Financial issues: loans, mortgage, investment

A risk-free investment was defined as one for which the investor is certain of the amount and timing of the expected returns. The returns from most investments do not fit this pattern. An investor typically is not completely certain of the income to be received or when it will be received. Investments can range in uncertainty from basically risk-free securities, such as T-bills, to highly speculative investments, such as the common stock of small companies engaged in high-risk enterprises.
Most investors require higher rates of return on investments if they perceive that there is any uncertainty about the expected rate of return. This increase in the required rate of return over the NRFR is the risk premium (RP). Although the required risk premium represents a composite of all uncertainty, it is possible to consider several fundamental sources of uncertainty. In this section, we identify and discuss briefly the major sources of uncertainty, including: (1) business risk, (2) financial risk (leverage), (3) liquidity risk, (4) exchange rate risk, and (5) country (political) risk.

The data used to determine the standard deviation is very important. Because it is a statistical measure, it is most accurate when a large amount of data is applied. For example. you might find that 1 standard deviation of the crude oil daily price move is only SO.25 per barrel when measured over the past 10 years, but during the 6 months of the Gulf War the same measurement yielded $.50, twice as large.
Most trading applications using the standard deviation tend to apply short data intervals to its calculation, such as 20 days. This short period is not likely to represent the same price distribution as a 10-year calculation; therefore, the probabilities given by the resulting standard deviation value must be interpreted differently. While it is less likely that the price will make a move of 3 standard deviations compared with 1 standard deviation, the probabilities can be misleading. Statistics tell us that there is only a 1% chance that prices will move a distance of 3 standard deviations higher or lower; however. that value is reliable only when measured over a long data period. If you selected 20 days of unusually low volatility, the chance of a 3standard deviation move Would be very high.
The frequency distribution is another very practical approach to measuring price distributions. It has the advantage of having a much clearer visual interpretation. While the standard deviation gives us what appears to be a highly mathematical probability, the large error factor that is caused by small amounts of data may make its usefulness about the same as the frequency distribution.