10-19The Risk-Return TradeofThe general rule:◦The more volatile (or risky) a return is, the greater the return will be expected to be.
10-20Risk StatisticsThere is no universally agreed-upon definition of risk.The measures of risk that we discuss are variance and standard deviation.◦Variance and standard deviation measure the dispersion of actual returns around the security’s mean return◦The standard deviation is the standard statistical measure of the spread of a sample, and it is the measure used in most cases.◦Its interpretation is facilitated by a discussion of the normal distribution.
10-21Normal DistributionA large enough sample drawn from a normal distribution looks like a bell-shaped curve.ProbabilityReturn on large company common stocks99.74%– 3– 48.8%– 2– 28.6%– 1– 8.4%011.8%+ 132.0%+ 252.2%+ 372.4%The probability that a yearly return will fall within 20.2 percent of the mean of 11.8 percent will be approximately 2/3.68.26%95.44%
Normal DistributionThe return of large company stocks has a standard deviation of 20.2 from 1926 through 2012.That standard deviation can be interpreted as follows:
10-23Variance and Standard Deviation23
EXAMPLE – RETURN AND VARIANCEYearActual ReturnAverage ReturnDeviation from the MeanSquared Deviation1.15.105.045.0020252.09.105-.015.0002253.06.105-.045.0020254.12.105.015.000225Totals.00.0045Variance = .0045 / (4-1) = .0015 Standard Deviation = .0387310-24Average Return = (15 + 9 + 6 + 12) / 4 = 10.5