1. Interest Rates
Fin 200

2. The Cost of Money
The interest rate is the price paid to borrow debt capital (the required return of the bondholder). Likewise equity holders expect a return (the required return of the shareholder). What impacts the level of interest rates?
Production Opportunities
Time Preference for Consumption
Risk
Inflation

3. Review of Key Factors Impacting Interest Rate Volatility
Federal Reserve and Monetary Policy
Discount Window
Reserve Requirements
Open Market Operations

4. Review of Key Factors Impacting Interest Rate Volatility
Fisher model of the Savings Market
Two main participants: Households and Business
Households supply excess funds to Businesses who are short of funds.
Loanable funds theory expands this to allow individuals, business and governments to both borrow and save.
The Saving or supply of funds is upward sloping (saving increases as interest rates increase)
The investment or demand for funds is downward sloping (demand for funds decease as interest rates increase)

5. Saving and Investment Decisions
Saving Decision
Marginal Rate of Time Preference
Trading current consumption for future consumption
Expected Inflation
Income and wealth effects
Generally higher income – save more
Federal Government
Money supply decisions
Business Decisions
Short term temporary excess cash.
Foreign Investment

6. Borrowing Decisions Borrowing Decision
Marginal Productivity of Capital
Expected Inflation
Other

7. Equilibrium in the Market
Interest Rate S D
Dollars

8. Equilibrium in the Market
Original Equilibrium
Decrease in Income S’ S S D D
Increase in Marg. Prod Cap
Increase in Inflation Exp. S’ S S D’ D’ D D

9. Multiple Markets
The market for investment capital is not one single demand and supply relationship. It can be thought of as being separated by the amount of risk in the borrowing (the chance that the firm will repay the debt) and the length of time for the debt (bond).
The different markets are interrelated.
If the risk free cost of borrowing increases, the rate paid on more risky borrowing also increases. Generally the higher the risk, the higher the return.

10. Differences in Return
The differences in return paid between two different types of borrowing (low risk corporate vs. high risk corporate with the same maturity for example) is the risk premium or yield spread.

11. Yield Spreads and Risk Premiums
The difference in required return between two assets, the difference in required return represents the difference in risk.
Often bonds that are the same except for the possibility of default are compared, implying that the yield spread is a measure of the default risk

12. Long Term Average Yearly Yields Over Time (Moody’s)

13. Bond Ratings and Average Yield Spreads vs
Bond Ratings and Average Yield Spreads vs. US Treasuries (long term bonds)
Rating Spread Rating Spread
AAA .20% B+ 2.5%
AA .50% B 3.25%
A+ .80% B %
A 1.0% CCC 5.00%
A % CC 6.00%
BBB 1.5% C 7.5%
BB 2.0% D 10.0%

14. Yield Spread Monthly Data Jan 1919 – June 2004 (Moodys)

15. Yield Spreads

16. Impact of Maturity
It is often the case that the return on similar assets that differ only in their maturity differ also have a interconnected relationship.
Usually the long term asset has a higher return than the short term asset. However this is not always the case.

17. General Model of Interest Rates
The relationship between assets of different riskiness and maturity can be broken down into a very general idea.
The return paid on an asset that matures I t years, rt should be thought of being a combination of its riskiness and maturity compared to a risk free asset.

18. Quoted Interest Rate
The quoted interest rate is then equal to a base rate, the real risk free rate of interest, plus premiums that account for differences in maturity and riskiness.

19. The quoted rate r = r*+ IP + DRP + LP + MRP Where:
r* = The real risk free rate of interest
IP = The inflation premium
DRP =The default risk premium
LP = The liquidity premium
MRP = the Market Risk Premium

20. The real risk free rate of interest
r* is the rate that would be paid on an asset with zero default risk, and an expected interest rate of zero.
It is the actual increase in purchasing power you should expect to receive. It depends on the productivity of the borrowers assets and the marginal time preference mentioned earlier.

21. Nominal Risk Free Rate and the Inflation Premium
The nominal, or risk free rate of interest is then the real rate plus a premium (IP) added to account for expected inflation in the future.
rRF = r*+ IP
Ideally the premium should be based upon expected inflation over the life of the security. Usually these are based on historical rates of inflation and the current economy.

22. The other premiums
DFR = The extra return associated with a higher chance of default (BBB corporate bonds vs. treasury bonds for example)
LP = Liquidity Premium The extra return associated with the market for an asset being less liquid making it harder to sell the asset for cash

23. The other premiums
MRP = Market Risk Premium A longer term bond has higher interest rate risk (TVM says the impact of a change in interest rates will be larger on a cash flow received further in the future). Therefore, the longer the maturity of the bond the higher the quoted interest rate.

24. Yield Curves
Graph of maturity (horizontal axis) vs. yield (vertical axis) for a group of bonds with similar risk.
Often represented using US gov’t bonds, it is usually upward sloping, implying that the longer the commitment the higher the required return for the investor (the higher the opportunity cost of capital).

25. Recent Yield Curve

26. Long Term vs. Short Term Interest rates

27. Why does the Yield Curve usually slope upwards?
Three things are observed empirically concerning the yield curve:
Rates across different maturities move together
More likely to slope upwards when short term rates are historically low, sometimes slope downward when short term rates are historically high
The yield curve usually slope upward

28. Three Explanations of the Yield Curve
The Expectations Hypothesis
Segmented Markets Theory
Preferred Habitat Theory

29. Expectations Hypothesis
Long term rates are a representation of the short term interest rates investors expect to receive in the future
Assumes that bonds of different maturities are perfect substitutes
In other words, the expected return from holding a one year bond today and a one year bond next year is the same as buying a two year bond today.

30. Expectations Hypothesis
Let
Rt = today’s time t interest rate on a one period bond
Ret+1 = expected interest rate on a one period bond in the next period
R2t = today’s (time t) yearly interest rate on the two period bond

31. The One Period Return Twice
If the strategy of buying an one period bond in two consecutive years is followed the return is:
(1+Rit)(1+Ret+1) – 1 which reduces to Rt+Ret+1
(Rt)(Ret+1) can be dropped

32. The 2 Period Return
If the strategy of investing in the two period bond is followed the return is:
(1+R2t)(1+R2t) - 1 = 1+2R2t+(R2t)2 - 1
This simplifies to
2R2t
(R2t)2 is small enough it can be dropped.

33. Set the two equal to each other
2R2t = Rt+Ret+1
R2t = (Rt+Ret+1)/2
In other words, the two period interest rate is the average of the two one period rates

34. Expectations Hypothesis
When the yield curve is upward sloping it is expected that short term rates will be increasing (the average future short term rate is above the current short term rate).
Likewise when the average yield curve is downward sloping the average of the future short term rates is below the current rate. (Fact 2)
As short term rates increase the long term rate will also increase. (Fact 1)
This however does not explain Fact 3

35. Segmented Markets Theory
Interest Rates for each maturity are determined by the supply and demand for bonds at each maturity.
Different maturity bonds are not perfect substitutes for each other.
Longer term bonds have a higher interest rate risk (and associated Market Risk Premium), therefore they should have a higher return
Implies the yield curve usually slopes up.

36. Preferred Habitat Theory
Combines the other two – The interest rate on the long term bond will equal an average of the short term rates, plus a liquidity premium and market risk premium, that responds to the supply and demand for that bond.
In other words the bonds are substitutes, but savers might have a preference for one maturity over another (they are not perfect substitutes)

37. Preferred Habitat Theory
The long term rate should include a premium associated with them. To attract savers who prefer a shorter maturity, the long term bond will need to pay an additional amount (or market risk and liquidity premiums).
Thus according to the theory a rise in short term rates still causes a rise in the average of the future short term rates. Therefore the long and short rates move together (Fact 1).

38. Preferred Habitat Theory
The explanation of Fact 2 from the expectations hypothesis still works. In the case of a downward sloping yield curve, the term premium (interest rate risk) must not be large enough to compensate for the currently high short term rates (Current high inflation with an expectation of a decrease in inflation). Since the demand for the short term bonds will increase, the yield on them should fall in the future.

39. Preferred Habitat Theory
Fact three is explained since it will be unusual for the term premium to be so small that the yield curve slopes down.

40. Predicting Future Short Term Interest Rates Movements
Steep Yield Curves
Short term interest rates are expected to increase
Flat Yield Curves
Short term interest rates are expected to decrease slightly
Downward sloping Yield Curves
Short term interest rates are expected to decrease.

41. Changes in the Yield Curve
These ideas can also be used to analyze changes in the shape of the yield curve. As the yield curve starts to become more steep it indicates that the average future short term rate is starting to increase. The current short term rate is to low.
A shift in the Yield curve that remains approximately the same slope is indicating that future expectations about both short term and long term rates are moving together (the real rate of interest is increasing and not just short term rates are changing)