2.2 Risk of a Single Asset

Where will the seagull go? Will it fly toward the sea, turn around and walk away? Will it look your way or look to the surf? This range of possibility is one way to see risk. Observing how oftne the bird flies away, compared to how often it stays can provide us a measure of risk.

This section considers some mathematical ways of measuring volatility -- and thus risk.

2.2.1 - Probability distribution

Assessing the risk of a single asset requires that we have some sense for the range of possible outcomes. For example, a judge sentencing a youthful offender might consider different scenarios: (1) worst case (pessimistic), the offender will commit only another minor crime; (2) expected case (normal), she will commit no more crimes; (3) best case (optimistic), she will dissuade other youth from committing crimes. Given this distribution, what should the judge do? (More 2.2.1>>)

2.2.2 - Expected return

What is the expected return when you roll two dice? Suppose the number you throw represents the return, and suppose you throw the dice thousands of times. What would you expect your return to be on average? We can compute the expected return for each possible result and then sum these results. (More 2.2.2>>)

2.2.3 - Standard deviation (s)

Variability can be measured. That is, risk can be quantified! The most common measure of risk is the standard deviation -- a numerical measure of the dispersion around the expected value. Here is how the standard deviation is calculated for our two dice probability distributions: (More 2.2.3>>)

2.2.4 - Normal distribution

If a dice-throwing distribution were normally distributed (a classic "bell curve"), a standard deviation indicates the percentage of likely results around the mean. Specifically, 38.3% of all returns are within one-half standard deviation of the expected return; 68.3% of all returns are within one standard deviation of the average return, and 95.4% of the returns are within two standard deviations of the average return. The larger the standard deviation, the greater the dispersion and the greater the risk. (More 2.2.4>>)

2.2.5 - Coefficient of variation

What happens when there are two distributions with different expected returns? How do you decide which distribution involves greater dispersion and thus greater risk? For example, suppose you are presented with two investment strategies. (More 2.2.5>>)

Whence the seagull?