We need to estimate the level of new mortgages drawn down over time. If residential mortgages were rising very rapidly (and this is usually the case when real estate bubbles develop) a reasonable first approximation is to take the net increase in mortgage loans and assume that it is close to the gross increase. This may be done at the system level or for individual banks. Some countries actually publish gross drawdowns and these should be used when available.
Next we estimate how much of these loans have been repaid. Based on our example of a 20-year mortgage we know approximately how much capital is repaid in each year.
We are only interested in the loans made in 1995, 1996 and 1997. These are the only loans that are at risk of being “under water”. A mortgage taken out in 1995 is approximately six years old and hence approximately 17% of the original principal has been repaid. This could be done on a quarter by quarter basis but besides from adding complexity and increasing the risk of computational error it does little to increase the accuracy of the estimates.
We then calculate the estimated balance outstanding and subtract it from the current estimated value of the properties bought. This shows that the only properties at risk were those bought between 1Q96 and 4Q96.
Finally, we can make a reasonable first-cut estimate of the level of negative equity. Approximately 12% of mortgage loans, by value, have negative equity with the level of negative equity highest for people who bought in 3Q96 at approximately 30% of their outstanding balance.
Part of the reason for including this example is to illustrate how in an imperfect world, where the data to arrive at a definitive answer either does not exist or is not reported, it is still possible with many problems to make some reasonable quantified conclusions using the data that is available, some clear approximations and a bit of creativity.
This method of estimating the level of mortgages with negative equity will not work in markets with significant levels of mortgage securitization.
Tags: banks, credits, loans, mortgages
Commodity prices are expressed in such diverse units as cents per pound, dollars per bushel, and yen per dollar. Since we will be interested in price changes rather than in absolute prices, and since we will be wanting to compare price change distributions across a number of different commodities, it will be immensely useful to express all price changes as percentages of their absolute price levels.
If every daily price change- whether the commodity be soy- beans, live cattle, sugar, or Japanese yen- is made dimensionless by dividing that price change by the absolute price of its future and then multiplying by one hundred, then all resulting measures of “spread” will be expressed as dimensionless percentages and will thereby be directly comparable. (If every option price is also expressed as a percentage of its futures price, then every option price will also be expressed in the same units as the daily price changes in its future.) One thing is immediately clear from the “spread” of each of these distributions about its mean value: During 1996, coffee prices were much more variable than silver prices.
The degree of “spread” of a set of numbers about the average value (mean) of that set of numbers is most commonly specified by its standard deviation, a statistic which can be calculated for any set of numbers or for any continuously variable distribution. The calculation of the standard deviation of a set of numbers involves taking the square root of squares of differences from the mean. Another measure of spread of a distribution is its mean absolute h a t i o n , which, in the case of daily price changes, is the average value of these price changes taking all readings as positive. In classical statistical analysis, the mean absolute deviation is much less used than the standard deviation. This is unfortunate, since the mean absolute deviation as a measure of variability has many advantages, not least of which is its ease of visualization and its simplicity of calculation.
Be that as it may, there is no denying that the standard deviation is the statistic conventionally used in developing option price models. Realistically, therefore, and for comparison purposes if for nothing else, the standard deviation has to be incorporated into any independently derived option pricing formula that I or anyone else dares to come up with!
Tags: commodities, commodity prices, debt, interest, loans, spread