215 Chapter 4 & 5
Q: An economist has concluded that near the point of equilibrium, the demand curve and supply curve for one-year discount bonds can be estimated using the following equations: Bd: Price = -⅖Q +940 Bs: Price = Q + 500 What is the expected equilibrium price and quantity of bonds in this market?
-⅖Q + 940 = Q + 500 -7/5Q = -440 Q = 314.2857 P = 814.2857
Dutch Auction
A method of issuing securities (common stock) by which investors place bids indicating how many shares they are willing to buy and at what price. The price the stock is then sold for becomes the lowest price at which the issuing company can sell all the available shares. Auction style (reflects the market demand) Anybody could put in bids for a certain number of shares at a certain price - then the highest price at which every available share could be sold becomes the price for all shares Lowest successful bid became price that everyone got shares at A publicized interview with Playboy magazine violated the SEC rules because it contained comments about company before the IPO process Google also issued IPO shares to its employers before the IPO process which violated the SEC rules and the shares were forced to be brought back by google. $85 per share Angered underwriters and the companies who usually profit
Asset
A piece of property that is a store of value Could be a car, house, boat but in this case we are looking at a bond
Yield curve
A plot of the yields on bonds with differing terms to maturity but the same risk, liquidity, and tax considerations Describes the term structure of the interest rates for particular types of bonds, such as government bonds Can be upward-sloping, flat, and downward-sloping (inverted) Upward = most usual = long-term IRs are above short-term IRs Flat = short and long term interest rates are the same Inverted = long term interest rates are below short term interest rates
An increase in IRs is associated with what direction in bond prices and capital when terms to maturity are longer than the holding period?
A: An increase in IRs is associated with a fall in bond prices and capital losses when the terms to maturity are longer than the holding period.
Q: Your parents buy a $10,000 20 year bond with a 4% coupon rate when you are born. They want to sell it when you turn 18, at that time the IR is 6%. Will the price be higher, lower, or equal to $10,000?
A: Because the IR is now 6%, and IR and price are inversely related, so the price is going to be lower than 10,000. IR risk: the holding period is less than the maturity of the bond, and during this time the IR increased.
Q: Is an increase in the length of time to maturity, associated with a higher or lower rate of return?
A: It is associated with a lower rate of return.
Q: What is the expected return on a bond if the return is 4% three fourths of the time and 6% one-fourth of the time?
A: R^e = p1R1 + p2R2 = (.75)(.04)+(.25)(.06) = .03+.015 = .045 or 4.5%
Demand Curve Consider a one-year discount bond Face value = $1,000 P = $950 vs. P = $900 Q: At what price is the quantity of bonds demanded greater?
A: The lower price of $900
Q: When the IR changes, is the resulting price change larger or smaller with greater years to maturity?
A: The resulting price change is larger with greater years to maturity.
Q: Your parents buy a 10-year $10,000 bond at face value with a 6% coupon rate. When it matures, they reinvest the face value into a 5-year bond. The coupon rate for the newly issued bond is 4%.
A: They would have been better off purchasing a bond with a longer maturity. Holding period is longer than the time to maturity, and the IR decreased.
When does the return equal the initial yield to maturity?
A: When the time to maturity = the holding period
Is the liquidity premium theory consistent with empirical fact three?
Also explains fact three, which states that yield curves typically slope up, by recognizing that the liquidity premium rises with a bond's maturity because of investor's preferences for short-term bonds Even if short-term interest rates are expected to stay the same on average in the future, long-term interest rates will be above short-term interest rates, and yield curves will typically slope upward.
Is the liquidity premium theory consistent with empirical fact two?
Also explains why yield curves tend to have an especially steep upward slope when short term IRs are low and to be inverted when short term interest rates are high because investors generally expect short-term interest rates to rise to some normal level when they are low, the average of future expected short-term rates will be high relative to current short-term rate. Also the additional boost of a positive liquidity premium, long-term IRs will be substantially higher than current short-term rates and the yield curve will have a steep upward slope If short-term rates are high though, people will expect them to come down so long-term rates will drop below short-term rates because the average of expected future short-term rates will be so far below current short term rates that despite positive liquidity premiums, the yield curve will slope down
Relationship between the expectations theory and the liquidity premium
Because the liquidity premium is always positive and typically grows as the term to maturity increases, the yield curve implied by the liquidity premium theory is always above the yield curve implied by the expectations theory and generally has a steeper slope
Comparing roles in different markets
Bond market: supply = borrowers, demand = lenders, government is a borrower Market for loanable funds: supply = savers (lenders), demand = borrowers, government is a saver
Problems with expectations theory
But this theory doesn't explain why the curve usually slopes upward
A steeply upward-sloping yield curve indicates that:
Future short term IRs are expected to rise
A steeply mildly-sloping yield curve indicates that:
Future short term IRs are expected to stay the same
downward sloping yield curve
Future short term interest rates expected to fall sharply
Expected inflation: If we expect an increase in inflation, this will lead to an increase in the price of real assets, leading to an increase in the nominal capital gains on real interests because you sell them at a higher price in the future This would _________ our demand for bonds
Decrease. Another reason: We know i (nominal interest rate) = r + π^e So r = i - π^e If expected inflation is increasing, real earnings are decreasing, therefore we have lower expected return which causes demand to fall Demand curve shifts left
Risk: An increase in risk leads to a ______ in demand
Decrease. Demand curve shifts left Call risk: With certain types of bonds, companies can choose to pay it off before the maturity date
Advantages to expectations theory
Elegant theory to explain why the term structure of IRs (represented by yield curves) changes at different times When the curve is upward sloping, short term IRs are expected to rise in the future When the yield curve is inverted the average of future short term IRs is expected to be lower than the current short term rate, implying that short term interest rates are expected to fall, on average, in the future When the curve is flat the short term interest rates are not expected to change, on average, in the future Also explains why interest rates on bonds with different maturities move together over time A rise in short term rates will raise people's expectations of future short term rates and bc long term rates are the average of expected future short term rates, a rise in short term rates will also increase long term rates When short term rates are low, people expect them to rise to some norma level in the future and the average of future rates is high relative to the current rate so long term rates will be higher than short term And if short term rates are high people will expect them to decrease in the future
Shifts in the Supply of Bonds Expected profitability of investment opportunities
Expansionary period → Expect future customers → increase in the supply for bonds → supply curve shifts right Other factors that could shift the curve out: investment tax credit, new inventions/ideas
Is the liquidity premium theory consistent with empirical fact one?
Explains fact 1 (IRs on different maturity bonds move together over time: a rise in short-term interest rates indicates that short-term interest rates will, on average, be higher in the future)
Theory of portfolio choice
Helps us understand how much of an asset people want to hold in their portfolio Four primary components: wealth, expected returns, risk, and liquidity Influence whether we buy or sell bonds and thus influence the IR
Q: Given your answer to part (a), which is the expected IR in this market (Face value = $1000)?
IR = (FV - price)/price i = (1000-814.2857)/814.2857 = 22.8%
Two important features of IR behavior for bonds with the same maturity
IRs on different categories of bonds differ from one another any given year Spread between them varies over time Municipal bond interest rates are higher than those on US gov bonds in the 1930s but lower after Spread between the IRs on Baa corporate bonds (Riskier than Aaa corporate bonds) and US gov bonds is large during the depression, smaller during the 1940s and 60s, then widens after
Wealth
If we have an increase in wealth we will most likely both increase our consumption and our savings so increase the assets demanded (unless the asset is inferior)
Liquidity More people are trading in the market: easier to buy or sell without losing value _________ in demand → shift to the _______
Increase, right
A good theory of the term structure of interest rates must explain what important empirical facts?
Interest rates on bonds of different maturities move together over time When short term interest rates are low, yield curves are more likely to have an upward slope; when short term interest rates are high, yield curves are more likely to slope downward and be inverted Yield curves almost always slope upward Three theories have been put forward to explain the term structure of interest rates or the relationship among interest rates on bonds of different maturities Expectations theory, market segmentation theory, and the liquidity premium theory
Problems with market segmentation theory
Market segmentation theory cannot explain facts 1 and 2: It views the market for bonds of different maturities as completely segmented, there is no reason for a rise in IRs on a bond of one maturity to affect the IR on a bond of another maturity Also it is not clear how demand and supply for a short versus long-term bonds change with the level of short-term IRs, so the theory cannot explain why yield curves tend to slope upward when short term IRs are low and to be inverted when short-term IRs are high
Risk
Measure of uncertainty associated with an asset's returns Measured with standard deviation An increase in risk of an asset will lead to a decrease in asset demand
Income Tax Consideration
Municipal bonds are not default-free: state and local govs defaulted during the great depression and recently in San Bernardino, Boise County etc. They also aren't as liquid as treasury bonds Interest payments on municipal bonds are exempt from federal income taxes which has the same effect on the demand for municipal bonds as an increase on their expected return
Japan's Negative Interest Rates Explained
Negative interest rates Mean depositors pay money to save their money Banks normally get interest for depositing funds in central banks With negative rates, central banks charge a fee instead The idea is to encourage banks to put their money to more productive use, lending it to households and businesses Supposed to lower the cost of borrowing for everyone Used by countries with really low inflation or deflation trying to lift consumer prices Bankers are mad because between the new fees they are paying the central bank and a general decline in lending income, profits at commercial banks are being squeezed by negative rates Deflation hasn't stopped and some people think negative interest rates undermine public confidence in the economy
Term structure of interest rates
Relationship among IRs on bonds with different terms to maturity Another factor that influences the interest rate on a bond is its term to maturity Bonds with identical risk, liquidity, and tax characteristics may have different interest rates because the time remaining to maturity is different
Expected returns: If we expect that the interest rate will increase, we will ________ want to purchase today
Not. An increase in the expected interest rate leads to a decrease in the demand for bonds → shift to the left On other assets: If we think there is an increase in the expected return on stocks it will decrease our demand for bonds → shift to the left
Example: What effect will a sudden increase in the volatility of gold prices have on interest rates? Why? Draw a supply-and-demand diagram to show your answer.
Price goes up, interest rate goes down
Credit rating agencies
Provide information on whether a corporation is likely to default on its bonds Investment advisory firms that rate the quality of corporate and municipal bonds in terms of the probability of default Largest are Moody's Investor Service and Standard and Poor's Bonds with low risk of default = investment-grade and have a rating of Baa or BBB and above Bonds below this are speculative-grade or junk bonds Also known as high-yield bonds because higher IRs
Risk structure of IRs
Relationship among interest rates of bonds with the same term to maturity But risk, liquidity, and income tax all play a role in determining the risk structure Also the term to maturity affects interest rate Explained by three factors: default risk, liquidity, and the income tax treatment of a bond's interest payments As a bond's default risk increases, the risk premium on that bond rises, greater liquidity explains why treasury bonds have lower interest rates, if a bond has a favorable tax treatment like municipal bonds its interest rate will be lower
Evidence on the Term Structure Does the slope of the yield curve provide information about movements of future short-term interest rates?
Researchers found that the spread between long- and short-term interest rates does not always help predict future short-term interest rates, a finding that may stem from substantial fluctuations in the liquidity (term) premium for long-term bonds More recent research using more discriminating tests shows that the term structure contains quite a bit of information for the very short run (over the next several months) and the long run (over several years) but is unreliable at predicting movements in interest rates over the intermediate term (the time in between) Research also finds that the yield curve helps forecast future inflation and business cycles
In general people are
Risk averse
Default risk
Risk of default occurs when the issuer of the bond is unable or unwilling to make interest payments when promised or to pay off the face value when the bond matures US Gov bonds are considered to have no default risk bc the fed gov can always increase taxes to pay off obligations Called default-free bonds Spread between IRs on bonds with default risk and default-free bonds, both of the same maturity = risk premium Indicates how much additional interest people must earn to be willing to hold that risky bond Bonds with default risk always have positive risk premium, and the higher the default risk is, the larger the premium will be If the possibility of default increases because a corporation begins to suffer large losses, the default risk on corporate bonds will increase, and the expected return on these bonds will decrease
SPAC (according to MATTEO)
SPAC-AKA blank check companies, is a company with no commercial operations that is formed strictly to raise capital through an IPO for the purpose of acquiring ("reverse merger") an existing company At the time of their IPOs, SPACS have no existing business operations or even stated targets for acquisition Investors in SPACs can range from well-known private equity funds to the general public SPACS have two years to complete an acquisition or they must return their funds to investors Being acquired by a SPAC can also offer business owners what is essentially a faster IPO Profess under the guidance of an experienced partner SPACs have been around for decades. In recent years, they've become more popular
Market segmentation theory
Sees markets for different maturity bonds as completely separate and segmented IR for each bond with a different maturity is determined by the supply and demand for the bond with no effects from expected returns on other bonds with other maturities Key assumption: Bonds of different maturities are not subsidies at all, so the expected return from holding a bond of one maturity has no effect on the demand for a bond of another maturity Opposite of expectations theory The argument for why bonds of different maturities are not substitutes is that investors have strong preferences for bonds of one maturity but not for another, so they will be concerned with the expected returns only for bonds of the maturity they prefer This might occur because they have a particular holding period in minds and if they can match the maturity of the bond to the desired holding period, they can obtain a certain risk at all If the term to maturity equals the holding period the return is known for certain because it equals the yield exactly, and no interest-rate risk exists Differing yield curve patterns are accounted for by supply-and-demand differences associated with bonds of different maturities In the typical situation the demand for long-term bonds will have lower prices and higher than that for short-term bonds, long-term bonds will have lower prices and higher interest rates, and hence the yield curve will typically slope upward
Direct listing
Sell shares direct to the public without an intermediary Didn't hire an underwriter, instead they hired a financial advisor which caused them only 29 million euro (usually the underwriting process tends to be more expensive). Explained that they were not raising capital with the IPO Goal was to allow existing shareholders to sell shares in the open market $132 per share - reference price Opened at $165.90
Liquidity Premium Theory
States that the IR on a long term bond will equal an average of short term IRs expected to occur over the life of the long term bond plus a liquidity premium (also referred to as a term premium) that responds to supply and demand conditions for that bond Key assumption: bonds of different maturities are substitutes, which means that the expected return on one bond does influence the expected return on a bond of a different maturity, but it allows investors to prefer one maturity over another Bonds of different maturities are assumed to be substitutes, but not perfect substitutes Investors prefer short term bonds bc these bonds bear less IR risk So investors must be offered a positive liquidity premium to induce them to hold longer-term bonds This outcome would modify the expectations theory by adding a positive liquidity premium to the equation that describes the relationship between long and short term IRs
Change in IR due to a business cycle expansion
Supply curve has a large rightward shift because investment purchases are sensitive to business cycles Demand also shifts to the right by a smaller amount because of marginal propensity to save/marginal propensity to consume Price goes down, interest rate goes up, and quantity increases
Changes in the IR due to increase in expected inflation
Supply curve shifts right because repaying debt will be cheaper Demand curve shifts left because lower expected return Price goes down, interest rate goes up We cannot determine the size of the change in quantity because it depends on the relative size of the shifts
Particularly attractive feature of the liquidity premium theory
Tells you what the market is predicting about future short-term interest rates just from the slope of the yield curve. A steeply rising yield curve, as in panel (a) of Figure 5.6, indicates that short-term interest rates are expected to rise in the future. A moderately steep yield curve, as in panel (b), indicates that short-term interest rates are not expected to rise or fall much in the future. A flat yield curve, as in panel (c), indicates that short-term rates are expected to fall moderately in the future. Finally, an inverted yield curve, as in panel (d), indicates that short-term interest rates are expected to fall sharply in the future.
Liquidity
The ability to easily convert an asset into cash if the need arises this influences the interest rate as well More liquid = more desirable US Treasury bonds = most liquid of all long-term bonds Because they are so widely traded they are the easiest to sell quickly Risk premium is more accurately called a risk and liquidity premium An asset is liquid if the market has many buyers and sellers of it An increase in liquidity will lead to an increase in asset demand
Expectations theory
The interest rate on a long term bond will equal an average of the short term interest rates that people expect to occur over the life of the long-term bond Says that the reason interest rates on bonds of different maturities differ is that short term interest rates are expected to have different values at different future dates Key assumption: Buyers of bonds do not prefer bonds of one maturity over another so they will not hold any quantity of a bond if its expected return is less than that of another bond with a different maturity: perfect substitutes If bonds with different maturities =perfect substitutes the expected return must be equal
Government budget If government spending is greater than taxes, the spending has to be funded through the sale of bonds
The supply curve will shift right
Expected returns
The weighted average of all possible returns R^e = p1(R1) + p2(R2) + ... pn(Rn) p = probability of the occurrence of the return, R = return, R^e = expected return, n = number of possible outcomes, Ri = return in the i possible outcome, Pi = probability of occurrence of the return of Ri An increase in the R^e relative to an alternative asset will lead to an increase in asset demanded
Shifts in the demand for bonds
Wealth: An increase in wealth leads to an increase in asset demand Demand curve shifts to the right Increase in wealth could be caused by many things ex. business cycle expansion or an increase in the propensity to save
Bond with default risk
Will always have a positive risk premium An increase in its default risk will raise the risk premium
Flat yield curve
future short-term interest rates expected to fall moderately
How can the liquidity premium theory explain the occasional appearance of
inverted yield curves if the liquidity premium is positive? It must be that at times short-term interest rates are expected to fall so much in the future that the average of the expected short-term rates is well below the current short-term rate. Even when the positive liquidity premium is added to this average, the resulting long-term rate will still be lower than the current short-term interest rate.
Expected inflation: Fisher equation : r = i - π^e If we expected inflation to increase,
that will lead to a decrease in the real interest rate which is good for borrowers (lowers cost of borrowing) → increase in supply of bonds → supply curve shifts right
