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280 NATURE OF CAPITAL AND INCOME [Cmar. XVI

cult to state what the riskless rate of interest is, since some
slight risk attaches to almost every investment. Accordingly
 it is usual to regard the commercial rate as a true
“rate of interest.” The best course, therefore, is to recognize
 all three as rates of interest, distinguishing them,
when necessary, as “riskless,” “mathematical,” and
“commercial. ”’

§9

When we speak of the riskless value or the riskless rate,
we intend by the employment of the word “riskless,”
to exclude from consideration the chance element entirely
— not only the risk of receiving less, but also the chance of
receiving more than the specified income. For cases are
not wanting in which the mathematical and commercial
values of a security are, by reason of the chance that it
will prove extra-profitable, more than its riskless value.
Take, for instance, a $100 share of preferred stock, on
which a minimum income of 5 per cent, or $5, is assured.
If the true rate of interest be 4 per cent, the value of such
stock should be $125. This is the “riskless’ value. The
mathematical value, however, will be greater, say $150,
inasmuch as there is a probability that the holder will
receive more than $5 a year, and practically no probability
 that he will receive less. And the commercial value
will be still different, falling, by reason of the caution of
the investor, somewhat below the mathematical, say to
$130.
Another instance is that of United States government
bonds. The national banks which invest in these receive,
besides the interest, a special privilege in the form of permission
 to issue bank notes. This additional benefit may
be regarded as a species of additional income, and materially
enhances the value of the bonds. For this reason,
United States government bonds are not used for
investment purposes, except among those in whom the ele-