CHAPTER 5: UNDERSTANDING RISK
Core Principle 2, risk requires compensation, is the focus of Chapter 5. Risk is
defined as a measure of uncertainty about the future payoff to an investment over a
specific time horizon relative to a benchmark. Much of the discussion in the text deals
with risk as it applies to financial instruments, though nonfinancial examples are
everywhere. For example, you risk being hit by a car crossing the street after class.
Two measures of risk are introduced: the variance of the returns on an asset and
the value at risk. You probably know the concept of the variance: the sum of probability-
weighted squared deviations of all the possible outcomes from the expected outcome.
The value at risk is, roughly, the worst-case scenario which occurs with a given
probability. And both concepts might be applied to the same issue. For example,
monetary policy might primarily focus on output fluctuations (that is, smoothing out the
ups and downs of the business cycle or, technically, minimizing the variance of output
over time) but also want to avoid a repeat of the Great Depression, a “worst-case” event.
The definition of risk also refers to time since, as you learned in chapter 4, time
has value (Core Principle 1). For instance, as you save for retirement, you have risk that a
low return over roughly a 40-year professional career will leave you with a retirement
portfolio that will not support you when you want to retire. This is a concern since funds
you invest today may earn high, low, or moderate returns over the period – that’s the
uncertainty referred to in the definition of risk.
The concept of risk is only half of Core Principle 2. The other half is that risk
requires compensation. Suppose you own an insurance agency that issues automobile
policies. Some of your clients have never had an accident, while others have had quite a
few. Would you charge each type the same premium for a given amount of coverage?
Those with many accidents represent, on average, a bigger risk to your company in terms
of claims payouts than those with no accidents. So you’d probably charge the reckless
drivers higher premiums; risk requires compensation. (If you charged the same premiums
to both types, the good drivers would likely find a company that discounts the premiums
of drivers with clean accident histories. Then you’d be left with just the reckless drivers.)
DISCUSSION/EXTENSIONS OF THE BASICS
Review of Basic Statistical Concepts
: Risk, both its measurement and many of its
applications, is often thought about in terms of basic statistical techniques. One key
concept, the variance, is presented in appendix 5B on text page 123 in equation (A4).
While we will discuss this concept in a moment, the idea of an expected value is needed