Interest rates (Chapter 6)

What four factors affect the cost of money? The price, or cost, of debt capital is the interest rate. The price, or cost, of equity capital is the required return. The required return investors expect is composed of compensation in the form of dividends and capital gains. What four factors affect the cost of money? Production opportunities Time preferences for consumption Risk Expected inflation

“Nominal” vs. “Real” rates k = represents any nominal rate k* = represents the “real” risk-free rate of interest. Like a T-bill rate, if there was no inflation. Typically ranges from 1% to 4% per year. kRF = represents the rate of interest on Treasury securities.

Determinants of interest rates r = r* + IP + DRP + LP + MRP r = required return on a debt security r* = real risk-free rate of interest IP = inflation premium DRP = default risk premium LP = liquidity premium MRP = maturity risk premium

Premiums added to r* for different types of debt IP MRP DRP LP S-T Treasury  L-T Treasury S-T Corporate L-T Corporate

Exam type question Given the following data, find the expected rate of inflation during the next year. r* = real risk-free rate = 3%. Maturity risk premium on a 1-year corporate bond= 0.5%. Default risk premium on a 1-year corporate bond= 1.5%. Liquidity premium on a 1-year corporate bond = 0.5%. Going interest rate on 1-year corporate bond = 7.5%. a. 3.5% b. 4.5% c. 2.0% * d. 5%

Yield curve and the term structure of interest rates Term structure – relationship between interest rates (or yields) and maturities. The yield curve is a graph of the term structure. The 2010 Treasury yield curve is shown at the right.

Hypothetical yield curve Years to Maturity Real risk-free rate 5 10 15 1 10 20 Interest Rate (%) Maturity risk premium Inflation premium An upward sloping yield curve. Upward slope due to an increase in expected inflation and increasing maturity risk premium.

What is the relationship between the Treasury yield curve and the yield curves for corporate issues? Corporate yield curves are higher than that of Treasury securities, though not necessarily parallel to the Treasury curve. The spread between corporate and Treasury yield curves widens as the corporate bond rating decreases. Since corporate yields include a default risk premium (DRP) and a liquidity premium (LP), the corporate bond yield spread can be calculated as:

Representative Interest Rates on 5-Year Bonds in March 2010

Illustrating the Relationship Between Corporate and Treasury Yield Curves

What determines the yield curve?: Pure Expectations Hypothesis (PEH) The PEH contends that the shape of the yield curve depends on investor’s expectations about future interest rates. If interest rates are expected to increase, L-T rates will be higher than S-T rates, and vice-versa. Thus, the yield curve can slope up, down, or even bow. Assumes that the maturity risk premium for Treasury securities is zero. Long-term rates are an average of current and future short-term rates. Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as riskier. If the pure expectations theory is correct, you can use the yield curve to “back out” expected future interest rates.

Exam type question The real risk-free rate, k*, is expected to remain constant at 3 percent per year. Inflation is expected to be 2 percent per year forever. Assume that the expectations theory holds; that is, there is no maturity risk premium. Which of the following statements is most correct? a.The yield curve for corporate bonds must be flat, but corporate bonds will yield more than 5 percent. b.The Treasury yield curve is upward sloping for the first 10 years, and then downward sloping. c.The Treasury yield curve is flat and all Treasury securities yield 5 percent. * d.Statements a and c are correct.

An Example: Observed Treasury Rates and Pure Expectations Maturity Yield 1 year 6.0% 2 years 6.2 3 years 6.4 4 years 6.5 5 years If the pure expectations theory 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?

One-Year Forward Rate 0 1 2 6.0% x% 6.2% (1.062)2 = (1.060) (1 + X) 0 1 2 6.0% x% 6.2% (1.062)2 = (1.060) (1 + X) 1.12784/1.060 = (1 + X) 6.4004% = X The pure expectations theory says that one-year securities will yield 6.4004%, one year from now. Notice, if an arithmetic average is used, the answer is still very close. Solve: 6.2% = (6.0% + X)/2, and the result will be 6.4%.

Another example of future expected interest rates Bank of America has the following CD rates: 2.8% for a 2-year (24 months) CD, and 2.4% for a 1-year (12 months) CD. What is the expected 1-year rate (yield), one year from now You know Two-year rate (= 2.8%) and One-year rate now (= 2.4%) Expected 1-year rate (yield), one year from now is found from : 2-year yield(2.8%) = (1-year(2.4%) + x%) / 2 2.8% x 2 = 2.4% + x% 5.6% - 2.4% = x% 3.2% = x% PEH says that one-year CD rate, one year from now, will yield 3.2%

Exam type question One-year government bonds yield 4 percent and 2-year government bonds yield 4.5 percent. Assume that the expectations theory holds. What does the market believe the rate on 1-year government bonds will be one year from today? a. 5.50% b. 5.0% * c. 5.75% d. 5.25%

Other factors that influence interest rate levels (section 6.7) Federal reserve policy Federal budget surplus or deficit Level of business activity International factors

Learning objectives Problems ST-1,ST-3a, 6-2 to 6-6 Questions 6-2, 6-3 Discuss the four fundamental factors that affect the cost of money Discuss the determinants of market interest rates Distinguish between real and nominal interest rates What is the yield curve, and what type of shapes might have? Know how to calculate the 1-year expected rate/yield (forward rate) one year from now given the spot rates Discuss the pure expectations theory and other factors that influence interest rate levels (i.e. FED policy, deficits, international markets, economic activity) Interest rates and business decisions (see text section 6.8) Problems ST-1,ST-3a, 6-2 to 6-6 Questions 6-2, 6-3