Finance and Economics Discussion Series: Accessible Versions of Figures in 201053^{*}

This figure illustrates the timing of events in the two-period theoretical model of the loan contract.

Loan application, underwriting, and loan disbursement occur at the beginning of the first period. The first payment is due at the end of the first period. The loan payoff is scheduled for the end of the second period.

Figure 1 is a bar chart showing the percentage of subprime first mortgages that are ARMs (y-axis) at different loan to value intervals (x-axis) for originations between 1998 and the first quarter of 2006.

The percentage of first mortgages that are ARMs rises from about 40 percent at loan to value (LTV) less than 60 percent to a high of 63 percent at LTV between 80 and 89 percent. The percentage of ARMs falls to about 56 percent at LTV 90 to 99 percent and continues falling at higher LTV intervals. In the highest LTV interval, 120 percent or greater, about 13 percent of mortgages are ARMs.

Figure 2 shows by year from 1998 to 2006 (x-axis) the percentage of second mortgages that are ARMs (y-axis).

For every year except 2002, the percentage of ARMs is less than 30 percent. For six of the nine years (1998-2001, 2005, and 2006), the percentage of ARMS is 20 percent or less.

Figure 3 is a graph based on the theoretical model and shows the difference between the expected value of an ARM and a FRM contract (y-axis) by loan to value (x-axis).

The figure shows a humped curve, with the difference (representing the value of an ARM over that of a FRM) increasing from lower to higher LTV to a maximum (at \tilde{L}) and then decreasing as loan to value continues increasing.

This figure shows the calculated values (in percentage points) of term spread and interest rate volatility variables (y-axis) between 1998 and 2006 (x-axis).

Term spread (calculated as the difference between 5 year Treasury rate and 1year Treasury rate in a month when the mortgage was originated) fluctuates between -1 and +1 percentage points until the end of 2001 and then rises sharply to about 2 percentage points in late 2001. Between the end of 2001 and mid-2004, term spread fluctuates between 1 and 2 percentage points. From mid-2004, term spread declines from about 1 and 1/2 percentage points to about zero in the first quarter of 2006.

Interest rate volatility (calculated as the difference between the highest one year Treasury rate and the lowest one year Treasury rate over previous three years from the month of a loan origination) drops from about 2 percentage points to a little over 1 percentage point during 1998, increases to just under 2 percentage points at the beginning of 1999, and increases again slightly to a little over 2 percentage points in early 2000. In early 2001, volatility begins rising sharply reaching a maximum of about 5 percentage points around the first quarter of 2003. From late 2003 to the end of 2004, volatility declines from about 5 to 1 and 1/2 percentage points. Volatility begins increasing in 2005, rising to about 3 and 1/2 percentage points at the end of the first quarter of 2006.

Figure 5 shows the average teaser rate for hybrid mortgages and the 6-month LIBOR rate (y-axis) by year of origination (x-axis).

The 6-month LIBOR rate falls from about 5 and 3/4 percent in the first half of 2006 and then declines to about 5 percent. LIBOR rises from 5 percent in early 1999 to about 7 percent in mid-2000. At the end of 2000, LIBOR falls first rapidly (in 2001) and then more slowly (in 2002 and 2004) to about 1 percent. Early in 2004 LIBOR began rising from 1 percent, reaching 5 percent by the end of 2006.

The average teaser rate follows a similar pattern as the 6-month LIBOR but is about 4-5 percentage points higher throughout the 1996-2006 period.