Chapteer 2
Factors affecting nominal interest rates (6)
1. Inflation 2. Real risk-free rate 3. Default Risk 4. Liquidity Risk 5. Special Provisions 6. Term to Maturity
when the rate of interest is lower than the equilibrium interest rate
shortage of loanable funds - Some borrowers will be unable to obtain the funds they need at current rates. As a result, interest rates will increase, causing more suppliers of loanable funds to enter the market and some demanders of funds to leave the market.
A Higher Real Risk Free Rate indicates
society prefers to consume today rather than in future (the higher its time value of money/ rate of time preference)
the rate of interest is set higher than the equilibrium rate
surplus of loanable funds some suppliers will lower the offered interest rate to borrowers to become more competitive & borrowers will absorb the surplus
the relationship between maturity and yield to maturity
term structure
An investor wants to be able to buy 4 percent more goods and services in the future in order to induce her to invest today. During the investment period prices are expected to rise by 2 percent. Which statement(s) below is/are true? I. 4 percent is the desired real risk-free interest rate. II. 6 percent is the approximate nominal rate of interest required. III. 2 percent is the expected inflation rate over the period.
All are true
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. strong tendency of foreign investors
Real interest rate
An interest rate that has been adjusted to remove the effects of inflation to reflect the real cost of funds to the borrower and the real yield to the lender or to an investor.
Low Country/ Sovereign Risk
Increased inflow of foreign funds, - increased supply of funds -equilibrium falls, quantity increases
Liquidity Premium Theory
Investors prefer short-term liquid securities, BUT are willing to invest in long-term securities IF compensated with a premium for lower liquidity
Liquidity Risk Premium ("Illiquidity" Premium)
Liquid markets exist for most government securities, corporate stocks, some corporate bonds BUT many bonds don't trade regularly or on organized exchanges such as the NYSE (b/c FV comes at maturity), If investors wish to sell bonds quickly, they would get a lower price than if they waited until maturity to sell. SO, investors demand liquidity premium to compensate for bond's lack of liquidity and potential price discount from selling it early. Also exists for securities w/ longer maturities b/c more sensitive to interest rate changes / greater exposure to price risk (loss of capital value)
term structure of interest rates (yield curve)
a comparison of market yields on securities, assuming all characteristics (default risk, liquidity risk) EXCEPT maturity are the same +,-, 0
Inflation
a continual increase in the price level of a basket of goods and services IP measured using indexes such as Consumer Price Index (CPI) and Producer Price Index (PPI)
for securities that are not highly liquid, investors demand
a liquidity risk premium to the interest rate as compensation
The market segmentation theory assumes that investors and borrowers are generally unwilling to shift from one maturity sector without
adequate compensation in the form of an interest rate premium
Why do PV's decrease as interest rates increase?
as interest rates increase, fewer funds need to be invested at the beginning of an investment horizon to receive a stated amount at the end of the investment horizon.
The liquidity premium increases
as maturity increases
Weakness of Unbiased Expectations theory
assumes investors are risk neutral, when in reality investors are risk averse
According to thee liquidity premium theory, LT rates are
equal to geometric averages of current and expected short-term rates, plus liquidity risk premiums that increase with the security's maturity
implied forward one year rate for next year if in period 1 is AKA to
expected one year rate for year 2
forward rate
expected or "implied" rate on a short-term security that is to be originated at some point in the future
if interest rates rise, the value of investment portfolios of FIs and Individuals
fall; results in a loss of wealth
future value of an investment _____ as interest rates _______
increase; increase (Note also that as interest rates increase, future values increase at an increasing rate. The increase in future value is greater when interest rates rose by 4 percent, from 8 percent to 12 percent, compared to when they rose from 12 percent to 16 percent)
A 15-payment annual annuity has its first payment in nine years. If the payment amount is $1,400 and the interest rate is 7 percent, what is the most you should be willing to pay today for this investment?
investment value today = - pv (rate, nper, pmt, fv, 1) * Discount Factor of Year 9 Where, rate = 7% n= 15 pmt=1,400 fv=0 Discount factor of year 9 = 1.07^-9= .543934 PV0 = $1,400 × {[1 - 1.07^-15]/0.07}/1.078
annual inflation rate
percentage increase in the average price level from one year to the next [CPI (t+1) - CPI (t) / CPI (t)] x 100
high levels of actual or expected inflation
prices of goods/services will increase relative to present in the future
Special Provisions (SCP)
provisions that impact the security holder beneficially or adversely and as such are reflected in the interest rates on securities that contain such provisions
non-price restrictions
restrictions put on borrowers as a condition of borrowing fees, collateral, covenants
Besides Maturity, yield curves can also reflect investors' preferences on
the liquidity of a maturity in reality there are liquidity differences among securities traded at different points along the yield curve. For ex: yields on newly issued 30-year Treasury bonds may be less than yields on (seasoned issues) 10-year Treasury bonds if investors prefer new ("on the run") securities to previously issued ("off the run") securities. Specifically, since (historically) the Treasury issues new 10-year notes and 30-year bonds only at the long end of the maturity spectrum, an existing 10-year Treasury bond would have to have been issued 20 years previously (i.e., it was originally a 30-year bond when it was issued 20 years previously). The increased demand for the newly issued "liquid" 30-year Treasury bonds relative to the less liquid 10-year Treasury bonds can be large enough to push the equilibrium interest rate on the 30-year Treasury bonds below that on the 10-year Treasury bonds and even below short-term rates.
the nominal risk-free rate will be equal to the real risk-free rate only when
the market expects inflation rate to be zero
According to the fisher effect, when an investor purchases a security that pays interest.
the nominal risk free rate > real risk free rate, because of inflation
equilibrium interest rate
the only interest rate at which the quantity of loans demanded equals the quantity of loans supplied temporary equilibrium the "nominal rate"
default risk premium
the portion of a nominal interest rate or bond yield that represents compensation for the possibility of default difference between a quoted interest rate on a security (security j) and a Treasury security with similar maturity, liquidity, tax, and other features (such as callability or convertibility)
An arbitrage opportunity exists if
the return for holding a four-year bond to maturity does NOT equal the expected return for investing in four successive one-year bonds For example, if the investor could earn more on the one-year bond investments, he could short (or sell) the four-year bond, use the proceeds to buy the four successive one-year bonds, and earn a guaranteed profit over the four-year investment horizon.
According to the unbiased expectations theory, if the market is in equilibrium
the return for holding a four-year bond to maturity should equal the expected return for investing in four successive one-year bonds
as the supply of securities decreases in the short-term market and increases in the long-term market
the slope of the yield curve becomes steeper
the greater the number of compounding periods per year
the smaller the present value of a future amount
As the total wealth of financial market participants (households, businesses, etc.) increases,
the supply curve shifts down and to the right/ equilibrium interest rate falls Why? the absolute dollar value available for investment purposes increases
Explanations for the shape of the yield curve fall predominantly into three theories:
the unbiased expectations theory, the liquidity premium theory, and the market segmentation theory.
If the supply of short-term securities had increased while the supply of long-term securities had decreased,
the yield curve would have a flatter slope and might even have sloped down remember- supply and interest rates are + correlated, if supply decreases, rates decrease
one year forward rate for any year, n years into the future
= [ (1+ 1RN)^N / (1+ 1RN -1)^ (N-1)] - 1
Factors that functionally impact the fair interest rate on an individual security (putting the factors from diff markets together)
= f( IP, RFR, DRP, LRP, SCP, MP) IP and RFR apply to all securities, while rest vary on individual basis
Market Segmentation Theory
Assumes that investors do not consider securities with different maturities as perfect substitutes. Rather, individual investors and FIs have preferred investment horizons (habitats) dictated by the nature of the liabilities they hold. ex- banks prefer st bonds b/c st liabilities while insurance companies prefer lt bonds Thus, interest rates are determined by distinct supply and demand conditions within a particular maturity segment (e.g., the short end and long end of the bond market).
special provisions that provide benefits to the security issuer
Call-ability higher interest rates
Why are US treasury securities considered no risk?
Default probability is 0 b/c of govt's taxation powers and ability to print currency
Inflation (IP) and Interest Rates
Direct Relationship why? An investor must earn a higher interest rate when inflation increases to compensate for the increased cost of saving (forgoing consumption of real goods/services today and buying these same g/s at higher prices in the future)
If you earn 0.5 percent a month in your bank account, this would be the same as earning a 6 percent annual interest rate with annual compounding.
False
monetary expansion
Fed increases the supply of funds available in markets. Supply curve shifts down to right, Equilibrium rate falls, Quantity increases
Monetary policy
Government policy that attempts to manage the economy by controlling the growth in the money supply and thus interest rates.
Special provisions that provide benefits to the security holder
Tax free status, convertibility lower interest rates
Maturity Premium (MP)
The change in required interest rates as the maturity of a security changes
Operation Twist
When the Fed buys long-term government securities and sells short-term government securities The program involved the sale of $400 billion of short-term Treasuries in exchange for long-term Treasuries. The program was designed to lower rates on long-term bonds, while keeping short-term interest rates unchanged. By intentionally lowering yields, the Fed was forcing investors to consider other investments that would help the economy more. Many argue that the policy worked. In June 2012, the yield on the 10-year Treasury fell to a 200-year low.
flat yield curve
a yield curve that indicates that interest rates do not vary much at different maturities
Unbiased Expectations Theory
at a given point in time the yield curve reflects the market's current expectations of future short-term rates.
present values of security investments _____ as interest rates _____
decrease; increase also present values of investments decrease at decreasing rates, as interest rates increase The fall in present value is greater when interest rates rose by 4% ( from 12 % to 16 %) compared to when they rose by 4% from 8% to 12 %
the non-financial sectors of U.S business_____ far more loanable funds than they ____
demand; supply
governments demand funds to...
finance temporary imbalances between operating revenues (tax) and expenditures (road improvements, schools)
for investors, interest payments on municipal securities
free of federal, state, and local taxes
supply of loanable funds
funds provided to the financial markets by net suppliers of funds (savers)
Unbiased Expectations Theory posits that current LT interest rates are
geometric averages of current and expected future SHORT-term interest rates.
According to thee liquidity premium theory, longer maturities on securities
have higher risk of capital losses and are more sensitive to interest rate changes
In a growing economy, the demand for funds is _____ and interest rates will tend to ______.
high; increase
according to the unbiased expectations theory, the yield curve will be flat if
if future one-year rates are expected to remain constant each successive year into the future, then the four-year bond rate will be equal to the three-year bond rate
according to the unbiased expectations theory, the yield curve will slope up
if future one-year rates are expected to rise each successive year into the future EX- the current four-year T-bond rate will exceed the three-year bond rate, which will exceed the two-year bond rate,
r =
interest rate earned per period on an investment (the nominal interest rate/ number of compounding periods per year)
Callability
issuer has option to retire, or call, security prior to maturity at a preset price; higher interest rates
Term to Maturity
length of time a security has until maturity
interest rates for municipal bonds
less than a comparable taxable bond (ex. treasury bond)
All else equal, the convertible security holder requires a _____ interest rate than a comparable nonconvertible security holder
lower
quantity of loanable funds demanded
negatively relates to interest rates
the decrease in funds demanded with increasing interest rates will lead to a demand curve that is _______
negatively sloped
Fisher effect
nominal interest rate = inflation rate + real interest rate Nominal risk- free interest rates observed in financial markets (the one year Treasury Bill rate) must compensate investors for: 1. Any reduced purchasing power on funds (or principal) lent due to inflationary price changes (AKA inflation rate) 2. An Additional premium above the expected rate of inflation for forgoing present consumption (AKA real-risk free rate)
Real risk-free rate
nominal risk free rate that would exist on a security if no inflation were expected RFR on an investment= % increase in the buying power of a dollar therefore, measures society's relative time prefereence for consuming today rather than tomorrow
convertible (special) feature of a security
offers the holder the opportunity to exchange one security for another type of the issuer's securities at a preset price.
Annuity Due Value
ordinary annuity value x (1+r) investment pays at the beginning of the period, an extra interest payment is received for the original investment
riskiness of investment securities & interest rates
positive correlation EX: higher risk= higher rate demanded by the buyer
Nominal interest rates are important because they affect the _______ of most securities traded in the money and capital markets, at home and abroad
price
Liquidity Risk
risk that a security cannot be sold at a predictable price with low transaction costs at short notice
Default risk
risk that a security issuer will default on the security by missing an interest or principal payment
the loanable funds theory views the level of interest rates as being determined by
supply and demand for funds
For investors, interest payments on corporate bonds
taxable at state, local, and federal levels
The higher the yield on securities (the lower the price)
the higher the demand for them
nominal interest rate
the interest rate before taking inflation into account.
Country or Sovereign Risk depends on and is reflected by:
underlying economic conditions (inflation, unemployment, economic growth) if these improve in a country relative to others, the flow of funds to that country also increases
According to thee liquidity premium theory, investors will hold long term maturities only
when offered at a premium to compensate for future uncertainty in the security's value
Risk-free investments have rates of return:
with a standard deviation equal to zero; return is certain
Upward sloping yield curve
yields rise steadily with maturity Most common yield curve on average MP is positive
Default Risk Premiums tend to increase / decrease when
Increase when economy is contracting Decrease when economy is expanding why? inflation decrease when unemployment increases
For investors, interest payments on Treasury bonds
are taxable at the federal level but exempt from state and local (city) levels
When the governments budgeted expenditures exceed its tax revenues, its said to have a
budget deficit
According to the loanable funds theory, a change in the supply or demand curve for loanable funds...
causes interest rates to move
Disequilibrium in market forces causes
changes in 1. equilibrium (nominal) interest rate 2. quantity of funds traded in that market
Largest suppliers of loanable funds & what
1. Households with excess income 2. Households wanting to reallocate asset portfolio holdings
Factors that affect the demand for loanable funds for a financial security
1. Interest Rate 2. Utility derived from asset purchased with borrowed funds 3. Restrictiveness of nonprice conditions 4. Economic conditions
Factors that affect the supply of loanable funds for a financial security
1. Interest Rate 2. Total Wealth of Suppliers 3. Risk of Financial Security 4. Monetary expansion 5. Economic conditions
________ securities have a more active secondary market and hence are more ____ than _______ securities
1. ST 2. liquid 3. LT
During the financial crisis, Baa corporate bond rates spiked and 10-year T-note rates dropped significantly. In the loanable funds framework, this can be interpreted as...
1. a reduction in the supply of funds, due to uncertainty of credit quality of firms in the corporate bond market and 2. an increase in the supply of funds to the treasure notes market, as investors fled to quality investments 3. Equilibrium rate was higher in corp bond market and lower in Treasury Notes market
the quantity of loanable funds supplied increases when...
1. interest rates rise (the reward for supplying funds is higher) 2. high economic growth (as total wealth of consumer increases, they have more to supply) 3. low perceived risk of securities investments
According to the liquidity premium theory, the yield curve will slope up as long as _____ and upward yield curve may reflect expectations that ______
1. the liquidity premium increases with maturity fast enough 2. future interest rates will rise, be flat, or even fall ex: investors expectations that future short term rates will be flat, but because liquidity premiums increase with maturity, the yield curve will still slope up
inverted yield curve
A downward-sloping yield curve indicates that short-term interest rates are generally higher than long-term interest rates. generally don't last very long