Ch 6 Interest Rates
Suppose you are given the yields on the following Treasury securities. For simplicity, assume that there is no maturity risk premium. 1-yr security: 4.10% yield 2-yr security: 5.40% yield 3-yr security: 6.80% yield 4-yr security: 8.10% yield If you want to forecast the yield on a 2-year security one year from now, you need to build the following equation: _______. And the yield on 2-year security in one year would be _______.
(1 + 0.0410)^1 x (1 + z)^2 = (1 + 0.0680)^3 1.0410 x (1 + z)^2 = 1.21818643 (1 + z)^2 = 1.17020791 (1 + z) = 1.08176148 z = 0.08176148 = 8.18%
Suppose you are given the yields on the following Treasury securities. For simplicity, assume that there is no maturity risk premium. 1-yr security: 4.10% yield 2-yr security: 5.40% yield 3-yr security: 6.80% yield 4-yr security: 8.10% yield If you want to forecast the yield on a 1-year security in one year from now, you need to build the following equation: _______. And the yield on 1-year security in one year would be _______.
(1 + 0.0540)^2 = (1 = 0.0410)^1 x (1 + x)^1 1.110916 = 1.0410 (1 + x) 1.06716234 = 1 + x x = 0.06716234 = 6.72%
Suppose you are given the yields on the following Treasury securities. For simplicity, assume that there is no maturity risk premium. 1-yr security: 4.10% yield 2-yr security: 5.40% yield 3-yr security: 6.80% yield 4-yr security: 8.10% yield If you want to forecast the yield on a 1-year security in two years from now, you need to build the following equation: _______. And the yield on 1-year security in two years would be _______.
(1 + 0.0680)^3 = (1 + 0.0540)^2 x (1 + y)^1 1.21818643 = 1.110916 x (1 + y) 1.09656034 = 1 + y y = 0.09656034 = 9.66%
Suppose you are given the yields on the following Treasury securities. For simplicity, assume that there is no maturity risk premium. 1-yr security: 4.10% yield 2-yr security: 5.40% yield 3-yr security: 6.80% yield 4-yr security: 8.10% yield If you want to forecast the yield on a 3-year security one year from now, you need to build the following equation: _______. And the yield on 3-year security in one year would be _______.
(1 + 0.0810)^4 = (1 + 0.0410)^1 x (1 + r)^3 1.36553481 = (1.0410) x (1 + r)^3 1.31175294 = (1+r)^3 1.09467201 = 1 + r r = 0.09467201 = 9.47%
We can be sure of 2 things:
(1) IRs will vary (2) IRs will increase if inflation appears to be headed higher or decrease if inflation is expected to decline
List the various factors that influence the cost of money.
(1) production opportunities (2) time preferences for consumption (3) risk (4) inflation
The IR paid to savers depends on:
(1) the rate of return that producers expect to earn on invested capital (2) savers' time preferences for current vs future consumption (3) the riskiness of the loan (4) the expected future rate of inflation
Quantitative Problem: Today, interest rates on 1-year T-bonds yield 1.8%, interest rates on 2-year T-bonds yield 2.3%, and interest rates on 3-year T-bonds yield 3.5%. (a) If the pure expectations theory is correct, what is the yield on 1-year T-bonds one year from now? (b) If the pure expectations theory is correct, what is the yield on 2-year T-bonds one year from now? (c) If the pure expectations theory is correct, what is the yield on 1-year T-bonds two years from now? Be sure to use a geometric average in your calculations. Do not round intermediate calculations. Round your answer to four decimal places.
(a) (1 + 0.023)^2 = (1 + 0.018) x (1 + x) (1.023)^2 = (1.018) x (1 + x) x = 0.02802456 or 2.8025% (b) (1 + 0.035)^3 = (1 + 0.018) x (1 + x)^2 (1.035)^3 = (1.018) x (1 + x)^2 1.08911383 = (1 + x)^2 1.04360616 = 1 + x x = 0.04360616 or 4.3606% (c) (1 + 0.035)^3 = (1 + 0.023)^2 x (1 + x) (1.035)^3 = (1.023)^2 x (1 + x) 1.10871788 = 1.046529 x (1 + x) 1.05942394 = 1 + x x = 0.05942394 or 5.9424%
Suppose the real risk-free rate of interest is r* = 5% and it is expected to remain constant over time. Inflation is expected to be 1.40% per year for the next two years and 3.50% per year for the next three years. The maturity risk premium is 0.1 × (t−1)%, where t is number of years to maturity, a liquidity premium is 0.55%, and the default risk premium for a corporate bond is 1.30%. (a) The avg inflation during the first 3 years is _______. (b) What is the yield on a 3-yr T-bond? (c) What is the yield on a 3-yr BBB-rated bond? (d) If the yield on a 5-yr T-bond is 8.06% and a 6-yr T-bond is 8.53%, the expected inflation in 6 yrs is _______.
(a) (1.40% + 1.40% + 3.50%) / 3 = 2.10% = IP3 (b) IP3 = 2.10% MRP3 = 0.1 (3-1)% = 0.2% rT3 = r* + IP3 + MRP3 = 5% + 2.10% + 0.2% = 7.30% (c) rC3BBB = rT3 + DRP + LP = 7.30% + 1.30% + 0.55% = 9.15% (d) rT6 = r* + IP6 + MRP6 8.53% = 5% + IP6 + 0.1 x (6-1)% 8.53% = 5% + IP6 + 0.5% 3.03% = IP6 3.03% = (1.40% + 1.40% + 3.50% + 3.50% + 3.50% + x)/ 6 3.03% = (13.3% + x) / 6 18.18% = 13.3% + x 4.88% = x = expected inflation rate in 6th yr
Ace Products has a bond issue outstanding with 15 years remaining to maturity, a coupon rate of 8.6% with semiannual payments of $43, and a par value of $1,000. The price of each bond in the issue is $1,220.00. The bond issue is callable in 5 years at a call price of $1,086. (a) What is the bond's current yield? (b) What is the bond's nominal annual yield to maturity (YTM)? (c) What is the bond's nominal annual yield to call (YTC)? (d) Assuming interest rates remain at current levels, will the bond issue be called? The firm _______ call the bond.
(a) (8.6% x 1000) / 1220 = 0.0704918 = 7.05% (b) =RATE(15x2, 8.6%x1000/2,-1220,1000)x2 = 6.3099 = 6.31% (c) =RATE(5x2, 8.6%x1000/2, -1220, 1086)x2 = 5.0925 = 5.09% (d) should
Suppose the market offers the following Treasury securities: 1-yr security: 4.10% yield 2-yr security: 5.40% yield 3-yr security: 6.80% yield 4-yr security: 8.10% yield 5-yr security: 9.60% yield 6-yr security: 11.10% yield (a) 1-year Treasury security, 1 year from now (b) 2-year Treasury security, 2 years from now (c) 3-year Treasury security, 1 year from now (d) 4-year Treasury security, 2 years from now
(a) 1-year Treasury security, 1 year from now (1 + 0.0540)^2 = (1 = 0.0410)^1 x (1 + x)^1 1.110916 = 1.0410 (1 + x) 1.06716234 = 1 + x x = 0.06716234 = 6.72% (b) 2-year Treasury security, 2 years from now (1 + 0.0810)^4 = (1. 0.0540)^2 x (1 + x)^2 1.36553481 = 1.110916 x (1 + x)^2 1.22919718 = (1 + x)^2 1.10869165 = 1 + x x = 0.10869165 or 10.87% (c) 3-year Treasury security, 1 year from now (1 + 0.0810)^4 = (1 + 0.0410)^1 x (1 + r)^3 1.36553481 = (1.0410) x (1 + r)^3 1.31175294 = (1+r)^3 1.09467201 = 1 + r r = 0.09467201 = 9.47% (d) 4-year Treasury security, 2 years from now (1 + 0.1110)^6 = (1. 0.0540)^2 x (1 + x)^4 1.88054769 = 1.110916 x (1 + x)^4 1.69279017 = (1 + x)^4 1.14064573 = 1 + x x = 0.14064573 or 14.06%
An analyst evaluating securities has obtained the following information. The real rate of interest is 2.4% and is expected to remain constant for the next 5 years. Inflation is expected to be 2.1% next year, 3.1% the following year, 4.1% the third year, and 5.1% every year thereafter. The maturity risk premium is estimated to be 0.1 × (t - 1)%, where t = number of years to maturity. The liquidity premium on relevant 5-year securities is 0.5% and the default risk premium on relevant 5-year securities is 1%. (a) What is the yield on a 1-year T-bill? (b) What is the yield on a 5-year T-bond? (c) What is the yield on a 5-year corporate bond?
(a) What is the yield on a 1-year T-bill? r = r* + IP = 2.4% + 2.1% = 4.5% (b) What is the yield on a 5-year T-bond? r = r* + IP + MRP = 2.4% + [(2.1% + 3.1% + 4.1% + 5.1% + 5.1%)/ 5] + 0.1 x (5 - 1)% = 2.4% + 3.9% + 0.5% =6.8% (c) What is the yield on a 5-year corporate bond? 2.4% + 3.9% + 0.4% + 1% + 0.5% = 8.2%
Suppose the real risk-free rate of interest is r* = 5% and it is expected to remain constant over time. Inflation is expected to be 1.40% per year for the next 2 years and 3.50% per year for the next 4 years. The maturity risk premium is 0.1×(t−1)%, where t is the number of years to maturity, a liquidity premium is 0.55%, and the default risk premium for a corporate bond is 1.30%. (a) yield on 3-yr T-bond (b) yield on 3-yr corporate bond (c) yield on 6-yr T-bond (d) yield on 6-yr corporate bond (e) expected inflation in 7 yrs, if yield on 7-yr T-bond is 8.70%
(a) yield on 3-yr T-bond rT3 = r* + IP3 + MRP3 = 5% + [(1.40% + 1.40% + 3.50%) / 3] + 0.1 x (3-1)% = 5% + 2.10% + 0.2% = 7.30% (b) yield on 3-yr corporate bond rC3 = rT3 + DRP + LP = 7.30% + 1.30% + 0.55% = 9.15% (c) yield on 6-yr T-bond rT6 = r* + IP6 + MRP6 = 5% + [(1.40% + 1.40% + 3.50% + 3.50% + 3.50% + 3.50%) / 3] + 0.1 x (6-1)% = 5% + 2.80% + 0.5% = 8.30% (d) yield on 6-yr corporate bond rC6 = rT6 + DRP + LP = 8.30% + 1.30% + 0.55% = 10.15% (e) expected inflation in 7 yrs, if yield on 7-yr T-bond is 8.70% rT7 = r* + IP7 + MRP7 8.70% = 5% + [ (1.40% + 1.40% + 3.50% + 3.50% + 3.50% + 3.50% + x) / 7] + 0.1 (7-1)% 8.70% = 5% + [(16.8% + x) / 7] + 0.6% 3.1% = (16.8% + x) / 7 21.7% = 16.8% + x x = 4.90% = expected inflation in 7 yrs
Financial Crisis of 2007-2008
- Federal Reserve est. extremely low IRs - Hope: lower cost of capital --> encourage business investment + help repair damaged housing mkt + prop up stock & bond mkts - After crisis, it appeared econ was saved from total collapse, but was still weak and unemployment was high. - Fed Reserve response: "quantitative easing": Fed sys purchased lg amts of longer-term fin assets from leading fin institutions. Paid for these assets by injecting new funds into econ --> downward P on IRs - Fed pushed 10-yr Treasury rate <2%, shorter-term rates were close to 0 - Next decade: econ rebounded. Fed wants to return IRs back to "norm." However, further P from Pres + others to keep rates low
For example, if you know that the real rate of interest is 5% and it is expected to remain constant for the next 3 years, inflation is expected to be 1.40% next year, 3.50% the following year, and 4.90% the third year, then the average expected inflation rate over the next three years is (1.40% + 3.50% + 4.90%) / 3 = 3.27%. If also you can estimate that the maturity risk premium is 0.1 × (t−1)%, where t is number of years to maturity, then the yield on a 1-year Treasury bill, which has neither default risk premium nor liquidity risk premium, is as follows: rT1 = r* + IP1 + MRP1 = 5% + 1.40% + 0.1 x (1-1)% = 6.40% What is the yield on a 2- & 3-yr T-bill?
2-yr T-bill: = 5% + [(1.40% + 3.5%) / 2] + 0.1 x (2-1)% = 5% + 2.45% + 0.1% = 7.55% 3-yr T-bill: = 5% + 3.27% + 0.1x(3-1) = 5% + 3.27% + 0.2% = 8.47%
Suppose your friend is deciding between investing in two consecutive 1-year Treasury bonds and a 2-year Treasury bond. The yield on a 1-year bond is 4.10% today and the yield on a 2-year bond is 5.40%. You tell your friend that if the expected interest rate on a 1-year bond 1 year from now is _______, then she should be indifferent between the two options.
2-yr bond will yield the following amount per $1 you invested: Yield at the end of year 2 = $1 × ( 1 + 0.0540)^2 = $1.110916 1-yr bond: $1 x (1 + 0.0410) x (1 + x) = $1.110916 $1.0410 x (1 + x) = $1.110916 (1 + x) = $1.110916 / $1.0410 x = ($1.110916 / $1.0410) - 1 x = 0.06716234 or 6.716234% She should be indifferent between the two options if the expected IR on a 1-yr bond 1 yr from now = 6.72%
The Nominal, or Quoted, Risk-Free Rate of Interest, rRF = r* + IP
6-3B It is the quoted rate on a risk-free security such as a US T-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.
Which of the following bonds would have the largest duration? A. 10-year, zero coupon bonds B. 10-year, 7% annual coupon bonds C. 10-year, 3% annual coupon bonds D. 5-year, 3% annual coupon bonds E. 3-year, 7% annual coupon bonds
A. 10-year, zero coupon bonds
flight to quality
An increase in the demand for low-risk government bonds, coupled with a decrease in the demand for virtually every risky investment.
_______ bonds are exchangeable at the option of the holder for the issuing firm's common stock. Bonds can be issued with warrants giving the holder the option to purchase the firm's stock for a stated price, thereby providing a capital gain if the stock's price rises. _______ bonds contain a provision that allows holders to sell them back to the company prior to maturity at a prearranged price. _______ bonds pay interest only if the firm has earnings, while an indexed (purchasing power) bond bases interest payments on an inflation index to protect the holder from inflation.
Convertible; Putable; Income
True or False: The real risk-free rate is always greater than the nominal risk-free rate.
False The real risk-free rate, r*, is the nominal risk-free rate, rRF minus an inflation premium: r* = rRF −IP. Typically, the real risk-free rate is positive and less than the nominal risk-free rate. Rarely, however, in case of a deflation—when the expected inflation is negative—the real risk-free rate may exceed the nominal risk-free rate.
Macroeconomic factors have an important effect on both the general level of interest rates and the shape of the yield curve. These primary factors are: _______ _______ policy, the federal budget deficit or surplus, international factors like the foreign trade balance and interest rates abroad, and the level of _______ _______.
Federal Reserve; business activity
_______ _______ can also influence the allocation of capital and the level of IRs.
Government policy
Suppose that a 1-year Treasury bond currently yields 5.00%, and a 2-year bond yields 5.50%. As an investor, you have two options: Option 1: Buy a 2-year security and hold it for 2 years. Option 2: Buy a 1-year security, hold it for 1 year, and then at the end of the year reinvest the proceeds in another 1-year security.
In two years, Option 1 will yield the following amount per $1 you invested: Yield at the end of year 2 = $1 × ( 1 + 0.055)^2 = $1.113 The pure expectation theory implies that Option 2 should yield the same amount, which can be expressed as follows: Yield at the end of year 2 = $1 × (1 + 0.05) × (1 + x) = $1.113, where x stands for the expected IR on a 1-yr T-security 1 yr from now. $1 x (1 + 0.05) x (1 + x) = $1.113025 $1.05 x (1 + x) = $1.113025 (1 + x) = $1.113025 / $1.05 x = ($1.113025 / $1.05) - 1 x = 0.0600238 or 6.00238%
Potter Industries has a bond issue outstanding with an annual coupon of 6% and a 10-year maturity. The par value of the bond is $1,000. If the going annual interest rate is 8.6%, what is the value of the bond?
N = 10 FV = 1000 IR = 8.6 PMT = 1000 x 6% = 60 PV = ? PV = $830.16
Potter Industries has a bond issue outstanding with a 6% coupon rate with semiannual payments of $30, and a 10-year maturity. The par value of the bond is $1,000. If the going annual interest rate is 8.6%, what is the value of the bond?
N = 10 x 2 = 20 FV = 1000 IR = 8.6 / 2 = 4.3 PMT = (1000 x 6%) / 2 = 30 PV = ? PV = $827.93
_______ risk is the risk of a decline in a bond's value due to an increase in interest rates. This risk is higher on bonds that have long maturities than on bonds that will mature in the near future. _______ risk is the risk that a decline in interest rates will lead to a decline in income from a bond portfolio. This risk is obviously high on callable bonds. It is also high on short-term bonds because the shorter the bond's maturity, the fewer the years before the relatively high old-coupon bonds will be replaced with new low-coupon issues. Which type of risk is more relevant to an investor depends on the investor's _______, which is the period of time an investor plans to hold a particular investment.
Price; Reinvestment; investment horizon
supply & demand curves in capital markets
S-curve: upward slope D-curve: downward Intersection: IR
_______ interest rates are especially volatile, rising rapidly during booms and falling equally rapidly during recessions.
Short-term
Suppose you are contemplating between purchasing one two-year bond today versus purchasing two consecutive one-year bonds. Based on the video, which of the following describes what would make you indifferent between the two options?
The average of what a one-year bond pays today and what you expect a one-year bond will pay in one year from today is equal to what a two-year bond pays today.
A company is more likely to call its bonds if they are able to replace their current high-coupon debt with less expensive financing. A bond is more likely to be called if its price is _______ par -- because this means that the going market interest rate is less than its coupon rate.
above
Based on the video, to calculate the real risk-free rate you need to know the risk-free rate and _______. The real risk-free rate, r* =
an inflation premium, IP r* = rRF - IP
A(n) _______ is a long-term contract under which a borrower agrees to make payments of interest and principal on specific dates. There are four main types reflecting who the issuers are: _______, corporate, state and local government, and foreign. Each type differs with respect to _______ and expected return. All have some common characteristics even though they may have different contractual features.
bond; Treasury; risk
Inflationary pressures are strongest during _______ _______, also exerting pressure on rates.
business booms
In a free economy, _______, like other items, is allocated through a market system, where funds are transferred and prices are established.
capital
Consumers' time preferences for consumption establish how much:
consumption they are willing to defer and hence how much they will save at different IRs.
"current real rate of interest"
current interest rate MINUS current inflation rate (shows how much investors really earned after the effects of inflation are removed)
Companies raise capital in 2 main forms:
debt & equity
If the government spends more than it takes in as taxes, it runs a _______, which must be covered by additional borrowing or by printing money. If the government borrows money, this _______ the demand for funds and _______ interest rates. If the government prints money, the result will be _______ inflation, which will _______ interest rates.
deficit; increases; increases; increased; increase; deficit; higher
If U.S. businesses and individuals buy more goods from abroad than they sell (more imports than exports), the U.S. is running a foreign trade _______, which must be financed. This generally means that the U.S. borrows from nations with export _______. The larger the trade _______, the higher the tendency to borrow, so U.S. interest rates become highly dependent on interest rate levels abroad. Consequently, this interdependency _______ the Fed's ability to use monetary policy to control U.S. economic activity.
deficit; surpluses; deficit; constrains
Equity investors expect to receive _______ and _______, the sum of which represents the cost of equity.
dividends; capital gains
Interest rates have been on a _______ trajectory over the past 4 decades.
downward
Interest rate on 10-yr Treasury securities
fell below 0.5% for the first time in history in March 2020
Mortgage bonds are backed by _______ _______. First mortgage bonds are senior in priority to claims of second mortgage bonds. Debentures are long-term bonds that are not secured by a mortgage. Subordinated debentures are bonds having claims on assets only after senior debt has been paid in full in the event of liquidation. _______ bonds are rated triple B or higher, and many banks and other institutional investors are legally limited to only holding these bonds. In contrast, junk bonds are high-risk, high-yield bonds.
fixed assets; Investment-grade
Bonds care be _______-rate bonds with a constant coupon rate over the life of the bond, or they can be _______-rate bonds with a coupon rate that varies over time depending on the level of interest rates. _______ bonds pay no annual interest but are sold at a _______ par, thus compensating investors in the form of capital appreciation. An original issue issue discount (OID) bond is any bond originally offered at a price _______ par value.
fixed; floating; Zero coupon; discount below; below its
Higher risk leads to _______ interest rates.
higher
The _______ the expected rate of inflation, the _______ the required dollar return.
higher; larger
The Federal Reserve Board controls the money supply. To stimulate the economy, the Fed _______ the money supply. The initial effect would be to cause short-term rates to decline; however, a 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 is true when the Fed _______ the money supply.
increases; larger; tightens
The _______ is the price that lenders receive and borrowers pay for debt capital.
interest rate
For fixed-rate bonds it's important to realize that the value of the bond has a(n) _______ relationship to the level of interest rates. If interest rates rise, then the value of the bond _______; however, if interest rates fall, then the value of the bond _______. A _______ bond is one that sells below its par value. This situation occurs whenever the going rate of interest is above the coupon rate. Over time its value will _______ approaching its maturity value at maturity. A _______ bond is one that sells above its par value. This situation occurs whenever the going rate of interest is below the coupon rate. Over time its value will _______ approaching its maturity value at maturity. A par value bond is one that sells at par; the bond's coupon rate is equal to the going rate of interest. Normally, the coupon rate is set at the going market rate the day a bond is issued so it sells at par initially.
inverse; falls; rises; discount; increase; premium; decrease
Because of their additional default and liquidity risk, corporate bonds yield _______ _______ T-bonds with the same maturity. In addition, the yield spread between corporate and T-bonds is _______ the longer the maturity. This occurs because longer-term corporate bonds have _______ default and liquidity risk than shorter-term bonds, and both of these premiums are _______ in T-bonds.
more than; larger; more; absent
The _______ value of a bond is its stated face value or maturity value, and its coupon interest rate is the stated annual interest rate on the bond. The maturity date is the date on which the par value must be repaid. A _______ provision gives the issuer the right to redeem the bonds under specified terms prior to their normal maturity date, although not all bonds have this provision. Some bonds have _______ provisions which require the issuer to systematically retire a portion of the bond issue each year. Because sinking fund provisions facilitate their orderly retirement, bonds with these provisions are regarded as being _______ so they will have _______ coupon rates than similar bonds without these provisions.
par; call; sinking fund; safer; lower
The value of any financial asset is the _______ value of the cash flows the asset is expected to produce.
present
Most capital in the U.S. is allocated through the _______ ________, where the _______ ______ is the price.
price system; interest rate
Longer maturity bonds have high _______ risk but low _______ risk, while higher coupon bonds have a higher level of _______ risk and a lower level of _______ risk. To account for the effects related to both a bond's maturity and coupon, many analysts focus on a measure called _______, which is the weighted average of the time it takes to receive each of the bond's cash flows.
price; reinvestment; reinvestment; price; duration
The _______ _______ theory states that the shape of the yield curve depends on investors' expectations about future IRs. The 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 don't view long-term bonds as being riskier than short-term bonds.
pure expectations
Nominal, or quoted, rate, r =
r = rRF + DRP + LP + MRP r = the quoted, or nominal, rate of interest on a given security IP = inflation premium. IP is equal to the avg expected rate of inflation over the life of the secuirty. The expected future inflation rate is not necessarily equal to the current inflation rate, so IP is not necessarily equal to current inflation 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 0 for US Treasury securities, but it rises as the riskiness of the issuer increases. 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 ver low for Treasury securities & for securities issued by lg, strong firms, but it is relatively high on securities issued by sm, privately held firms. MRP = maturity risk premium. As we will explain later, longer-term bonds, even T-bonds, are exposed to a significant risk of price declines due to increases in inflation and IRs, and a maturity risk premium is charged by lenders to reflect this risk.
Suppose the yield on 30-day Treasury bills is currently 7.07%. Also, you collected the following information on current interest rate premiums: IP = 4.15% LP = 0.70% MRP = 1.80% DRP = 2.75% The real risk-free rate of return is _______.
r* = rRF - IP = 7.07% - 4.15% = 2.92%
real risk-free rate of interest, r*
r* = the real risk-free rate of interest and the rate that would exist on a riskless security in a world where no inflation was expected not static, changes over time, dependent on economic conditions (1) rate of return that corps and other borrowers expect to earn on productive assets and (2) people's time preferences for current vs future consumption most experts believe r* typically fluctuates in the range of 1-3% best estimate of r* is the rate of return on indexed T-bonds Between 2011-2020, rate on indexed T-bonds has often been neg. --> b/c of Fed Res policies that have pushed IRs on T-securities below the rate of expected inflation
Unlike T-securities, corporate bonds have both a default risk premium and a liquidity risk premium. Suppose that the liquidity premium on 3-yr bonds is LP = 0.55%, and the default risk premium on 3-yr bonds is DRP = 1.30%. Real Rate of Interest = 5% Inflation 1st year = 1.40% Inflation 2nd year = 3.50% Inflation 3rd year = 4.90% The formula for calculating the yield on a corporate bond is: _______. The yield on a 3-yr corporate bond is _______.
rcorp = r* + IP + DRP + LP + MRP = 5% + [(1.40% + 3.50% + 4.90%)/3] + 0.55% + 1.30% + 0.1 x (3-1)% = 10.32%
Business conditions influence interest rates. During a _______, the demand for money and the inflation rate tend to fall and the Fed tends to _______ the money supply to stimulate the economy. As a result, there is a tendency for interest rates to decline during _______. During _______, short-term rates decline more sharply than long-term rates because (1) the Fed operates mainly in the short-term sector, so the Fed's intervention has the strongest effect there; (2) Long-term rates reflect the average expected inflation rate over the next 20 to 30 years and this expectation doesn't change much due to the level of current inflation. So, short-term rates are _______ volatile than long-term rates.
recession; increase; recessions; recessions; more
If we could accurately forecast interest rates, financing decisions would be easy. Although it's difficult to predict future interest rate levels, it is easy to predict that interest rates will fluctuate. Therefore, 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. The firm's optimal financial policy depends on the nature of the firm's assets—the easier its assets can be sold, the more feasible it is for the firm to use _______-term debt. Consequently, it is logical for a firm to finance current assets with _______-term debt and to finance fixed assets with _______-term debt.
short; short; long
The term structure of IRs describes the relationship between long- & short-term rates. When these data are plotted, the resulting graph is called a _______ _______. A(n) _______ yield curve is upward sloping because investors charge higher rates on longer-term bonds, even when inflation is expected to remain constant. A(n) _______ yield curve occurs when IRs on intermediate-term maturities are higher than rates on both short- & long-term maturities. A(n) _______ yield curve is downward sloping and indicates that investors expect inflation to decrease. The shape of the yield curve depends on expectations about future inflation and the effects of maturity on bonds' risks.
yield curve; normal; humped; abnormal
Pure Expectations Theory
- used to explain the yield curve - the yield on longer-term bonds is made up of what the market expects the yield to be on shorter-term bonds in the future
risk premium
the excess return required from an investment in a risky asset over that required from a risk-free investment
Suppose you had bought a 30-yr T-bond at a nominal IR = 3% and the inflation avg 4% over the next 30 yrs. Then the real IR would turn out to be _____.
3-4 = -1
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.
Goldilocks policy
keeping the economy strong without triggering inflation
Producers' expected returns on their business investments set an _______ limit to how much they can pay for savings.
upper
