Financial issues: loans, mortgage, investment

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.

If investors expected the price level to increase during the investment period, they would require the rate of return to include compensation for the expected rate of inflation. Assume that you require a 4 percent real rate of return on a risk-free investment but you expect prices to increase by 3 percent during the investment period. In this case, you should increase your required rate of return by this expected rate of inflation to about 7 percent [(1.04 × 1.03) – 1]. If you do not increase your required return, the $104 you receive at the end of the year will represent a real return of about 1 percent, not 4 percent. Because prices have increased by 3 percent during the year, what previously cost $100 now costs $103, so you can consume only about 1 percent more at the end of the year [($104/103) – 1]. If you had required a 7.12 percent nominal return, your real consumption could have increased by 4 percent [($107.12/103) – 1].