Chapter 6: Interest Rates Managerial Finance
3 main theories to explain the shape of the yield curve:
(Pure) Expectations theory Maturity preference theory Market segmentation theory
Quoted interest rate =
r = r* + IP + DRP + LP + MRP The equation can be rewritten as: Nominal, or quoted, rate = r = rRF + DRP + LP + MRP
(Nominal risk-free rate of interest): rRF =
r* + IP
In a recession (expansion) business spending drops (increases) and rates go down (up). Recession slows demand → businesses don't borrow →
rates go down
Increased borrowing by the Federal government increases interest rates. Higher demand for funds →
rates go up
because of changing market forces, investors perceive that Market H has become relatively more risky. This changing perception will induce many investors to
shift toward safer investments—referred to as a "flight to quality."
Historically, long-term rates are generally above short-term rates because of the maturity risk premium; so all yield curves usually
slope upward. For this reason, people often call an upward-sloping yield curve a "normal" yield curve and a yield curve that slopes downward an inverted or "abnormal" yield curve.
On the other hand, if the market expects inflation to decline in the future, long-term bonds will have a
smaller inflation premium than will short-term bonds. Finally, because investors consider long-term bonds to be riskier than short-term bonds because of interest rate risk, the maturity risk premium always increases with maturity.
There is a price for each type of capital, and these prices change over time as
supply and demand conditions change.
r=
the quoted, or nominal, rate of interest on a given security.
r*=
the real risk-free rate of interest, r* is pronounced "r-star," and it is the rate that would exist on a riskless security in a world where no inflation was expected.
The Maturity Preference Theory is one of the theories used to try to help explain
the shape of the yield curve.
The Yield curve changes continuously and can take on different shapes. The yield curve can be
upward sloping, which means that long-term securities have higher yields than short-term securities. A flat yield curve would simply mean that the rates on long and short-term securities are about the same. With a downward slope to the yield curve, short-term rates are higher than long-term rates. In the U.S., we have had all of these different yield shapes at one time or another in our history.
Yield curve can be used to obtain insights into what the market thinks future interest rates will be, the calculations above (although they appear to be precise) will only approximate these expectations unless the pure expectations theory holds or we know with certainty the exact maturity risk premium. Because neither of these conditions holds, it is difficult to know
for sure what the market is forecasting. Note too that even if we could determine the market's consensus forecast for future rates, the market is not always right. So a forecast of next year's rate based on the yield curve could be wrong. Therefore, obtaining an accurate forecast of interest rates for next year—or even for next month—is extremely difficult.
We can use the Expectations theory to estimate the market's forecast of future short-term rates. Those forecasted future rates are called
forward rates.
Higher default risk (The risk that the issuer of debt will fail to make scheduled payments) →
higher interest rate
Higher liquidity risk (The risk associated with the difficulty of selling an asset quickly without loss of value) →
higher interest rate
Higher maturity risk (Longer-term securities are riskier than short-term securities) →
higher interest rate
Maturity preference theory says that since longer terms are riskier, there must be a premium for investors. Longer loan term →
higher premium
A liquidity premium is required to compensate investors for the difficulty associated with selling an asset. Lower liquidity (harder to sell like a family home) →
higher required return
Maturity premium reflects the fact that, in general, long-term securities are riskier than short-term maturities. Lower term to maturity →
higher required return
The normal shape of the yield curve is upward sloping. This means that most of the time, long-term interest rates are
higher than short-term interest rates.
Four key factors that affect interest rates:
-Production opportunities -Time preference for consumption -Risk -Expected inflation
Short-term treasury faces
inflation risk
Long-term treasury faces
inflation risk and maturity risk
Short-term corporate bonds face
inflation risk, default risk, and liquidity risk
Long-term corporate bonds face
inflation risk, default risk, liquidity risk, and maturity risk.
The supply curve in each market is upward sloping, which indicates that
investors are willing to supply more capital the higher the interest rate they receive on their capital. Likewise, the downward-sloping demand curve indicates that borrowers will borrow more if interest rates are lower. The interest rate in each market is the point where the supply and demand curves intersect.
Higher interest rates mean higher costs, which mean that consumers will spend
less on things like houses and cars (and vice versa).
Although "investing short" preserves one's principal, the interest income provided by short-term T-bills is
less stable than that on long-term bonds.
The direction of interest rates affects financing decisions and whether to use
long-term (they may pay a higher rate but will lock it in for a longer period of time) or short-term debt.
(Pure) Expectations theory
long-term interest rates are an average of short-term rates and expected future short-term rates.
The yield curve (which is a graph of the term Structure of Interest Rates) shows the relationship between term to maturity and the
yield to maturity.
Suppose I can lend money to (buy bonds from) Bad-Idea.com or Amazon. Both bonds are paying 6%. Which should I pick?
Amazon
"normal" yield curve
An upward-sloping yield curve.
Federal reserve impacts interest rates through their open market operations where they buy and sell securities.
Buying securities (goes up) → interest rates go down (investors are paying a higher price for the same expected cash flows) Selling securities (goes down) → interest rates go up
In the U.S. what measure do we determine changes in when we calculate inflation?
Consumer price index (Bureau of Labor Statistics)
Several key macroeconomic factors which influence interest rates:
Federal funds rate Open market purchases Federal spending Global relationships Business activity
Risk
In a financial market context, the chance that an investment will provide a low or negative return. Risk is uncertainty. The higher the uncertainty, the higher the interest rate.
If a large meteorite is expected to hit the planet in five years, what would this do to longer term interest rates?
Increase
If businesses have a whole lot of production opportunities, what would this do (all else equal) to interest rates?
Increase
Combining the Expectations Theory and the Maturity Preference Theory gives us a better picture of what is happening with the yield curve. Remember, we want to understand the relationship between time and interest rates.
Inflations expected to increase → Long-term rates will be higher than short-term rates Inflation expected to decrease → long-term rates may be lower than short-term rates
If you thought short-term rates were going to drop in the future, do you think long-term rates would be higher or lower than short-term rates?
Lower. The expectations theory shows how beliefs about future interest rate directions affect current long-term rates.
What is the risk wih treasury bills?
Purchasing power risk (aka Inflation Risk) is the chance that inflation ends up differently than we expected.
Expected return on 2-year series=
Rate on 2-year bond - MRP
International investors can buy debt all over the globe, so U.S. rates must remain competitive. Rates too low → Foreign investors sell →
Rates go up
Any debt asset other than Treasury Bills has other risks to consider, too. Required return =
Real RF rate of return + Inflation premium + Default risk premium + Liquidity premium + Maturity risk premium
Maturity preference theory
Since longer terms are riskier, there must be a premium for investors who lend long term.
Inflation
The amount by which prices increase over time.
Market segmentation theory
There is no relationship between short and long-term rates. Supply and demand functions in sectors of the market move independently.
What shape would you expect the yield curve to be if inflation was expected to remain unchanged?
Upward.
Suppose current 1-year T-bills are yielding 4%. You think that yields on 1-year T-Bills will be 5% next year (forward rate). Assuming that you have a 2-year investment horizon, would you lock in a 2-year note yielding 4.25% per year? At a 2-year rate would you be indifferent?
Your choice is two 1-year securities in a row or buy and hold 2-year security.
Government policy can also influence the allocation of capital and the level of interest rates. For example, the federal government has
agencies that help designated individuals or groups obtain credit on favorable terms. Among those eligible for this kind of assistance are small businesses, certain minorities, and firms willing to build plants in areas with high unemployment. Still, most capital in the United States is allocated through the price system, where the interest rate is the price.
The Yield to Maturity on a bond is the rate you expect to get if you hold the
bond until it matures.
short-term interest rates are especially volatile, rising rapidly during
booms and falling equally rapidly during recessions. (The shaded areas of the chart indicate recessions.)
(Pure) expectations theory combine with maturity preference theory to create the
combined expectations/maturity preference
In general, the quoted (or nominal) interest rate on a debt security, r, is
composed of a real risk-free rate, plus several premiums that reflect inflation, the security's risk, its liquidity (or marketability), and the years to its maturity.
DRP=
default risk premium. This premium reflects the possibility that the issuer will not pay the promised interest or principal at the stated time. DRP is zero for U.S. Treasury securities, but it rises as the riskiness of the issuer increases.
When plotting the Yield curve,
find the yield to maturities of securities that differ only by term to maturity. Focus on impact of differences in maturity. U.S. Treasury securities are usually used.
Federal funds rate is the overnight rate at which banks lend reserves to
other banks. The Federal Reserve sets the target federal funds rate, which directly impacts short-term interest rates.
Treasury bonds (long-term bonds) face both
purchasing power risk and maturity risk.
T-Bills are assumed to be default risk-free, but there is a big market for its debt. And T-Bills are very liquid, therefore maturity risk is not an issue. A risk for T-Bills inflation, or
purchasing power risk.
Market segmentation theory says supply and demand functions in sectors of the market move independently.
+: Debt markets by maturity move independently. Different investors focus on different sectors. -: Some investors will move to different maturities for good opportunities. Traders looking for even minor premiums.
A Basis point is just 1/100 of 1% so
100 basis points = 1%.
An increase in the demand for funds raises rates, while a decline in demand lowers rates. Therefore, bond traders would push up the
2-year yield and simultaneously lower the yield on 1-year bonds. This buying and selling would cease when the 2-year rate becomes a weighted average of expected future 1-year rates.
The current interest rate minus the current inflation rate (which is also the gap between the inflation bars and the interest rate curve) is defined as the
"current real rate of interest." It is called a "real rate" because it shows how much investors really earned after the effects of inflation are removed.
On a day-to-day basis, a variety of macroeconomic factors may influence one or more of these components; hence, macroeconomic factors have an important effect on both the general level of interest rates and the shape of the yield curve. The primary factors are
(1) Federal Reserve policy, (2) the federal budget deficit or surplus, (3) international factors, including the foreign trade balance and interest rates in other countries, and (4) the level of business activity.
Long-term bonds have higher yields for two reasons:
(1) Inflation is expected to be higher in the future. (2) There is a positive maturity risk premium.
The effect of maturity risk premiums is to raise interest rates on long-term bonds relative to those on short-term bonds. This premium, like the others, is difficult to measure, but
(1) it varies somewhat over time, rising when interest rates are more volatile and uncertain, and then falling when interest rates are more stable; and (2) in recent years, the maturity risk premium on 20-year T-bonds has generally been in the range of one to two percentage points.
We see that the interest rate paid to savers depends
(1) on the rate of return that producers expect to earn on invested capital, (2) on savers' time preferences for current versus future consumption, (3) on the riskiness of the loan, and (4) on the expected future rate of inflation.
The four most fundamental factors affecting the cost of money are
(1) production opportunities, (2) time preferences for consumption, (3) risk, and (4) inflation.
As you probably learned in your economics courses,
(1) the money supply has a significant effect on the level of economic activity, inflation, and interest rates. (2) In the United States, the Federal Reserve Board controls the money supply.
Real rate precise calculation:
(1+Nominal) = (1+Real)(1+Inflation) Real=((1+Nominal)/(1+Inflation)) -1 convert percentages to decimals
Because inflation increased from 1972 to 1981, the general tendency during that period was toward higher interest rates. However, since the 1981 peak, the trend has generally been downward. The shaded areas in the graph represent recessions, during which
(a) the demand for money and the rate of inflation tended to fall and (b) the Federal Reserve tended to increase the money supply in an effort to stimulate the economy. During recessions, short-term rates decline more sharply than long-term rates. This occurs for two reasons: (a) The Fed operates mainly in the short-term sector, so its intervention has the strongest effect there. (b) Long-term rates reflect the average expected inflation rate over the next 20 to 30 years, and this expectation generally does not change much, even when the current inflation rate is low because of a recession or high because of a boom.
inverted or "abnormal" yield curve
A downward-sloping yield curve. Short term bonds pay higher yields than longer term bonds. Usually signals current or future recession.
yield curve
A graph showing the relationship between bond yields and maturities. So short-term rates were higher than long-term rates, and the yield curve was thus downward sloping. Short-term rates had dropped below long-term rates, the yield curve was upward sloping.
liquidity premium (LP)
A premium added to the equilibrium interest rate on a security if that security cannot be converted to cash on short notice and at close to its "fair market value."
inflation premium (IP)
A premium equal to expected inflation that investors add to the real risk-free rate of return. equal to the average expected inflation rate over the life of the security into the rate they charge. As discussed previously, the actual interest rate on a short-term default-free U.S. Treasury bill, rT-Bill, would be the real risk-free rate, r*, plus the inflation premium (IP): rT-Bill= rRF = r* + IP
maturity risk premium (MRP)
A premium that reflects interest rate risk.
pure expectations theory
A theory that states that the shape of the yield curve depends on investors' expectations about future interest rates. The term structure of interest rates, often simply referred to as the "expectations theory." The expectations theory assumes that bond traders establish bond prices and interest rates strictly on the basis of expectations for future interest rates and that they are indifferent to maturity because they do not view long-term bonds as being riskier than short-term bonds. If this were true, the maturity risk premium (MRP) would be zero, and long-term interest rates would simply be a weighted average of current and expected future short-term interest rates.
humped yield curve
A yield curve where interest rates on intermediate-term maturities are higher than rates on both short- and long term maturities.
Corporate bond yield spread =
Corporate bond yield - treasury bond yield
If my customers aren't buying, and businesses cut way back on new projects, what would this do (all else equal) to interest rates?
Decrease
Changes in interest rates also have implications for savers. For example, if you had a 401(k) plan—and someday most of you will—you would probably want to invest some of your money in a bond mutual fund. You could choose a fund that had an average maturity of 25 years, 20 years, or on down to only a few months (a money market fund). How would your choice affect your investment results and hence your retirement income?
First, your decision would affect your annual interest income. For example, if the yield curve was upward sloping, as it normally is, you would earn more interest if you chose a fund that held long-term bonds. Note, though, that if you chose a long-term fund and interest rates then rose, the market value of your fund would decline. On the other hand, if rates declined, your fund would increase in value. If you invested in a short-term fund, its value would be more stable, but it would probably provide less interest income per year. In any event, your choice of maturity would have a major effect on your investment performance and therefore on your future income.
Expected inflation
Higher expected inflation means higher interest rates. Investors are interested in the increase in their purchasing power.
What do we call the general condition where prices are rising in the economy?
Inflation
rRF= r*+IP.
It is the quoted rate on a risk-free security such as a U.S. Treasury bill, which is very liquid and is free of most types of risk. Note that the premium for expected inflation, IP, is included in rRF.
LP=
Liquidity (or marketability) premium. This is a premium charged by lenders to reflect the fact that some securities cannot be converted to cash on short notice at a "reasonable" price. LP is very low for Treasury securities and for securities issued by large, strong firms, but it is relatively high on securities issued by small, privately held firms. MRP = maturity risk premium. As we will explain later, longer-term bonds, even Treasury bonds, are exposed to a significant risk of price declines due to increases in inflation and interest rates, and a maturity risk premium is charged by lenders to reflect this risk.
Production opportunities
More production opportunities mean a higher demand for funds. A higher demand for funds means higher interest rates.
Nominal rates are stated or observed rates. These are the rates you see everywhere. Nominal rate =
Real rate of return + Inflation premium (the same equation as risk free rate)
Expected inflation has an especially important effect on the yield curve's shape, especially the curve for U.S. Treasury securities. Treasuries have essentially no default or liquidity risk, so the yield on a Treasury bond that matures in t years can be expressed as follows:
T-bond yield = r*t + IPt + MRPt
default risk premium (DRP)
The difference between the interest rate on a U.S. Treasury bond and a corporate bond of equal maturity and marketability. The average default risk premiums vary over time, and tend to get larger when the economy is weaker and borrowers are more likely to have a hard time paying off their debts.
Borrowers bid for the available supply of debt capital using interest rates
The firms with the most profitable investment opportunities are willing and able to pay the most for capital, so they tend to attract it away from inefficient firms and firms whose products are not in demand.
production opportunities
The investment opportunities in productive (cash generating) assets.
time preferences for consumption
The preferences of consumers for current consumption as opposed to saving for future consumption.
Nominal, or quoted, risk-free rate
The rate of interest on a security that is free of all risk; rRF is proxied by the T-bill rate or the T-bond rate; rRF includes an inflation premium. To be strictly correct, the risk-free rate should be the interest rate on a totally risk-free security—one that has no default risk, no maturity risk, no liquidity risk, no risk of loss if inflation increases, and no risk of any other type. However, as the recent downgrade of U.S. Treasuries illustrates, there is no such security; hence, there is no observable truly risk-free rate. However, one security is free of most risks—a Treasury Inflation Protected Security (TIPS), whose value increases with inflation. Short-term TIPS are free of default, maturity, and liquidity risks and of risk due to changes in the general level of interest rates. However, they are not free of changes in the real rate.
real risk-free rate of interest, r*
The rate of interest that would exist on default-free U.S. Treasury securities if no inflation were expected. It may be thought of as the rate of interest on short-term U.S. Treasury securities in an inflation-free world. The real risk-free rate is not static—it changes over time, depending on economic conditions, especially on (1) the rate of return that corporations and other borrowers expect to earn on productive assets and (2) people's time preferences for current versus future consumption. Borrowers' expected returns on real assets set an upper limit on how much borrowers can afford to pay for funds, whereas savers' time preferences for consumption establish how much consumption savers will defer—hence, the amount of money they will lend at different interest rates.
term structure of interest rates
The relationship between bond yields and maturities. The term structure is important to corporate treasurers deciding whether to borrow by issuing long- or short-term debt and to investors who are deciding whether to buy long- or short-term bonds. Therefore, both borrowers and lenders should understand (1) how long- and short-term rates relate to each other and (2) what causes shifts in their relative levels.
interest rate risk
The risk of capital losses to which investors are exposed because of changing interest rates.
reinvestment rate risk
The risk that a decline in interest rates will lead to lower income when bonds mature and funds are reinvested. We should also note that although long-term bonds are heavily exposed to interest rate risk, short-term bills are heavily exposed to reinvestment rate risk. When short-term bills mature and the principal must be reinvested, or "rolled over," a decline in interest rates would necessitate reinvestment at a lower rate, which would result in a decline in interest income.
foreign trade deficit
The situation that exists when a country imports more than it exports.
Time preference for consumption
There is always a preference for consumption now versus later. The charge to delay consumption and lend your money out is the interest rate.
One recent study estimates that both the default risk premium and liquidity premium vary over time, and that the majority of the corporate bond yield spread can be attributed to default risk. Corporate bonds' default and liquidity risks are
affected by their maturities. For example, the default risk on Coca-Cola's short-term debt is very small because there is almost no chance that Coca-Cola will go bankrupt over the next few years. However, Coke has some bonds that have a maturity of almost 76 years, and although the odds of Coke defaulting on those bonds might not be very high, there is still a higher probability of default risk on Coke's long-term bonds than on its short-term bonds.
Despite a few recent concerns about the Treasury's long-run ability to service its growing debt, we generally assume that U.S. Treasury securities are free of
default risk in the sense that one can be virtually certain that the federal government will pay interest on its bonds and pay them off when they mature. Therefore, we assume that the default risk premium on Treasury securities is zero. Further, active markets exist for Treasury securities, so we assume that their liquidity premium is also zero. Thus, as a first approximation, the rate of interest on a Treasury security should be the risk-free rate, rRF, which is the real risk-free rate plus an inflation premium, rRF = r* + IP.
If the federal government spends more than it takes in as taxes, it runs a
deficit, and that deficit must be covered by additional borrowing (selling more Treasury bonds) or by printing money. If the government borrows, this increases the demand for funds and thus pushes up interest rates. If the government prints money, investors recognize that with "more money chasing a given amount of goods," the result will be increased inflation, which will also increase interest rates. So the larger the federal deficit, other things held constant, the higher the level of interest rates.
Inflation peaked at about 13% in 1980. But interest rates continued to increase into 1981 and 1982, and they remained quite high until 1985 because people feared another increase in inflation. Thus, the "inflationary psychology" create
during the 1970s persisted until the mid-1980s. People gradually realized that the Federal Reserve was serious about keeping inflation down, that global competition was keeping U.S. auto producers and other corporations from raising prices as they had in the past, and that constraints on corporate price increases were diminishing labor unions' ability to push through cost-increasing wage hikes. As these realizations set in, interest rates declined.
Although the real risk-free rate, r*, varies somewhat over time because of changes in the
economy and demographics, these changes are random rather than predictable. Therefore, the best forecast for the future value of r* is its current value. However, the inflation premium, IP, varies significantly over time and in a somewhat predictable manner.
If the market is not in equilibrium, buying and selling will quickly bring about
equilibrium.
All this interdependency limits the ability of the Federal Reserve to use monetary policy to control economic activity in the United States. For example, if the Fed attempts to lower U.S. interest rates and this causes rates to fall below rates abroad,
foreigners will begin selling U.S. bonds. Those sales will depress bond prices, which will push up rates in the United States. Thus, the large U.S. trade deficit (and foreigners' holdings of U.S. debt that resulted from many years of deficits) hinders the Fed's ability to combat a recession by lowering interest rates.
If interest rates go up, the values of many assets, such as bonds, will
go down (and vice versa).
Because maturity risk premiums are positive, if other things were held constant, long-term bonds would always have
higher interest rates than short-term bonds. However, market interest rates also depend on expected inflation, default risk, and liquidity, each of which can vary with maturity.
A default premium compensates for the risk that the issuer of debt will fail to make scheduled payments. Higher default risk →
higher required return
U.S. firms also invest and raise capital throughout the world, and foreigners both borrow and lend in the United States. There are markets for
home loans; farm loans; business loans; federal, state, and local government loans; and consumer loans. Within each category, there are regional markets as well as different types of submarkets. For example, in real estate, there are separate markets for first and second mortgages and for loans on single-family homes, apartments, office buildings, shopping centers, and vacant land. And, of course, there are separate markets for prime and subprime mortgage loans. Within the business sector, there are dozens of types of debt securities and there are several different markets for common stocks.
The goal of quantitative easing is to
increase liquidity in financial markets.
If the Fed wants to stimulate the economy, it
increases the money supply. The Fed buys and sells short-term securities, so the initial effect of a monetary easing would be to cause short-term rates to decline. However, a larger money supply might lead to an increase in expected future inflation, which would cause long-term rates to rise even as short-term rates fell. The reverse holds if the Fed tightens the money supply. The Fed's job is to promote economic growth while keeping inflation at bay. This is a delicate balancing act.
IP=
inflation premium. IP is equal to the average expected rate of inflation over the life of the security. The expected future inflation rate is not necessarily equal to the current inflation rate, so IP is not necessarily equal to current inflation.
It is important to note that the inflation rate built into interest rates is the
inflation rate expected in the future, not the rate experienced in the past. Note also that the inflation rate reflected in the quoted interest rate on any security is the average inflation rate expected over the security's life. Thus, the inflation rate built into a 1-year bond is the expected inflation rate for the next year, but the inflation rate built into a 30-year bond is the average inflation rate expected over the next 30 years.
The risk that a borrower will default, which means the borrower will not make scheduled interest or principal payments, also affects the
market interest rate on a bond: The greater the bond's risk of default, the higher the market rate. Once again, we are assuming that Treasury securities have no default risk; hence, they carry the lowest interest rates on taxable securities in the United States. For corporate bonds, bond ratings are often used to measure default risk. The higher the bond's rating, the lower its default risk and, consequently, the lower its interest rate.
Assets with higher trading volume are generally easier to sell and are therefore
more liquid. The average liquidity premiums also vary over time. During the recent financial crisis, the liquidity premiums on many assets soared. The market for many assets that were once highly liquid suddenly dried up as everyone rushed to sell them at the same time. The liquidity of real assets also varies over time. For example, at the height of the housing boom, many homes in "hot" real estate markets were often sold the first day they were listed. After the bubble burst, homes in these same markets often sat unsold for months.
It is also important to recognize that actions that lower short-term rates won't
necessarily lower long-term rates. Lower rates could cause foreigners to sell their holdings of U.S. bonds. These investors would be paid with dollars, which they would then sell to buy their own currencies. The sale of dollars and the purchase of other currencies would lower the value of the dollar relative to other currencies, which would make U.S. goods less expensive, which would help manufacturers and thus lower the trade deficit. Note also that during periods when the Fed is actively intervening in the markets, the yield curve may be temporarily distorted. Short-term rates may be driven below the long-run equilibrium level if the Fed is easing credit and above the equilibrium rate if the Fed is tightening credit. Long-term rates are not affected as much by Fed intervention.
Real rate of return % =
nominal rate of return % - inflation rate %
All of the rates we see in the market are
nominal rates.
Real rates reflect your increase in purchasing power. Real rates subtract effects
of inflation.
Higher interest rates mean higher costs, which mean that some business
opportunities will be lost (and vice versa).
The interest rate is the
percentage cost of debt. Borrowers have to pay the interest and lenders demand the interest.
If the term risk-free rate is used without the modifiers real or nominal, people generally mean the
quoted (or nominal) rate, and we follow that convention in this book. Therefore, when we use the term risk-free rate, rRF , we mean the nominal risk-free rate, which includes an inflation premium equal to the average expected inflation rate over the remaining life of the security.
In general, we use the T-bill rate to approximate the short-term risk-free rate and the T-bond rate to approximate the long-term risk-free rate. So whenever you see the term risk-free rate, assume that we are referring to the
quoted U.S. T-bill rate or to the quoted T-bond rate. Our definition of the risk-free rate assumes that, despite the recent downgrade, Treasury securities have no meaningful default risk. And for convenience, we will assume in our subsequent problems and examples that Treasury securities have no default risk.
It is difficult to measure the real rate precisely, but most experts believe that r* typically fluctuates in the range of 1% to 3%. Perhaps the best estimate of
r* is the rate of return on indexed Treasury bonds. It is interesting to note that between 2011 and 2017, the rate on indexed Treasury bonds has often been negative. These negative real rates of interest have arisen largely because of Federal Reserve policies that have pushed interest rates on Treasury securities below the rate of expected inflation.
Corporate bond yield =
r*t + IPt + MRPt + DRPt + LPt
When the economy is expanding, firms need capital, and this demand pushes
rates up. Inflationary pressures are strongest during business booms, also exerting upward pressure on rates. Conditions are reversed during recessions: Slack business reduces the demand for credit, inflation falls, and the Federal Reserve increases the supply of funds to help stimulate the economy. The result is a decline in interest rates.
The Risk-free return includes a
real rate of return and a premium for expected inflation. Risk-free rate = Real RF rate of return + Inflation premium Higher expected inflation → higher required return
U.S. treasury bills are a
risk-free asset. Treasury bills are short term debt and treasury bonds are long term debt.
Businesses and individuals in the United States buy from and sell to people and firms all around the globe. If they buy more than they sell (that is, if there are more imports than exports), they are said to be
running a foreign trade deficit. When trade deficits occur, they must be financed, and this generally means borrowing from nations with export surpluses. Thus, if the United States imported $200 billion of goods but exported only $100 billion, it would run a trade deficit of $100 billion, and other countries would have a $100 billion trade surplus. The United States would probably borrow the $100 billion from the surplus nations. At any rate, the larger the trade deficit, the higher the tendency to borrow. Note that foreigners will hold U.S. debt if and only if the rates on U.S. securities are competitive with rates in other countries. This causes U.S. interest rates to be highly dependent on rates in other parts of the world.
Longer-term corporate bonds also tend to be less liquid than
shorter-term bonds. Because short-term debt has less default risk, someone can buy a short-term bond without doing as much credit checking as would be necessary for a long-term bond. Thus, people can move in and out of short-term corporate debt relatively rapidly. As a result, a corporation's short-term bonds are typically more liquid and thus have lower liquidity premiums than its long-term bonds.
Financing decisions would be easy if we could make accurate forecasts of future interest rates. Unfortunately, predicting interest rates with consistent accuracy is nearly impossible. However, although it is difficult to predict future interest rate levels, it is easy to predict that interest rates will fluctuate—they always have, and they always will. That being the case,
sound financial policy calls for using a mix of long- and short-term debt as well as equity to position the firm so that it can survive in any interest rate environment. Further, the optimal financial policy depends in an important way on the nature of the firm's assets—the easier it is to sell assets to generate cash, the more feasible it is to use more short-term debt. This makes it logical for a firm to finance current assets such as inventories and receivables with short-term debt and to finance fixed assets such as buildings and equipment with long-term debt.
In recent years, inflation has been quite low, averaging about 2% a year, and it was even negative in 2009, as prices fell in the midst of the deep recession. However, long-term interest rates have been
volatile because investors are not sure if inflation is truly under control or is about to jump back to the higher levels of the 1980s. In the years ahead, we can be sure of two things: (1) Interest rates will vary. (2) Interest rates will increase if inflation appears to be headed higher or decrease if inflation is expected to decline.
