Chapter Six

1. Chapter Six Real Interest Rates

2. What Are Real Interest Rates? • Investors care about how much they can purchase with the dollars they earn, not merely the quantity of dollars • When investments do not keep pace with inflation, investors lose purchasing power • A more accurate measure of well-being is based on the amount of goods and services one can buy, not how much income is earned • “Real” figures account for inflation in financial matters • Nominal interest rate = the amount of interest paid expressed as a percentage of the principal • Real interest rate = the nominal interest rate adjusted for expected or actual inflation

3. Expectations of Inflation • Expected inflation is more often used to adjust the nominal interest rate • What matters in people’s decisions to borrow or lend is what they think they will be paying or earning • This is known as the expected real interest rate (or ex-ante real interest rate) Expected real interest rate = nominal interest rate – expected inflation rate

4. Expectations of Inflation(cont’d) • The realized real interest rate (or ex-post real interest rate) is the nominal rate adjusted for actual inflation • This measure matters more “after the fact” • The expected real interest rate is more relevant in decision-making because we cannot know for certain what the actual inflation rate will be Realized real interest rate = nominal interest rate – actual inflation rate

5. Impact of Unexpected Inflation • Who gains and who loses from unexpected inflation? • Lower than expected inflation hurts the borrower and helps the lender, who is paid back in dollars worth more than they had predicted when making the loan • Higher than expected inflation hurts the lender and helps the borrower, who pays back their loan with dollars worth less than those they originally spent

6. Unexpected Inflation (cont’d) • When actual & expected inflation differ, the expected real rate differs from the realized real rate • When actual inflation is less than expected, realized real rates increase • When actual inflation is greater than expected, realized real rates decrease

7. Why Inflation Risk is a Problem • Investors deplore inflation for two reasons • The value of their returns is reduced by inflation • The unpredictability of inflation increases the risk to the real return on their investments • The riskiness of inflation matters just as much as the rate of inflation to investors • The risk to real return can be expressed as the of the probabilities and outcomes standard deviation faced by the investor • Higher standard deviations signify higher risk of inflation, and hence higher risk to real returns

8. Avoiding the Problems of Unexpected Inflation • Investors and borrowers have several ways of avoiding the risk and uncertainty of inflation • Adjustable rate mortgages allow interest rates on a loan to adjust as market interest rates change • Inflation-indexed securities offer opportunities to borrow and lend in real rather than nominal terms

9. Real Present Value • Allows concept of “real interest rates” to be applied to past returns, expected returns, and yields to maturity • Present value formulas are used with real terms in lieu of dollar terms

10. Real Present Value (cont’d) • There exist a variety of uses for this formula • The present value P of given future real amounts (the f terms) for a given expected real interest rate r • Future real amounts (the f terms) given an expected real interest rate r and a current principal value P • The average past return r given real income received (the f terms) and the original amount invested P • The expected future return r given expected future income (the f terms) and the original amount invested P • The real yield to maturity of a security r given promised future payments (the f terms) and the current price of the security P

11. What Affects Real Interest Rates? • Investment decisions would be easier if changes in real interest rates were predictable • Two factors may cause changes in expected real interest rates • Changes in the expected inflation rate • Changes in phases of the business cycle

12. Measuring Real Interest Rates • Data on nominal interest rates and actual inflation rates are easily obtainable, while measuring expected inflation rates is more difficult. • Forecasts of the future inflation rate by economists are useful, and with them one can calculate • Expected real interest rates • Realized real interest rates • What do we find? • Expected and real interest rates often move together

13. Measuring Real Interest Rates(cont’d) Despite some large points of divergence, real interest rates and realized real interest rates move relatively closely together

14. The Fisher Hypothesis • A rise in the expected inflation rates leads to a rise in the nominal interest rate, while expected real interest rates remain the same • Anticipated inflation affects the prices of goods, as well as the number of dollars a security pays, but not any inflation-adjusted amount • That is, dollar payments adjust to the same change in the inflation rate • Example: If inflation is 4% instead of 3%, all dollar payments will compensate by being 1% higher

15. The Fisher Hypothesis (cont’d) Please insert Figure 6.4 When expected inflation rises, the supply of bonds increases and the demand decreases in proportionate amounts. Thus, the nominal interest rate, the price of borrowing, also increases by the same amount.

16. Real Interest Rates in Recession • We expect less borrowing during a recession, which should lower the expected real interest rate • But people may also save less, which would raise the expected real interest rate by decreasing demand for debt securities • As demand and supply both decrease, the resulting effect is ambiguous

17. Real Interest Rates in Recession (cont’d) Please insert Figure 6.5 Overall trend is for supply to decrease more than demand, causing expected real interest rates to decline during a recession.

18. Application to Everyday Life:The Effect of Taxes on Interest Rates • Like inflation, taxes also reduce the return of investors • The government often “earns” more in real dollars than the investor, as taxes are imposed on nominal, not real, returns • When accounting for inflation, effective real tax rates are much higher than stated tax rates • “A significant …loss even at a low rate of inflation” (Feldstein)

19. The Societal Effects of Taxation • In general, higher tax rates reduce economic efficiency • Because of the additional erosion of returns due to taxes, people save and invest less when inflation is high than when inflation is low • Reducing inflation thus leads to large social benefits • After-tax realized real interest rates have often been negative, discouraging saving and investing and slowing economic growth

20. Expected Inflation and Real Interest Rates A tendency to move in the same direction is present, but only when other variables are not in play

21. The Societal Effects of Taxation (cont’d) • Demand and supply for debt securities depends more on after-tax expected real interest rates than before-tax expected real interest rates • Can the distortions of taxes be eliminated? • Impose taxes on real interest income • Calculation can be difficult • Reduce inflation to zero • Though progress has been made, seems unlikely