understand and be comfortable with taking risks. Creating wealth is the object of making investments, and risk is the energy that in the long run drives investment returns. Investor tolerance for taking risk is limited, though. Risk quantifies the likelihood and size of potential losses, and losses are painful. When a loss occurs it implies consumption must be postponed or denied, and even though returns are largely determined by random events over which the investor has no control, when a loss occurs it is natural to feel that a mistake was made and to feel regret about taking the risk. If a loss has too great an impact on an investor's net worth, then the loss itself may force a reduction in the investor's risk appetite, which could create a significant limitation on the investor's ability to generate future investment returns. Thus, each investor can only tolerate losses up to a certain size. And even though risk is the energy that drives returns, since risk taking creates the opportunity for bad outcomes, it is something for which each investor has only a limited appetite. But risk itself is not something to be avoided. As we shall discuss, wealth creation depends on taking risk, on allocating that risk across many assets (in order to minimize the potential pain), on being patient, and on being willing to accept short-term losses while focusing on long-term, real returns (after taking into account the effects of inflation and taxes). Thus, investment success depends on being prepared for and being willing to take risk. Because investors have a limited capacity for taking risk it should be viewed as a scarce resource that needs to be used wisely. Risk should be budgeted, just like any other resource in limited supply. Successful investing requires positioning the risk one takes in order to create as much return as possible. And while investors have intuitively understood the connection between risk and return for many centuries, only in the past 50 years have academics quantified these concepts mathematically and worked out the sometimes surprising implications of trying to maximize expected return for a given level of risk. This body of work, known today as modern portfolio theory, provides some very useful insights for investors, which we will highlight in this chapter.