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1 Bianco Research L.L.C. An Arbor Research & Trading Affiliated Company Independent Objective Original February West Armitage, Chicago IL Special Report By James A. Bianco, CMT (847) What Is the Proper Level for Interest Rates? The average growth rate of U.S. real GDP between 1971 and 2001 was 3.1%. The average unemployment rate over the same 30-year period was 6.3%. Last week, real GDP for 2002 was reported to have grown at 2. (down from a yearover-year real GDP growth rate of 3.3% as of Q3 2002). The latest reported unemployment rate (January 2003) was 6.. Despite these fairly average readings, the general sentiment is focused on a weak economy. The Fed decided to cut the targeted fed funds rate to 1.25% last November and talk still persists they may cut again. The yields of the 5-year and 10-year Treasury Notes are near their lowest levels in 40 years. That begs the question, where should interest rates be? This commentary attempts to answer that question using a mathematical fair value calculation comprised of nominal GDP (a measure of real growth and inflation) and Federal debt (a measure of supply). We compare our fair value result to the yield of the 5-year Treasury Note (a proxy to where interest rates actually are in the market). We believe the difference between where rates should be and where they actually are indicates what the market is expecting, and discounting, for the future. Using Nominal GDP to Value Interest Rates Chart 1 on the next page shows what we believe is the best valuation yardstick for the bond market. The blue bars in the top panel show the year-overyear change in nominal GDP (real GDP plus inflation). The red line in the top panel shows the month-end yield of the 5-year Treasury Note. (We chose the 5-year Treasury Note because it represents the middle of the yield curve and it is close to the average interest rate of all Treasury securities. Any other point on the yield curve, or even corporate bond yields, could have been used and would show similar results.) The green bars in the bottom panel show the difference between the yield of the 5-year Treasury Note and the year-overyear change in nominal GDP. As of December 31, 2002 (the latest GDP measure), nominal GDP was 4.13%, the 5-year Treasury Note was 3.0, netting a difference between the two of -1.09%.

2 Bianco Research, L.L.C. Page 2 of 9 Special Report, February 2003 Chart YoY Change in Nominal GDP Year-over-year Change in U.S. Nominal GDP and the Yield of the 5-year U.S. Treasury Note Last () Nominal GDP Annual Growth = 4.13% Last () 5-Year Treasury Yield = Year Treasury Note Difference between the Yield of the 5-year U.S. Treasury Note and the Change in Year-over-year U.S. Nominal GDP Last (December 2002) Difference = -1.09% Dec-68 Dec-70 Dec-72 Dec-74 Dec-76 Dec-78 Dec-80 Dec-82 Dec-84 Dec-86 Dec-88 Dec-90 Dec-92 Dec-94 Dec-96 Dec-98 Dec-00 Think of this measure as an asset valuation model. If the asset, in this case the entire U.S. economy as measured by nominal GDP, returns a rate higher than the prevailing interest rate (the 5-year Treasury Note), then it makes sense for a business to borrow and expand. One can make money in such an environment because the asset has a higher return than the cost of borrowing. This will cause an increase in the demand for credit and put upward pressure on the price of credit -- interest rates. This will last as long as interest rates are below the yearover-year change in nominal GDP (or at least the perception that interest rates are below expected nominal GDP). Alternatively, if interest rates (5-year Treasury Note) are higher than the returns provided by the economy (nominal GDP), then borrowing to buy is a moneylosing proposition. In this case, the demand for credit will fall because the profit incentive is not present. This will drive the price of credit (interest rates) down as long as interest rates are above the expected growth rate, or perceived growth rate, of nominal GDP. This is only a slight variation of the widely used real rate concept. The real rate concept suggests that the fair value of interest rates is inflation plus a fixed number -- 3%. The nominal GDP concept suggests the fair value of interest rates is inflation plus a variable -- real GDP. Inflation plus real GDP equals nominal GDP. By using variable real GDP instead of a fixed 3% for the real interest rate premium, we believe our nominal GDP concept is a better way to value interest rates. Further, where in finance is a marketbased relationship fixed over all time periods and in all cycles? Using real GDP as a proxy for the proper level of real rates means the higher real growth (real

3 Bianco Research, L.L.C. Page 3 of 9 Special Report, February 2003 GDP), the higher real interest rates should be. How the Supply Matters Conversely, when an economy slips into recession The top panel below (blue line) shows gross federal (negative real GDP), real rates should also be debt as a percentage of nominal GDP. The bottom negative. This makes more sense than a fixed 3% panel (red line) shows the year-over-year change in level for real interest rates. gross federal debt as a percentage of nominal GDP (the growth rate of the top panel). Chart % Gross U.S. Federal Debt as a Percentage of U.S. Nominal GDP Last (December 2002) = 60.59% 7 65% % 55% % 45% % 35% 3 3 Year-over-year Change in Gross U.S. Federal Debt as a Percentage of U.S. Nominal GDP (The Growth Rate of Debt as a Percentage of Nominal GDP) 5% 5% 3% 3% 1% 1% -1% -1% % -3% - Last (December 2002) = % -5% Dec-68 Dec-70 Dec-72 Dec-74 Dec-76 Dec-78 Dec-80 Dec-82 Dec-84 Dec-86 Dec-88 Dec-90 Dec-92 Dec-94 Dec-96 Dec-98 Dec-00 Notice, as the budget deficit peaked in the early 1990 s so did debt as a percentage of nominal GDP (top panel). When the federal government was recently running a surplus, the growth rate of debt was negative (bottom panel). Now, with the surplus gone, the growth rate of debt has turned positive again. When assessing the deficit/surplus situation of the federal government, we believe federal debt as a percentage of nominal GDP and its growth rate (the year-over-year change in federal debt as a percentage of nominal GDP) are the key measures to examine.

4 Bianco Research, L.L.C. Page 4 of 9 Special Report, February 2003 Tying Them Together Chart 3 below shows every panel of the two previous charts. Our intention is to show how the federal deficit/surplus interacts with interest rates. It is our belief that a deficit/surplus affects interest rates relative to nominal GDP. A deficit/surplus does not render our nominal GDP valuation model useless. Rather, we believe it acts as a bias to nominal GDP. Chart Year-over-year Change in U.S. Nominal GDP and the Yield of the 5-year U.S. Treasury Note YoY Change in Nominal GDP 5-Year Treasury Note Difference between 5-year U.S. Treasury Note and YoY Change in U.S. Nominal GDP Average = % Average = 2.3 Average = 0.31% Year-over-year Change in Gross U.S. Federal Debt as a Percentage of U.S. Nominal GDP Average = -0.5 Average = 2.61% Average = -0.77% Gross U.S. Federal Debt as a Percentage of U.S. Nominal GDP Gross Federal Debt to GDP 31.5 (Sep. 81) Gross Federal Debt to GDP 67.65% (Dec. 93) Dec-68 Dec-70 Dec-72 Dec-74 Dec-76 Dec-78 Dec-80 Dec-82 Dec-84 Dec-86 Dec-88 Dec-90 Dec-92 Dec-94 Dec-96 Dec-98 Dec-00

5 Bianco Research, L.L.C. Page 5 of 9 Special Report, February 2003 The chart above has two green vertical dotted lines. The first line centers on September 1981 when debt to GDP was at a multi-year low and on the verge of exploding higher. The second line centers on December 1993 when debt to GDP was at a multidecade high and about to turn lower (it was higher in the aftermath of WW2). Between 1968 and 1981 (the left-most third of the Chart 3), interest rates were often below nominal GDP (first two panels) -- by an average of 1.87%. In this environment of low debt to GDP ratios and a negative debt growth rate of -0.5 (the bottom two panels), nominal GDP was still an effective valuation tool. However, one s view of fair value had to be biased to a level below nominal GDP given the positive (very little) supply situation. Between 1981 and 1993 (the middle third of the chart), interest rates were often above nominal GDP by an average of 2.3. In this environment of high debt levels and high debt growth rates, nominal GDP was still an effective valuation tool. However, one s view of fair value had to be biased to a level above nominal GDP given the negative (too much) supply situation. Since 1994 (the right-most third of the chart), interest rates have moved in tandem with nominal GDP averaging a difference of only 0.31%. For most of this period, we saw high debt levels and negative debt growth rates. These conflicting readings cancelled each out and interest rates and nominal GDP track each other closely. With debt growth turning positive again (the deficit coming back), we would look for the bias of interest rates relative to nominal GDP to become more like that seen in the middle third of this chart (1981 to 1993). Interest rates were typically well above nominal GDP during this period. Measuring the Bias The change in the supply of Treasury debt has an impact on the level of interest rates. No one doubts this. However, our contention is its effect has been vastly overstated. All supply does is bias one s view of where interest rates should be relative to the main input to the fair value measure nominal GDP. The scatter graphs below and on the next page are mathematical attempts to measure this bias. They show the relationship between supply, interest rates and nominal GDP. Chart 4 (below) starts in 1983 and Chart 5 (next page) starts in Chart 4 5% The relationship between Treasury Supply, Nominal GDP and Interest Rates Jun 1983 to Date 5-Year Treasury Yield - YoY Nominal GDP 3% 1% (1%) () y = x R 2 = (3%) () (0.3) (0.2) (0.1) "Supply" = (5 * Debt to GDP) + (5* Debt Growth Rate)

6 Bianco Research, L.L.C. Page 6 of 9 Special Report, February 2003 Chart 5 The relationship between Treasury Supply, Nominal GDP and Interest Rates 5% Jan 1969 to Date 5-Year Treasury Yield - YoY Nominal GDP 3% 1% (1%) () (3%) () (5%) () y = x R 2 = (7%) (0.3) (0.2) (0.1) "Supply" = (5 * Debt to GDP) + (5* Debt Growth Rate) The Y axis on the prior two charts is the difference between the 5-year Treasury Note and nominal GDP. This difference is also shown as a time series on the bottom panel of Chart 1. The X axis is an geometrically weighted average of the two supply measures shown in the two panels of Chart 2 debt to nominal GDP (top panel) and the yearover-year change of this relationship (bottom panel). Also shown on these charts is a linear regression line and the formula for calculating this line. The upward sloping line means the more positive the supply situation ( X axis), the lower the 5-Year Treasury Note yield should be relative to nominal GDP ( Y axis). No surprise here. As these charts show, the relationship between supply and interest rates since 1969 (Chart 5) was weak (r2 =.2072). Since June 1983 (Chart 4), the deficit has become an issue for the market and there has been a stronger linear relationship (r2 =.4245). It is this time period s regression equation we use for our analysis. Plugging the current figures into the linear regression equation shown on Chart 4 shows the 5- year Treasury note should trade 154 basis points above the annualized growth rate of nominal GDP. Adding this bias factor to nominal GDP suggests the fair value of the 5-year Treasury Note is 5.83% (4.13% Q Nominal GDP plus a supply bias factor of 1.7 equaling 5.83%). This fair value measure was 279 basis points above the December 31 yield of the 5-year Treasury Note of 3.0. Mathematically, it follows the form of: Y = The deviation between the yield of the 5- Year Treasury Note and the annualized growth rate of nominal GDP (bottom panel of the chart on page 1) X = "Supply" -- the geometric average of the two supply measures show on the chart on page 2. Or, the square root of [(5 * Debt to GDP) * (5 * Debt Growth Rate)] (5 * 60.59%) * (5 * 2.4) = 0.1 Y = ( * X) = (5.7498* 0.1) Fair Value = Annualized growth of Nominal GDP + Y 5.83% = 4.13% It is interesting to note that, as late as May 2001, this linear equation suggested the 5-year Treasury Note should trade 35 basis points below nominal GDP. Currently, the exploding budget deficit has turned the growth rate of debt to GDP positive (bottom

7 Bianco Research, L.L.C. Page 7 of 9 Special Report, February 2003 panel of the chart on page 2) suggesting the 5-year Treasury Note should trade 170 basis points above nominal GDP. This represents a 205 basis point reversal in the fair value calculation just due to the changing supply outlook in 19 months! To further illustrate how supply and nominal GDP relate to interest rates, we constructed the chart Chart 6 below. It shows the calculated fair value of the 5- year Treasury Note (thick blue line, top panel) as compared to the actual 5-year yield (thin red line, top panel). The bottom panel (green bars) shows the difference between the 5-Year Treasury Note and its calculated fair value. 1 The Yield of the 5-year U.S. Treasury Note Versus Calculated Fair Value Year Treasury Note (Thin Line) Calculated Fair Value (Thick Line) 5.83% Difference between the Yield of the 5-year U.S. Treasury Note and The Calculated Fair Value Most extreme since May Last (December 2002) = -2.79% - Dec-68 Dec-70 Dec-72 Dec-74 Dec-76 Dec-78 Dec-80 Dec-82 Dec-84 Dec-86 Dec-88 Dec-90 Dec-92 Dec-94 Dec-96 Dec-98 Dec-00

8 Bianco Research, L.L.C. Page 8 of 9 Special Report, February 2003 Conclusion The year-over-year change of Q nominal GDP was 4.13%. This was 1.09% above the yield of the 5-year Treasury Note on December 31 (3.0). After adjusting the year-over-year change in nominal GDP for supply, the calculated fair value for the 5- year Treasury Note rises to 5.83%. This was 279 basis points above the 5-year s yield on December 31 and 284 basis points above its current level of 2.99%. Given a static snapshot of the economy and supply, interest rates appear to be greatly under valued. What does this mean? We believe interest rates currently reflect the expectations of a significant slowing in the economy (nominal GDP) and/or a further narrowing of the deficit. Since it is improbable the deficit will actually narrow anytime soon, and will likely widen further, it is likely the current market expectations reflect the belief that the economy (nominal GDP) is going to slow a great deal. However, in order for interest rates to stay at their current level, or move lower, fair value needs to plunge. This means a combination of much lower nominal GDP and/or a narrower deficit is not only expected, but it is already priced in. Why does the market believe this? Returning to the statistics we started the commentary with, we note the following: the average growth rate of U.S. real GDP between 1971 and 2001 was 3.1% and the average unemployment rate over the same 30-year period was 6.3%. Last week, 2002 real GDP was reported at 2. (down from a year-over-year growth rate of 3.3% the quarter before) and the unemployment rate was reported at 6. for October. Has the market over-reacted? If it has, will interest rates move up in the future in order to restore fair value? Notice, we use this fair value calculation to help us determine what the market is pricing in. We do not believe deviations from fair value mean interest rates are at the wrong level. Deviations from fair value only tell us what the market expects from the economy and the outlook for supply. The fact interest rates and fair value are far apart suggests the market has priced in, and expects, bad news looking ahead.

9 Bianco Research, L.L.C. Page 9 of 9 Special Report, February 2003 Bianco Research L.L.C West Armitage, Suite 4 Chicago IL Phone: (847) Fax (847) research@biancoresearch.com Arbor Research & Trading, Inc Hart Road, Suite 260 Barrington IL Phone (847) Fax (847) inforequest@arborresearch.com For more information about the contents/ opinions contained in these reports: President (847) James A. Bianco jbianco@biancoresearch.com Research Analysts (847) /1534 John J. Kosar jkosar@biancoresearch.com Greg Blaha gblaha@biancoresearch.com Scott Mikkelsen smikkelsen@biancoresearch.com For subscription/service Information: Arbor Research & Trading, Inc. Director of Sales & Marketing (800) Fritz Handler fritz.handler@arborresearch.com Patrick Lovett pat.lovett@arborresearch.com Peter Forbes peter.forbes@arborresearch.com For more information about Arbor Research & Trading and its services: Director of Fixed-Income Sales (800) Daniel Lustig dan.lustig@arborresearch.com Director of International Sales (847) James L. Perry james.perry@arborresearch.com Anne Schultz anne.schultz@arborresearch.com Arbor Research & Trading (UK) LTD 75 Cannon Street London England EC4N 5BN Phone Fax For more information: Director of Arbor (UK) Neil Tritton neil.tritton@arborresearch.com Sean Fletcher sean.fletcher@arborresearch.com Ben Gibson ben.gibson@arborresearch.com Copyright 2003 Bianco Research, L.L.C. All rights reserved. This material is for your private information, and we are not soliciting any action based upon it. This material should not be redistributed or replicated in any form without prior consent of Bianco Research. The material is based upon information that we consider reliable, but we do not represent that it is accurate or complete, and it should not be relied upon as such.