Chapter 4 The Behavior of Nominal Interest Rates

Chapter 4 The Behavior of Nominal Interest Rates 1 How does inflation effect pricing of financial instruments?  Nominal versus real rates of interest i. Real rates  Lend a friend $100 for one year at 0% interest when inflation is 0%. What happens to your ability to consume goods in one year?  Suppose inflation is 10%. What happens to amount you can consume inone year?  The increase in $ amount represents the nominal interest rate.  The increase in your ability to consume is the real interest rate.  Similar examples on p. 56 2 Continue… ii. Real interest rate is the equilibrium rate at which claims to future consumption are traded for current consumption   r = ln (Cfuture) - ln (Ctoday) This rate is what was determined in Chapter 3 iii. Nominal interest rate       Most financial instruments promise $ not consumption. The nominal interest rate account for changes in prices and consumption R=ln (Pfuture x Cfuture)-ln (Ptoday • Ctoday) =(ln Pfuture-ln Ptoday)+(ln Cfuture-ln Ctoday) Inflation  = ln Pfuture - ln Ptoday. R=+r Book looks at discrete compounding on p. 57. 3 Expected inflation and nominal interest rates. i. Should you use actual inflation or expected inflation to determine the nominal interest rate?   Interest rates are used for forward decisions You do not know today what the inflation rate will be in the next year. 4 Continue… ii. Rational individuals would seek to maintain purchasing power in the face of anticipated inflation  R = e + r e  Here superscript means expected rate of return over the holding period for the investment.  re is determined based on analysis of Chapter 3  e is determined based on macro-economic analysis, i.e. given expected monetary policy over the next year. Some people argue that inflation lowers the expected real rate of return. Chami, Cosimano and Fullenkamp.  Evidence chart from Stephen Sharpe paper 5 Continue…  U.S. tax code effects interest rate The tax is levied on the nominal rate so that nominal rate has to increase more to keep real rate constant.  Example, 10% return with 5% inflation and 30% tax bracket. re = R - .3 R - e (1-.3) 10% - 5% = 2%  15% return with 10% inflation re = .7(15%) - 10% = .5%  Thus nominal rate needs to increase by more than 5% to keep same real rate. 6 • Exhibit 4.1 7 Empirical Evidence Regarding Inflation and Nominal Interest Rates (1) i. See Exhibit 4.1  Nominal rate and inflation are strongly correlated.  Difference between R = e is no constant.  Inflation tends to move before the nominal interest rate.  Problem neither e or re are observable.The chart list actual inflation.  Part of the difference is based on  - e. Expected inflation may not adjust quickly enough.  re = R - e = R -  + (e - ). 8 Exhibit 4.1 Annual inflation and single-year interest rates, 1955-1995 9 Empirical Evidence Regarding Inflation and Nominal Interest Rates (2) ii. Expected inflation and inflation proxies.   Based on past data for forecast of future inflation. Survey data of expected inflation  Livingston survey  Blue chip forecast  Long-term interest rates relative to TIP bonds. TIP bonds are inflation index bonds  Movement of long-term minus short-term interest rates 10 Empirical Evidence Regarding Inflation and Nominal Interest Rates (3) iii. Extracting Estimates from Theoretical Models --Yash Meahra model 1.) Divide the nominal rate into three parts Rnt  Ret  ( Rmt  Ret )  ( Rnt  Rmt ) 2.) The real rate was determined in chapter 3 1 Ret  g0  s0  g1 yt  s1 yt  Rdef t g2  s2 3.) The market real rate versus the real rate   ( Rmt  Re t )   h(  realmoney) 11 Continue… Demand & Supply Relationship market rate minus real rate Supply ( Rnt  Rmt )   e t Demand Real money supply 1 Rnt  g0  s0  g1  yt  s1 yt  Rdef t  h realmoney    e t g2  s2 12   Exhibit 4.2 Inflation and nominal interest rates: a cross-country comparison 13 Exhibit 4.3 Inflation and Nominal Interest Rates: A Cross-Country Comparison 14 Long term relationship Rnt  a0  a1 e t  a2 RFRt  a3 FP  a4 ln ryt  a5  ln ryt  ut t Short term relationship called error correction model  Rnt  c0  c1   e  c2  RFRt  c3  FPt  c4  ln ryt  a5   ln ryt t  c61  Rnt 1  c62  Rnt  2  c63  Rnt  3  c64  Rnt  4  c7 ut 1    Rnt  c0  c1   e  c2  RFRt  c3  FPt  c4  ln ryt  a5   ln ryt t  c61  Rnt 1  c62  Rnt  2  c63  Rnt  3  c64  Rnt  4  Rnt 1  a 0  a1 e1  t    c7   a 2 RFRt 1  a 3 FPt 1    a4 ln ryt 1  a5  ln ryt 1    15 Simulation Model - - Regression Model - Required Input - - T-Bill Rate Impact - A*B Product Description constant pt pt e A coefficient (0.2200) 0.7100 0.6100 0.1200 (0.3700) 0.3700 B variable 1.0000 (0.5000) (0.2300) 2.1000 4.7100 1.8000 3.7300 (0.7000) 0.0200 (0.1400) 0.0100 Actuals Rate 5.52 5.53 5.39 5.41 4.71 4.52 Change (0.2200) R1t-5 (0.3550) R1t-4 R1t-3 (0.1403) R1t-2 0.2520 R1t-1 (1.7427) R1t 0.6660 1.2682 Predicted  R1t 0.1610 Actual  R1t 0.0014 0.0056 0.0015 (0.1023) 0.01 (0.14) 0.02 (0.70) (0.19) RFRt ln ry t R1t-1 pt-1 pt-1 e RFRt-1 R1t-1 R1t-2 R1t-3 R1t-4  R1t 0.3400 (0.2300) 0.0700 (0.0400) 0.1500 4.61 4.52 University of Notre Dame College of Business Administration Fin 462: Banking & the Money Market Predicting Treasury Bill Rates Source: "Some Key Empirical Determinants of Short-Term Nominal Interest Rates" by Yash P. Mehra 16