9
Using Investment
increased the rate at which they were building new homes. Let’s look at a graph, Figure 9.1, showing the new home build rate during this period.
From Figure 9.1, even though there is a natural yearly cycle embedded within the data, it appears that housing starts began to drop off in the second quarter of 2006. But let’s analyze this further with some quantita- tive statistical techniques. This gets rather involved, so those of you less comfortable with mathematics may prefer to just use Figure 9.1 rather than doing quantita- tive analysis. But for those of you who want to persevere, here goes! The more information and confidence you can glean from data, the better.
First, so we can more easily do our analysis, let’s take out the seasonal change. We will start with 2001 data, because it looks like that is when the volume upswing began. We will include the data through 2005, just before the upward swing leveled off. We don’t want to lose all the variation within each year, just the seasonal effect. We will calculate the average for each year and then the difference of each quarter from that average. Then, we will calculate the average differences for the first through fourth quarters. We will then remove the seasonal change averages for each year based on the average differences. This is shown in Figure 9.2.
0 600 500 400 300 200 Housing Starts in Thousands 100
Years/Quarters
Jan-00 Apr-00 Jul-00 Oct-00 Jan-01 Apr-01 Jul-01 Oct-01 Jan-02 Apr-02 Jul-02 Oct-02 Jan-03 Apr-03 Jul-03 Oct-03 Jan-04 Apr-04 Jul-04 Oct-04 Jan-05 Apr-05 Jul-05 Oct-05 Jan-06 Apr-06 Jul-06 Oct-06 Jan-07 Apr-07
FIGURE 9.1 U.S. Housing Starts (1000s) by Quarter
Data Source:http://www.census.gov/const/quarterly_starts_completions_cust.xls Quantitative
Statistical Techniques A method of collecting, analyzing, and interpreting data, with emphasis on numerical statistical analysis
We are going to want to calculate a sigma (a mea- sure of variation) on this data, so we want to remove the annual upward slope due to the volume increase and only look at the sigma variation over the whole period.
We are removing the upward slope only for the purpose of calculating a sigma. After calculating a sigma, we will restore the upward slope for further analysis. There are other mathematical ways to do this, and if you feel com- fortable with those other methods, that is fine. Our goal is to project the average housing starts for 2006 as if the upward trend had continued from the earlier years to see how the actualhousing start data in 2006 compare with this housing starts projection.
When we do these calculations, it shows that, if the upward trend of housing starts would have contin-
ued, including the seasonal effects, the January 1, 2006, projected value would have been 401, and the April 1, 2006, projected value would have been 506.
When we calculated the sigma (a measure of variation) for the years 2001 through 2006, without the seasonal cycle and without the volume increase, we got a sigma of 13.6.
Statistically, in a normal distribution of data, 95 percent of expected numbers would fall between the average and ⫹/⫺2 sigma. Two sigma, in this example, is
100 500 450 400
300 350
200 250
150
Starts in Thousands
Year
Jan-01 Mar-01 May-01 Jul-01 Sep-01 Nov-01 Jan-02 Mar-02 May-02 Jul-02 Sep-02 Nov-02 Jan-03 Mar-03 May-03 Jul-03 Sep-03 Nov-03 Jan-04 Mar-04 May-04 Jul-04 Sep-04 Nov-04 Jan-05 Mar-05 May-05 Jul-05 Sep-05
FIGURE 9.2 Quarterly Housing Starts without Seasonal Effects
Data Source:http://www.census.gov/const/quarterly_starts_completions_cust.xls
Seasonal Change Predictable changes that are caused by annual events and therefore not indicative of any real long-term change
2⫻13.6 ⫽27.2. That means that, for this study, if the actualhousing starts for January 1, 2006, are between 401 ⫹/⫺27, (between 374 and 428), then we can’t be sure that the actual January 1, 2006, housing starts are significantly different than what we would have expected if the earlier upward trend had continued. And, since the actual January 1, 2006, housing starts were 382, which is between 374 and 428, we can notsay that there is a significant change. This is consistent with our earlier observation that we couldn’t see a definitive change on Figure 9.1 until April 1, 2006. Now, let’s see if the April 1, 2006, numbers are significantly different than if the upward trend had continued.
Key Point
Statistically, in a normal distribution of data, 95 percent of expected numbers would fall between the average and ⫹/⫺2 sigma.
Key Point
Statistically, in a normal distribution of data, 99.7 percent of expected numbers would fall between the average and ⫹/⫺3 sigma.
If the actual housing starts for April 1, 2006, are between 506 ⫹/ two sigma, which is 506 ⫹/⫺27 (between 479 and 533), then we can’t be sure that the April 1, 2006, actual housing starts are significantly different than what would have been expected if the earlier upward trend had continued. Since the actual April 1, 2006, housing starts were 433, which is well below the low pro- jected value of 479, we can be sure, with 95 percent confidence, that the second quarter 2006 housing starts aresignificantly different than the projected starts if the upward trend had continued. In fact, statistically, in a normal distribution of data, 99.7 percent of expected numbers would fall between the average and
⫹/⫺3 sigma. If the actual housing starts for April 1, 2006, are outside the range of 506 ⫹/⫺ three sigma, which is 506 ⫹/⫺40.5 (between 465.5 and 546.5), then we can be 99.7 percent sure that the April 1, 2006, housing starts are sig- nificantly different than what we would have expected if the earlier upward trend had continued. Since the actual April 1, 2006, housing starts were 433, which is well below the low projected value of 465.5, we can be 99.7 percent sure that the second quarter 2006 housing starts are significantly different than the projected starts if the upward trend had continued.
This could have been valuable data for any investor because of the possi- bility of short selling any stock that is heavily dependent on new housing. Short selling is where you sell a stock you do not own because you think the price of
the stock is going to fall. To do this, by means of your broker, you borrow the stock from an existing owner, sell it, and then buy it back later so you can return the stock to its original owner. Of course, you hope to be able to buy it back at a lower price so you profit from the drop in price.