In these notes: 
I.   Bonds: An introduction
II.  Bond prices and PDV
III.  How changes in market interest rates affect bond prices
IV.  Yield to maturity, or Internal rate of return
V. Understanding changes in interest rates: Supply & demand in the bond market
-- A. Introduction:  Bond prices are inversely related to interest rates
-- B. Asset demand in general:  The Theory of Asset Demand
-- C. Shifts in the demand for bonds
-- D. Shifts in the supply of bonds
-- E. Summary and more examples
VI. Supply & demand in the bond market:  Applications
-- A. Effect of changes in the expected rate of inflation on interest rates
-- B. Effects of business-cycle expansions (and recessions) on interest rates

I.  BONDS:  AN INTRODUCTION

Recall that a bond is a formal IOU, with a promise to repay an initial amount borrowed plus a fixed amount of interest, according to a particular schedule.
-- The market price of a bond is the present-day value of its future payments (ignoring for now such considerations as default risk and tax treatment).

There are two main types of bonds -- coupon bonds and discount bonds (or zero-coupon bonds).

(1) COUPON BONDS
-- These sell at (or near) their face value (at par). So a $1000 coupon bond would sell for about $1000. The reason someone would want to own it is for the coupons (regular interest payments).
-- A coupon bond offers a particular interest rate,  i_coupon, also known as the coupon rate, or CURRENT YIELD.

Coupon rate = dollar value of the yearly coupon payment, divided by the face value of the bond.
Annual coupon payment =  i_coupon * (face value of bond) 

Some coupon bonds (such as U.S. Treasury coupon bonds) are sold at auction and, as auction prices are not set in advance, a those coupon bonds will not necessarily sell for exactly their face value.  Unless the coupon rate and the market interest rate are exactly the same, a $1000 coupon bond would sell for a bit more or a bit less than $1000.  If so, the effective interest rate on the bond will be a bit different from its coupon rate.

Most Treasury bonds and corporate bonds are coupon bonds.

(2) DISCOUNT BONDS -- These sell at less than their face value (FV) and pay no interest/coupons until the bond matures.  Ex.:  a U.S. savings bond.

The price (P_d) and interest rate (i_d) of a new discount bond are jointly determined.  Whatever price the bond sells for, we can calculate its interest rate by applying the internal-rate-of-return formula we learned earlier:

The simplest case is a 1-year discount bond, since the 1/n term becomes 1 and therefore drops out:

Ex.: a one-year, $1000 discount bond that sells for $900 would have an interest rate of

i_d = ($1000)/($900)^(1/1) - 1 = 1.111 - 1 = .111 = 11.1%

Ex.: a two-year, $1000 discount bond that sells for $900 would have an interest rate of

i_d = ($1000)/($900)^(1/2) - 1 = (1.111)^(1/2) - 1 = 1.054 - 1 = .054 = 5.4%

(The bond's face value is a constant, by the way. For a discount bond, the variables are the price and the interest rate.)

Just as the formula for i_d is the same as the internal-rate-of-return formula, a discount bond's price P_d is equal to its present-day value (PDV.  And recall that the PDV and internal-rate-of-return formulas are themselves just rearrangements of the future value (FV) formula).

--> A discount bond's price and its interest rate have an exact inverse relation. The higher the interest rate, the lower the bond's initial price (the greater the discount) relative to its face value.

II.  BOND PRICES AND PDV

Again, the appropriate price of a bond is its PDV.  (PDV, after all, is defined as "what it's worth now." )

For a discount bond, calculating the PDV is simple, because there is just one payment.  We can just apply the basic PDV formula.  It's identical to the previous formula, except it uses the market interest rate i instead of the bond's interest rate i_d (these will be the same anyway, because in a competitive bond market all bonds with the same attributes will offer the same interest rate -- this is the "law of one price" from Econ 101)"

Exs.:

For a coupon bond, calculating the PDV is more complicated, because there are multiple payments, and they are made at different times.   Recall that the PDV of any future payment is the dollar amount of the payment divided by (1+i)ⁿ (which is the compounded gross interest rate), which implies that you have to compute the PDV's of each of those future payments separately and then add them up:

PDV of getting $50 per year forever, when i = 5%:

There is a shortcut, however, because those terms get smaller and smaller as n gets larger (e.g., the PDV of a $50 payment to be received 100 years from now is only 38 cents), and their sum converges into a finite number.  A series like this one is a geometric sum, which you may have learned about in high school.  Here is the general formula [see number (3) on the "Everything You Always Wanted to Know..." handout]:

PDV of a fixed payment (FP) in perpetuity (i.e., forever):
PDV = FP/(1+i) + FP/(1+i)² + ... + FP/(1+i)ⁿ + ...
         = FP * 1/i
         = FP/i

So that $50 perpetual yearly payment would be worth, if the market interest rate is 5%,

the same as a 1-, 2-, or n-year coupon bond making a $50 annual coupon payment when i = 5%.

It's been a couple centuries since anyone actually did auction off consol bonds in any significant quantity, but this formula does have some very practical uses, such as for pricing stocks.

[Not covered yet, but possibly of interest:  For something that pays a fixed amount over a finite time span -- like, say, a 10-year, $10-million-a-year NBA contract -- finding the PDV the standard way would involve adding up 10 separate terms and would be very time-consuming. There is, however, a shortcut, which makes use of that consol formula. Let us denote those fixed yearly payments as FP, for fixed payment.  The time-consuming way to compute the combined PDV of all those payments over n years is PDV = FP/(1+i) + FP/(1+i)² + ... + FP/(1+i)ⁿ
(formula (2) on PDV handout).  The shortcut involves applying the consol formula; we can calculate the PDV of an n-year series of fixed payments (FP) as the difference between the PDV of a consol that pays $FP per year forever and a consol that pays $FP per year starting n+1 years from now.  See formula (4) on the PDV handout.]

III.  HOW CHANGES IN MARKET INTEREST RATES AFFECT BOND PRICES

First recall that a discount bond's price and its interest rate have an exact inverse relation.  The higher the interest rate the bond pays, then the greater the "discount" (i.e., the lower the price) it must sell at.  This inverse relation between interest rates and bond prices is one of the key things to know about the bond market.

Ex.:  Consider a 1-year, $1000-face-value discount bond.  Recall:  P_d =  (Face Value) / [(1+ i_d)ⁿ ].  Let's consider a range of possible interest rates and what the bond's price will be at each interest rate:
 

There is a secondary, or resale, market for bonds.  For example, if you buy a 30-year Treasury bond, do you really want to hold onto it for that long? Might need the cash sooner than that. Can sell it to someone else. The price of an old bond will be affected by interest rate on new ones.

A bond's resale, or market, value is just its PDV, with i being the market interest rate:

Resale price of a discount bond = FV/[(1+i)ⁿ]

Ex. #1:  Back to the 1-year-, $1000-face-value discount bond in the previous example.  Now assume that the market interest rate is 5% and that this bond is paying that rate, which means it sold for $952.38.  Suppose you bought this bond today and that later in the day the interest rate abruptly changes.

(Scenario 1A:)  Suppose the market interest rate i falls from 5% to 1%.  How does this affect the value of your bond?  Consider that this means new bonds are paying 1%, while you have locked in a return of 5% with your bond.  So you have a superior bond that potential bond-buyers would love to have.  A new bond pays 1% and costs $990.10.  So for any price less than $990.10, anyone in the market would be happy to buy your bond.  If you sold your bond for $990.10 exactly, it would be just as good as a brand-new bond, as both pay $1000 a year from now.
-- The PDV math is the same as for the 1% row above.
---- If you sold your bond, your profit would be $990.10 - $952.38 = $37.72

(Scenario 1B:)  Suppose that i jumps from 5% to 10%.  Now new bonds are paying 10% interest and cost just $909.09.  This is bad news for the value of your bond.  To sell it, you would have to lower the price all the way to $909.09, to make it equivalent to a brand-new bond (same price, same face value).
---- If you sold your bond, your profit would be $909.09 - $952.38 = -$43.29

For longer-term bonds, the inverse effect of a change in the market interest rate is much stronger.

Ex. #2:  Now imagine that the bond is a 30-year discount bond with a face value of $1000.  And assume that the market interest rate is 5% and that this bond is paying that rate, which means it sold for $231.38 (=$1000/ [(1.05)³⁰]).  Suppose you bought this bond today and that later in the day the interest rate abruptly changes.

(Scenario 2A:)  Suppose the market interest rate i falls from 5% to 1%.  New bonds are paying 1%, while you have locked in a return of 5% for the next 30 years.  So your bond is vastly superior to a new bond.
-- Resale price and PDV of your bond = $1000/[(1.01)³⁰] = $741.92
---- If you sold your bond, your profit would be $741.92 - $231.38 = $510.54
(which is more than 13 times as much as your profit in Scenario 1A with the 1-year bond).

(Scenario 2B:)  Suppose that i jumps from 5% to 10%.  Now new bonds are paying 10% interest, and this is bad news for the value of your 5% bond. 
-- Resale price and PDV of your bond = $1000/[(1.10)³⁰] = $57.31
---- If you sold your bond, your profit would be $57.31 - $231.38 = -$174.07
(or four times as big a loss as in Scenario 1B with the 1-year bond).

Lesson:
IN THE SECONDARY BOND MARKET, THE PRICES OF ALL OLD BONDS ARE NEGATIVELY RELATED TO THE CURRENT (MARKET) INTEREST RATE.
-- This is equivalent to saying that the PDV of any already-issued bond declines whenever the market interest rate (i) goes up, and the PDV of any already-issued bond rises whenever the market interest rate (i) goes down.  This should make sense, as an increase in the market interest rate i lowers the PDV of any future payment.
---- If i goes up, old bonds are worth less than before (prices of old bonds fall) 
---- If i goes down, old bonds are worth more than before (prices of old bonds rise) 
-----> This is why bondholders LOVE falling interest rates.

The examples so far have been with discount bonds, but the inverse relation between market interest rates and old bond prices applies also to old coupon bonds (and especially to consols).
-- The only exception to the inverse relation between market interest rates and bond prices is new coupon bonds, which sell at their face value as long as they are paying a coupon rate equal to the market interest rate.  When market interest rates change, governments and businesses selling new coupon bonds adjust their coupon rates accordingly.

Summary:

How changes in current interest rates affect bond prices (and PDV's):

Bond type	Effect of an increase in the current interest rate on the bond's price and PDV
coupon bond (new)	unchanged (coupon rate, not price, should change.  However, if the new coupon rate is still lower than the current market interest rate, then the bond's price will fall.)
coupon bond (old)	price falls in resale market.
discount bond (new)	price falls
discount bond (old)	price falls in resale market

Because a rise in current market interest rates reduces the PDV and resale price of a previously issued bond, we say that bonds have INTEREST-RATE RISK, which is the risk that market interest rates might rise after you buy the bond, causing the resale price of your bond to fall.
-- Short-term bonds have some, but relatively little, interest-rate risk, because you'll get your money back pretty soon and can then invest it at the higher market interest rate.
-- Long-term bonds have a great deal of interest-rate risk, as they lock in a particular interest rate for a much longer period of time.  More precisely, the PDV of a long-term bond is a lot more sensitive to changes in the current market interest rate (i) than is the PDV of a short-term bond.

IV. YIELD TO MATURITY, or INTERNAL RATE OF RETURN

In the simplest cases, the yield to maturity and the interest rate are the same thing. These cases include:
* new discount bonds
* new consol bonds
* new coupon bonds that sell at their face value.

This is the same as the formula for the interest rate on a multi-year discount bond. Conceivably the bond's yield to maturity could be higher or lower than the market interest rate.

To generalize: the YIELD TO MATURITY on an asset is the value of i that would equate the price of the asset with the PDV of that asset's future stream of payments.
-- A bond that is priced properly, so that the price equals the PDV of the payment stream, will have a yield to maturity equal to the market interest rate.

= (annual coupon payment)/(face value of bond) + (rate of capital gain)
                                             |                                                   |
                                  current yield                                =0 if purchase price is same as face value;
                                                                                    positive if purchase price < face value;
                                                                                    negative if purchase price > face value

---- Ex.: a ten-year, $1000 bond that sells for exactly $1000 and has a coupon of $50 would have an interest rate of

In the case of a coupon bond, if the bond is sold for less than or more than its face value, or if the payments are irregular, then the yield to maturity and the interest rate won't be the same thing. 

-- If, based on the market interest rate, a bond is selling for less than its PDV (i.e., the bond is a bargain), then

-- If, based on the market interest rate, a bond is selling for more than its PDV (i.e., the bond is a ripoff), then

In such a case, finding the yield to maturity is more complicated. Again you would need to solve for i, but you'd need the help of a computer (a spreadsheet, maybe) to do it.  A trial-and-error approach might be your best bet.

V. UNDERSTANDING CHANGES IN INTEREST RATES:  SUPPLY & DEMAND IN THE BOND MARKET

A. INTRODUCTION: BOND PRICES ARE INVERSELY RELATED TO INTEREST RATES

The bond market behaves much like any other competitive market and can be represented with a supply-and-demand diagram.
-- [Drawn in class.  See Cecchetti's Figure 6.2 (page 131) for a similar graph].

Q: What does all of this have to do with interest rates?
A: Recall that for a new discount bond, the purchase price has an exact negative relationship with i.

i_b = [(FV/P_b)^(1/n) - 1 ] * 100%

(We could add an interest-rate axis to our bond-market diagram.  It would be a second vertical axis, pointing upside-down because of the inverse relation between interest rates and bond prices (the other vertical axis, which points up).  But adding an upside-axis is confusing.  It's better just to note what happens to the equilibrium price of bonds, and then say that the equilibrium interest rate moves in the opposite direction.)

As with the usual supply-and-demand model, the next step is to see what makes those demand and supply curves move. Shifts in those curves will, of course, affect the price and quantity of the good sold. In the case of bonds, those shifts will also affect the (equilibrium) interest rate, and in the opposite direction of how it affects the equilibrium price.

B.  ASSET DEMAND IN GENERAL:  THE THEORY OF ASSET DEMAND

The Theory of Asset Demand (also known as the Theory of Portfolio Choice) gives great insight into how a person optimally assembles a financial portfolio and what qualities are desirable in a financial asset. It helps us understand why some assets offer a higher return than others, and why rational people may still choose to hold assets that don't pay a very high return.

The Theory of Asset Demand is that the demand for a given financial asset depends on these four main factors:

(1) WEALTH
-- increase in wealth --> increased demand for all financial assets
-- The amount of increase depends on the type of asset.  For normal assets, you'll demand more of all of them as your wealth increases, but your demand for certain assets will increase much faster.  In particular, we distinguish between:
---- necessity assets-- e.g., checking account, cash
------ as wealth grows, demand for that asset grows, too, but less than proportionally (less than 1-for-1)
---- luxury assets -- e.g., stocks, bonds
------ as wealth grows, demand for that asset grows, too, and more than proportionally ("wealth elasticity of demand" > 1)

(2) EXPECTED RETURN (RET^e) of a particular asset, relative to the return on other assets
-- higher RET^e on a particular asset
--> increased demand for that asset
--> decreased demand for all other assets (substitutes)

(3) RISK, relative to other assets
-- If returns on two assets are equal, risk-averse people will prefer the lower-risk asset
-- increase in an asset's risk (relative to other assets)
--> decreased demand for that asset
--> increased demand for all other assets

(4) LIQUIDITY (convertibility into cash; spendability), relative to other assets
-- increase in an asset's liquidity (relative to other assets)
--> increased demand for that asset
--> decreased demand for all other assets

Together, the above list of factors and their effects on asset demand constitute the Theory of Asset Demand.

In sum (and stated more compactly): Theory of Asset Demand: The demand for an asset depends positively on:
[1] wealth;
[2] RET^e, relative to other assets;
[3] safety, relative to other assets;
[4] liquidity, relative to other assets.

Financial advisors often recommend an asset allocation much like the following to their clients:
                   60% stocks, 30% bonds, 10% "cash" (money-market funds, bank accounts).
The Theory of Asset Demand is consistent with that recommendation.  Most of your portfolio should be in stocks because their historical rate of return is the highest (about 10% per year), and only a small portion should be in "cash" assets because their rates of return are relatively low.  Holding bonds as well as stocks is advisable because it will lessen the overall risk of your portfolio.  And holding some "cash" assets is necessary because everybody needs some liquidity, in order to be able to make purchases.  Finally, if you as a college student have never thought about proper asset allocation before, the likely reason is that you do not have wealth available for personal investments.  Wealth, far more than any of the other three factors, is the main thing that bears on whether an individual will own financial assets or not.

C. SHIFTS IN THE DEMAND FOR BONDS

Enter the Theory of Asset Demand. Remember, this theory says there are four key factors that determine the demand for any financial asset and thus for bonds:

1. Wealth
2. RET^e (relative to other assets)
3. Safety of the bonds (")
4. Liquidity of the bonds (")

--> Loanable funds framework: these 4 factors cause the demand curve for bonds to shift

Thus, there are 4 main things that increase the demand for bonds (and hence cause the demand curve for bonds to shift out, or to the right:

1. increased wealth

2. increased RET^e (relative to other assets; to be specific, the real, after-tax expected return)
-- A. a decrease in the expected inflation rate (raises the expected real return on a bond)
-- B. a decrease in the tax rate on bond interest (raises the after-tax return)
-- C. a decrease in the expected return on other assets (e.g., stocks)
-- D. a decrease in the expected future interest rate (the return on today's bonds stays the same, but it has increased relative to future bonds; current bonds and future bonds are substitutes)

3. decreased riskiness of bonds (relative to other assets)

4. increased liquidity of bonds (relative to other assets)

The opposite of any of those 4 things, then, decreases the demand for bonds (and hence causes the demand curve for bonds to shift in, or to the left).

When the demand for bonds increases (i.e., demand curve for bonds shifts out), the result is a new equilibrium with a:
* higher equilibrium quantity of bonds
* higher equilibrium bond price
* lower equilibrium interest rate.
-- [I drew a graph of this shift in class.  A similar graph is Figure 6.4 in the book.]

When the demand for bonds decreases (i.e., the demand curve for bonds shifts in), the result is a new equilibrium with a:
* lower equilibrium quantity of bonds
* lower equilibrium bond price
* higher equilibrium interest rate.
-- [Also drawn in class.]
 

EXAMPLES OF THINGS THAT INCREASE THE DEMAND FOR BONDS (SHIFT Db TO THE RIGHT)	EXAMPLES OF THINGS THAT DECREASE THE DEMAND FOR BONDS (SHIFT Db TO THE LEFT)
Congress votes to make Treasury bond interest tax-exempt (increasing the after-tax interest rate on Treasury bonds) --> will increase demand for T-bonds (and will decrease demand for non-Treasury bonds)	Congress raises the top marginal tax rate (lowering the after-tax interest rate on Treasury, corporate bonds) --> will decrease D for T-bonds and corporate bonds (and will increase demand for municipal bonds, which are tax-exempt)
State governments start issuing insured bonds, guaranteeing that bondholders will be paid even if the state defaults on its obligation to them (decreasing the riskiness of municipal bonds) --> higher demand for municipal bonds (and decreased demand for non-municipal bonds)	During a shutdown of the federal government, Congressmen say that the Treasury will delay its scheduled payments to bondholders (increasing the riskiness of T-bonds) --> decreased demand for T-bonds
The mutual fund explosion makes bonds more liquid.	The e-trade explosion makes stocks more liquid (increased liquidity of substitute asset).

C. SHIFTS IN THE SUPPLY CURVE FOR BONDS

There are three main factors that cause the supply of bonds to increase (i.e., cause the supply curve of bonds to shift out or shift right). They are:

1. increase in expected profitability of (capital) investment opportunities
-- If firms become increasingly optimistic about how profitable future investments (i.e., new purchases of plant and equipment) will be, they will try to finance those investments, and will willingly pay a higher interest rate to the new bondholders who make those new investments possible.

2. increase in expected inflation
-- If firms expect the inflation rate to be much higher in the future than most people expect, they will look to sell more bonds, even at a somewhat higher interest rate, because the higher inflation in the future will lower the real interest rate they'll have to pay to their bondholders.

3. increased federal government deficits; or, increased state/local government willingness to undertake costly new spending projects
-- The government must sell bonds to finance its deficit (and debt). When the federal deficit rises, the government must offer more of its Treasury bonds for sale, at whatever price they will fetch. When state or local governments undertake big public investment projects not covered by current tax dollars, they too must sell bonds. Either increase in government bond offerings shifts out the supply curve of bonds.

When the supply of bonds increases (i.e., the supply curve for bonds shifts out), the result is a new equilibrium with a:
* higher equilibrium quantity
* lower equilibrium price
* higher equilibrium interest rate.
-- [Drawn in class.  Figure 6.3 in the book is the same graph.]

Given the 4 factors that shift the demand curve for bonds, and the 3 factors that shift the supply curve for bonds, we can use the loanable funds framework (i.e., the supply-and-demand framework, with interest rates thrown in as an extra vertical axis) for the bond market to see what will happen to interest rates whenever one of those factors is present. Some of the factors are unique to the demand side of the bond market, others to the supply side of the bond market. For those factors, analyzing their effects on the equilibrium price, quantity, and interest rates of bonds is straightforward. Where it gets complicated is in the handful of factors that shift both the supply and the demand curves for bonds. Two important factors that shift both curves, and which probably account for most of the variation in interest rates, are (1) economic fluctuations and (2) changes in expected inflation.

D. SUMMARY AND MORE EXAMPLES
 

EXAMPLES OF THINGS THAT INCREASE THE SUPPLY OF BONDS (SHIFT Sb TO THE RIGHT)	EXAMPLES OF THINGS THAT DECREASE THE SUPPLY OF BONDS (SHIFT Sb TO THE LEFT)
Congress passes a new investment tax credit, effectively subsidizing new physical capital investment by corporations (thus raising the after-tax profitability of business investment).	The federal government cuts defense spending by 25%.
State governments issue billions of dollars worth of bonds to finance new sports stadiums.	Business economists forecast recessionary times ahead (thus lowering the expected profitability of investment profjects).

In general, in supply-and-demand examples for any market, only one curve shifts.  (As you may recall, a sure way to lose points on a micro-principles exam is to draw both the supply and demand curves shifting on the same graph.)  But, in the case of the bond market, there are two big exceptions, noted in the third column of the summary table below:
 

Demand-shift factors:	Supply-shift factors:	Factors that shift both:
1. Wealth	1. Expected profitability	* Changes in expected inflation
2. RETe  (relative to other assets)	2. Expected inflation	* Economic expansions and contractions
3. Risk ( " )	3. Government deficits;  state government spending projects	* Tax cuts (increase after-tax RET on bonds, also increase government deficit)
4. Liquidity ( " )

Q1: What is the net effect of an increase in the expected inflation rate on the (nominal) interest rate?
Q2: What is the net effect of an expanding economy on the interest rate?
Let us consider each of those in the next section.

VI. SUPPLY & DEMAND IN THE BOND MARKET - APPLICATIONS

A. EFFECT OF CHANGES IN THE EXPECTED RATE OF INFLATION ON INTEREST RATES

If the expected rate of inflation (p^e) increases:
* Real RET^e on bonds falls ==> D_b falls
* Real cost of borrowing falls ==> S_b rises

==> Net effect of both shifts:
* P_b falls, unambiguously ==> i rises
* Q_b is unchanged

-- The change in the volume of bonds depends on the relative magnitudes of the supply and demand shifts. If they are exactly equal (which is a fair assumption, since people on the demand side and the supply side of the bond market are working off the same set of economic forcecasts of future inflation), then Q_b is unchanged.
-- [Drawn in class.  See Figure 6.6 in the book for the same graph.]

-- FISHER EFFECT: An increase in the expected inflation rate causes an increase in the nominal interest rate.
(If  p^e increases , then i increases, too.)
---- Likewise, a decrease in the expected inflation rate causes a decrease in the nominal interest rate. Now you know why nominal interest rates on 30-year Treasury bonds fell during the 1990s -- the decline was (mostly) caused by the decline in the inflation rate during the 1990s -- as the inflation rate fell, so did people's expectations of future inflation.
---- The expected real interest rate -- i - p^e -- does not change much, because of the Fisher effect.
---- The Fisher effect is named for Irving Fisher, the great early-20th-century economist.

A useful distinction to keep in mind when thinking about the Fisher effect:

* ex ante real interest rate, or expected real interest rate =  i - p^e
-- The Fisher effect says that the ex ante real interest rate won't change much in response to changes in inflation, since the nominal interest rate will change one-for-one in response to changes in the expected inflation rate, leaving the expected (or ex ante) real interest rate constant.
-- The ex ante real interest rate is virtually always positive (about 3% or so), because who would want to lend out money at a
zero or negative real interest rate?

vs.

* ex post real interest rate, or after-the-fact real interest rate = i - p^e
-- This is only observed after the holding period for a bond or other interest-bearing asset.   It is the interest rate earned on the asset minus the inflation rate that actually prevailed during the life of the asset.  It often differs from the expected real interest rate, because expectations are not always correct. If the actual inflation rate turns out to be much greater than expected, the ex post real interest rate will turn out to be much lower than expected and could even be negative (as was the case in much of the 1970s).

B. EFFECTS OF BUSINESS-CYCLE EXPANSIONS (AND RECESSIONS) ON INTEREST RATES

Let's look at what happens in an economic expansion. Once we're done, we'll note that the effect of an economic recession on interest rates is, predictably, the exact opposite.

In an expansion,
expected profits rise ==> companies invest more ==> S_b increases (shifts right);
real GDP increases, so wealth increases (also, expected default risk on bonds is lower) ==> D_b increases (shifts right)
==> Net effect of both shifts:
* Q_b rises (unambiguously)
* i?  (ditto for P_b)  The demand and supply shifts pull the interest rate in opposite directions. Effect on interest rate depends on which shift is larger (i.e., on the relative magnitudes of the two shifts).
---- Empirical studies have found that the supply shift is larger, so i increases (and P_b falls) in economic expansions.

In a recession, everything is just the opposite:
expected profits fall ==> companies invest less ==> S_b falls (shifts left);
real GDP falls, so wealth falls (and expected default risk on bonds is higher) ==> D_b falls (shifts left)
==> Net effect of both shifts:
* Q_b falls
* i falls and P_b rises, because, although the demand and supply shifts pull the interest rate in opposite directions, the supply curve shifts by more. To repeat:  the supply shift is larger, so i decreases in economic recessions.
-- [See Figure 6.7 in the book for a graph like the one I drew in class.]