be an important, very liquid, and low-risk portion of the overall portfolio. The problem is that some investors, uncomfortable with the potential losses from risky investments, put too much of their wealth in such funds and hold such positions too long. Over short periods of time, money market funds almost always produce steady, positive returns. The problem with such funds is that over longer periods of time the real returns (that is, the purchasing power of the wealth created after taking into account the effects of inflation and taxes) can be quite risky and historically have been quite poor. Modern portfolio theory has one, and really only one, central theme: In constructing their portfolios investors need to look at the expected return of each investment in relation to the impact that it has on the risk of the overall portfolio. We will come back to analyze in more detail why this is the case, but because it is, the practical message of portfolio theory is that sizing an investment is best understood ^Unfortunately, in the years 2000 and 2001 many employees, entrepreneurs, and investors in technology, telecommunications, and Internet companies rediscovered firsthand the risks associated with portfolios lacking diversification.