236 THE HANDBOOK OF PORTFOLIO MATHEMATICS
of a holding period, the period we measure returns and their variances, as
one year in this example:
Expected Variance
Investment Expected Return of ReturnToxico 9.5% 10%
Incubeast Corp. 13% 25%
LA Garb 21% 40%
Savings Account 8.5% 0%We can express expected returns as HPRs by adding 1 to them. Also, we
can express expected variance of return as expected standard deviation of
return by taking the square root of the variance. In so doing, we transform
our table to:
Expected Return Expected Standard
Investment as an HPR Deviation of ReturnToxico 1.095 .316227766
Incubeast Corp. 1.13 .5
LA Garb 1.21 .632455532
Savings Account 1.085 0The time horizon involved is irrelevant so long as it is consistent for
all components under consideration. That is, when we discuss expected
return, it doesn’t matter if we mean over the next year, quarter, five years,
or day, as long as the expected returns and standard deviations for all of
the components under consideration all have the same time frame. (That
is, they must all be for the next year, or they must all be for the next day,
and so on.)
Expected return is synonymous withpotential gains, while variance (or
standard deviation) in those expected returns is synonymous withpotential
risk.Note that the model is two-dimensional. In other words, we can say that
the model can be represented on the upper right quadrant of the Cartesian
plane (see Figure 7.4) by placing expected return along one axis (generally
the vertical or Y axis) and expected variance or standard deviation of returns
along the other axis (generally the horizontal or X axis).
There are other aspects to potential risk, such as potential risk of (prob-
ability of) a catastrophic loss, which E–V theory does not differentiate from