Return Analysis

Retail accounts give the clients of a bank the opportunity to deposit their money. The client lends money to the bank, whereas the bank borrows money from the client. Money on accounts is also called a retail deposit. Normally banks recompense their clients by paying an interest rate, yet these accounts pay little or no interest. Low interest rates can be justified by the fact that the costs of the banks for the infrastructure, staff and paperwork are substantial. In the following we present the basic interest calculation. The beginning value BV and the end value EV of a money account are related to the interest rate r: E V = B V 1 + r . $$ \mathrm{E}\mathrm{V}=\mathrm{B}\mathrm{V}\left(1+\mathrm{r}\right). $$ We assume that BV and EV are quoted in US dollars ($). However, our considerations in the following are applicable to any other reference currency. In relationship (1) the timespan between BV and EV is not specified and there is no reference point on the time axis. Sometimes interest rates are also called growth rates. Assuming that one investor $100 in an account and gets $200 out after 10 years and another investor turns $100 into $200 in just a year, the growth rates are obviously different. Interest rates are usually quoted on an annual basis. However, other timespans like days, months or 6-month (semi-annual) periods can also be appropriate in specific situations. We can see that interest rates always refer to a specific timespan. In this section and in Sect. 2.2, the timespan is arbitrary but fixed. We refer to this as the base period.