4. The Top 5 Banking Companies in the World, 1999 Bank Name Country Total assets Deutsche Bank AG Germany $735 billion UBS Group Switzerland $687 billion Citigroup United States $669 billion Bank of America United States $618 billion Bank of Tokyo Japan $580 billion
11. “ Real” Versus “Nominal” Rates k* = Real risk-free rate. T-bond rate if no inflation; 1% to 4%. = Any nominal rate. = Rate on Treasury securities. k k RF
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15. Treasury Yield Curve 0 5 10 15 10 20 30 Years to Maturity Interest Rate (%) 1 yr 5.2% 5 yr 5.8% 10 yr 5.9% 30 yr 6.0% Yield Curve (August 1999)
16. Yield Curve Construction Step 1:Find the average expected inflation rate over Years 1 to n: IP n = . n
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18. Step 2: Find MRP Based on This Equation: MRP t = 0.1%(t – 1). MRP 1 = 0.1% x 0 = 0.0%. MRP 10 = 0.1% x 9 = 0.9%. MRP 20 = 0.1% x 19 = 1.9%.
19. Step 3: Add the IPs and MRPs to k*: k RF t = k* + IP t + MRP t . k RF = Quoted market interest rate on treasury securities. Assume k* = 3%: k RF1 = 3.0% + 5.0% + 0.0% = 8.0%. k RF10 = 3.0% + 7.5% + 0.9% = 11.4%. k RF20 = 3.00% + 7.75% + 1.90% = 12.65%.
20. Hypothetical Treasury Yield Curve 0 5 10 15 1 10 20 Years to Maturity Interest Rate (%) 1 yr 8.0% 10 yr 11.4% 20 yr 12.65% Real risk-free rate Inflation premium Maturity risk premium
24. How does the volume of corporate bond issues compare to that of Treasury securities? Recently, the volume of investment grade corporate bond issues has overtaken Treasury issues. ‘ 95 ‘96 ‘97 ‘98 ‘99 600 450 300 150 Gross U.S. Treasury Issuance (in blue) Investment Grade Corporate Bond Issuance (in red) Billions of dollars
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27. Observed Treasury Rates Maturity 1 year 2 years 3 years 4 years 5 years Yield 6.0% 6.2% 6.4% 6.5% 6.5% If PEH holds, what does the market expect will be the interest rate on one-year securities, one year from now? Three-year securities, two years from now?
28. 0 1 2 5 6.0% 3 4 x% 6.2% PEH tells us that one-year securities will yield 6.4%, one year from now (x%). 6.2% = 12.4% = 6.0 + x% 6.4% = x%. (6.0% + x%) 2
29. 0 1 2 5 6.2% 3 4 x% 6.5% [ 2(6.2%) + 3(x%) ] 5 PEH tells us that three-year securities will yield 6.7%, two years from now (x%). 6.5% = 32.5% = 12.4% + 3(x%) 20.1% = 3(x%) 6.7% = x%.
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