## Absolute Risk Measurement

Risk is a complex concept, and some controversy surrounds attempts to define and measure it. Common risk measures that are satisfactory for most purposes are based on the observation that tight probability distributions imply low risk because of the correspondingly small chance that actual outcomes will differ greatly from expected values. From this perspective, project A is less risky than project B.

Standard deviation, shown as ct (sigma), is a popular and useful measure of absolute risk. Absolute risk is the overall dispersion of possible payoffs. The smaller the standard deviation, the tighter the probability distribution and the lower the risk in absolute terms. To calculate standard deviation using probability information, the expected value or mean of the return distribution must first be calculated as n

In this calculation, ni is the profit or return associated with the ith outcome; pi is the probability that the ith outcome will occur; and E(n), the expected value, is a weighted average of the various possible outcomes, each weighted by the probability of its occurrence.

The deviation of possible outcomes from the expected value must then be derived:

The squared value of each deviation is then multiplied by the relevant probability and summed. This arithmetic mean of the squared deviations is the variance of the probability distribution:

absolute risk

Overall dispersion of possible payoffs

The standard deviation is found by obtaining the square root of the variance:

The standard deviation of profit for project A can be calculated to illustrate this procedure:

Deviation

Deviation2

Deviation2 X Probability

\$4,000 - \$5,000 = -\$1,000 \$5,000 - \$5,000 = 0 \$6,000 - \$5,000 = \$1,000

\$1,000,000 \$1,000,000(0.2) = \$200,000 0 \$0(0.6) = \$0 \$1,000,000 \$1,000,000(0.2) = \$200,000

Standard deviation = ct = "MCT2 = -»\$400,000 = \$632.46

Using the same procedure, the standard deviation of project B's profit is \$3,826.23. Because project B has a larger standard deviation of profit, it is the riskier project.

relative risk

Variation in possible returns compared with the expected payoff amount 