Sec. 10] THE RISK ELEMENT 281 
ment of caution is unduly strong, but are held for the 
most part by national banks. It is therefore misleading 
to cite, as some have done, the rates of interest realized 
on government bonds as an indication of the true rate of 
interest. A similar benefit attaches to the bonds of the 
Credit Foncier in France. These are sold on a very low 
“basis” because of the chance, connected with them, of 
winning prizes. 
§ 10 
In the general case we have to do not simply with the 
risk of falling below a specified income, nor with the 
chance of rising above a specified income, but with both. 
Thus, the dividends from common stock have no fixed 
minimum as do those from good preferred stock, nor any 
fixed maximum as do the interest payments from bonds. 
They may vary, and vary widely, in either direction. The 
amount of variation may be measured with reference to any 
specified amount selected arbitrarily as a basis of com- 
parison. For instance, in the case of stock which has 
yielded, in successive years, the following percentages: 
5 5 6,5 5 4, 5 7,5 3, 4 5, we may for conven- 
ience take 5 per cent to serve for a basis of computa- 
tion. The stock has yielded 1 per cent or more in excess 
of this in two cases out of twelve; it has yielded 2 per cent 
in excess in one case out of twelve; it has fallen short by 
1 per cent or more in three cases out of twelve, and fallen 
short by 2 per cent in one case out of twelve. If these fre- 
quencies are our only guide for judging the future, they 
represent the probabilities of receiving the respective divi- 
dends. 
On the basis of the foregoing figures it is possible to calcu- 
late the “riskless” and the “mathematical” value of the 
stock, and, if we know the caution factor, it is possible to 
calculate the © commercial” value also. Thus, the “risk- 
less” value, in this case, signifies that value which the stock