remained the same over the last three months? 3. Have real interest rates increased, decreased or remained the same over the last two years? 4. Examine the information comparing recent U.S. inflation and long-term interest rates with the inflation and long-term interest rate experience of Japan. Are the results consistent with theory? II. Portfolio Theory 6. Risk and Risk Aversion The McGraw−Hill Companies, 2001           C H A P T E R S I X       RISK AND RISK AVERSION       The investment process consists of two broad tasks. One task is security and mar- ket analysis, by which we assess the risk and expected-return attributes of the en- tire set of possible investment vehicles. The second task is the formation of an optimal portfolio of assets. This task involves the determination of the best risk- return opportunities available from feasible investment portfolios and the choice of the best portfolio from the feasible set. We start our formal analysis of invest- ments with this latter task, called portfolio theory. We return to the security analy- sis task in later chapters. This chapter introduces three themes in portfolio theory, all centering on risk. The first is the ba- sic tenet that investors avoid risk and demand a reward for engaging in risky investments. The reward is taken as a risk premium, the difference between the expected rate of return and that available on alternative risk-free in- vestments. The second theme allows us to quantify investors personal trade- offs between portfolio risk and ex- pected return. To do this we introduce the utility function, which assumes that investors can assign a welfare or "util- ity" score to any investment portfolio depending on its risk and return. Fi- nally, the third fundamental principle is that we cannot evaluate the risk of an asset separate from the portfolio of which it is a part; that is, the proper way to measure the risk of an individual asset is to as- sess its impact on the volatility of the entire portfolio of investments. Taking this approach, we find that seemingly risky securities may be portfolio stabilizers and actually low-risk assets. Appendix A to this chapter describes the theory and prac- tice of measuring portfolio risk by the variance or standard deviation of returns. We discuss other potentially relevant characteristics of the probability distribution   154