Risk and Volatility: Econometric Models and Financial Practice

The advantage of knowing about risks is that we can change our behavior to avoid them. Of course, it is easily observed that to avoid all risks would be impossible; it might entail no flying, no driving, no walking, eating and drinking only healthy foods and never being touched by sunshine. Even a bath could be dangerous. I could not receive this prize if I sought to avoid all risks. There are some risks we choose to take because the benefits from taking them exceed the possible costs. Optimal behavior takes risks that are worthwhile. This is the central paradigm of finance; we must take risks to achieve rewards but not all risks are equally rewarded. Both the risks and the rewards are in the future, so it is the expectation of loss that is balanced against the expectation of reward. Thus we optimize our behavior, and in particular our portfolio, to maximize rewards and minimize risks. This simple concept has a long history in economics and in Nobel citations. Markowitz (1952) and Tobin (1958) associated risk with the variance in the value of a portfolio. From the avoidance of risk they derived optimizing portfolio and banking behavior. Sharpe (1964) developed the implications when all investors follow the same objectives with the same information. This theory is called the Capital Asset Pricing Model or CAPM, and shows that there is a natural relation between expected returns and variance. These contributions were recognized by Nobel prizes in 1981 and 1990. Black and Scholes (1972) and Merton (1973) developed a model to evaluate the pricing of options. While the theory is based on option replication arguments through dynamic trading strategies, it is also consistent with the CAPM. Put options give the owner the right to sell an asset at a particular