Interest Rates Flashcards
(93 cards)
1
Q
Why is interest charged?
A
- The interest rate on a loan should cover the opportunity costs of supplying credit so that the interest should include:
- Compensation for inflation
- Compensation for default risk
- Compensation for the opportunity cost of waiting (interest)
2
Q
What is the future value of a 1 year investment?
A
The future value of an investment (principal) in one year (FV1) with an interest rate i:
Principal x (1 + i) = FV1
3
Q
What is the future value of a n year investment?
A
Principal x (1+i)^n = FVn
4
Q
What is discounting and what is the equality?
A
- Discounting is the process of finding the present value of funds that will be received in the future
- Lets you compare financial assets
- Discounting: PV = FVn / (1+i)^n
5
Q
What is the price of an asset?
A
- The price of a financial asset is equal to the PV of the payments to be receiving from owning it
- Passet = PV of payments received
- For either debt or equity assets
- Passet = PV of payments received
6
Q
What is a simple loan?
A
The borrower receives from the lender an amount called the principal and agrees to repay the lender the principal plus interest on a specific date when the loan matures
7
Q
What is a fixed payment loan?
A
Requires the borrower to make regular periodic payments of principal and interest to the lender
8
Q
What is a discount loan?
A
The borrower repays the amount of the loan in a single payment at maturity but receives less than the face value of the bon initially
9
Q
What is a coupon bond?
A
Requires multiple payments of interest on a regular basis, and a payment of the face value at maturity
10
Q
What is face value?
A
Face value (or par value): amount to be repaid by the bond issuer (borrower) at maturity
11
Q
What is a coupon?
A
Coupon: annual fixed dollar amount of interest paid by the issuer of the bond to the buyer
12
Q
What is a coupon rate?
A
Coupon rate: the value of the coupon expressed as a percentage of the face value of the bond
13
Q
What is a coupon yield?
A
Current yield: the value of the coupon expressed as a percentage of the current price
14
Q
What is the maturity of a coupon bond?
A
length of time before the bond expires and the issuer makes the face value payment to the buyer
15
Q
Pcoupon bonds =
A
- Pcoupon bonds = C/(1+i)^1 + … + C/(1+i)^n + FaceValue/(1+i)^n
- Pcoupon bonds = PV of holding coupon bonds
- Inverse relationship between i and P
16
Q
What is yield to maturity?
A
- The interest rate i that makes the present value of the payments from an asset equal to the asset’s price today
- i where PVasset = Passet
- i where PV of future payments = value today
17
Q
What is the YTM of a fixed payment/student loan?
A
- For a fixed payment loan with fixed payments FP and a maturity of n years:
- Loan Value = FP/(1+i) + … + FP/(1+i)^n
18
Q
What is the YTM of a simple loan?
A
Loan = repayment/(1+i)^n
19
Q
What is the TYM of a discount loan?
A
- A one-year discount bond that sells for price P with face value FV
- i = (FV - P)/P
- P = FV/(1+i)^n
20
Q
What is the YTM of a coupon bond?
A
- For a bond that makes coupon payments (C = coupon rate x FV) and matures in n years:
- P = C/(1+i) + … + C/(1+i)n + FaceValue/(1+i)n
- Need to calculate i:
- YTM = (C + ((FV - Pbond)/n)) / ((FV + Pbond)/2)
21
Q
What is the YTM of a perpetuity?
A
A perpetuity does not mature, the priced of a coupon bond that pays an infinite number of coupons: P = C/i
22
Q
What is the correlation between Bond Yields and Maturities?
A
- If interest rates on newly issued bonds rise, the prices of existing bonds will fall
- If interest rates rise, existing bonds issued with lower interest rates become less desirable to investors, and their prices fall
- Yield to maturity and Bond prices move in opposite directions
23
Q
What is rate of return?
A
`- Return is a security’s total earnings
- For a bond, its return is the coupon payment plus the change in it’s price
- The rate of returns (R) is the return on a security as a % of the initial price
24
Q
R =
A
- For a bond, R equal the coupon payment plus the change in the price of a bond divided by the initial price:
- R = (C + Capital Gain) / Initial P
25
What is interest rate risk?
- The risk that the price of a financial asset will fluctuate in response to changes in the market interest rate
- Bonds with fewer years to maturity will be less affected by a change in market interest rates
- The longer the maturity, the lower (more negative) your return after one year of holding the bond (when the interest rate increases)
26
Fisher equation?
r = i - πe
27
What are the determinants of portfolio choice?
* Saver’s wealth
* Expected rate of return from different investments
* The degrees of risk in different ivnestments
* The liquidity of different investments
* The cost of acquiring information about different investments
* Diversification
28
How does a saver's wealth affect portfolio choice?
An increase in wealth generally increases the quantity demanded for most financial assets
29
What is the EV of different investments?
Expected return = (P1 * Value1) + (P2 * Value2)
30
How does liquidity affect portfolio choice?
The greater an asset’s liquidity, the more desirable the asset is to investors
31
How does the cost of acquiring information about different investments affect portfolio choice?
All else being equal, investors will accept a lower return on an asset that has lower costs of acquiring information
32
What is diversification and what types are there?
- Dividing wealth among many different assets to reduce risk
- Market (systematic) risk is risk that is common to all assets of a certain type
- Idiosyncratic (unsystematic) risk is risk that pertains to a particular asset rather than the market on the whole
33
How are a bonds price and yield to maturity linked and what does this imply?
- A bonds price P and its yield to maturity i are linked by Pcoupon bonds = C/(1+i)1 + … + C/(1+i)n + FV/(1+i)n
- Because C and FV do no change, once we know P in the bond market, we have determined equilibrium i
34
What factors shift bond demand?
* Wealth
* Expected return on bonds
* Risk
* Liquidity
* Information costs
* Expected inflation
35
What factors shift bond supply?
* Expected pretax profitability of physical capital investments
* Business taxes
* Expected inflation
* Government tax credits
* Government borrowing
36
How does wealth shift bond demand?
`An increase in wealth will shift the demand curve to the right
37
How does expected return shift bond demand?
- Increase in expected return relative to other assets (lower expected future interest rates), demand will shift right
- Higher expected future interest rates drops demand!
- Expected return on other assets is opposite
38
How does expected inflation shift bond demand?
Increased πe leads to a decrease in demand: holding bonds is relatively less attractive
39
How does risk shift bond demand?
Decrease in riskiness of bonds relative to other asserts increases demand
40
How does liquidity shift bond demand?
If liquidity of bonds increases, demand increasse
41
How does information costs shift bond demand?
Lower information costs increases demand
42
How does expected pre-tax profitability affect bond supply?
An increase in firms expectations of the profitability of investment in physical capital will shift the supply curve for bonds to the right
43
How do businesses taxes affect bond supply?
When business taxes are raises, the profits on new investments in physical capital declines, and firms issue fewer bonds
44
How does expected inflation affect bond supply?
Increase in πe reduces the expected real interest rate, and so supply of bonds increases as the real cost of borrowing falls
45
How do government tax credits affect bond supply
Increase in these leads to an increase in supply as these lower the cost of investment, thereby increasing the profitability of investment
46
How does government borrowing affect bond supply?
If nothing else changes, a larger government deficit and thus borrowing shifts the bond supply curve to the right
47
What is the effect of a recession on the bond market?
- An economic downturn reduces household wealth and thus the demand for bonds
- Fall in expected profitability reduces borrowers supply of bonds
- P BONDS MUST INCREASE
48
What is the effect of expected inflation on the bond martket?
- Higher inflation rates result in higher nominal interest rates because of Fisher effect, vice versa
- Changes in expected inflation can lead to changes in nominal interest rates before a change in actual inflation occurs
- An increase in expected inflation reduces investors expected real return, thus the demand curve for bonds shifts to the left
- The increase in expected inflation increases firms’ willingness to issue bonds, thus the supply curve for the bonds shifts to the right
49
What is the effect of unexpected deflation on the bond market?
An unexpected deflation will shift the demand curve for bonds to the right and the supply curve to the left. Price will increase, so bond investors will see capital gains
50
What is the liquidity preference framework/
- Keynesian model that determines the equilibrium interest rate in terms of the supply and demand for money (i vs Q money)
- There are two main categories of assets that people use to store their wealth: money and bonds
- Total wealth in the economy = BS + MS = BD + MD
- i.e. BS - BD = MS - MD
- If the money market is in equilibrium (MD = MS), then the bond market is also in equilibrium (BD = BS)
51
What happens as i increases in the LPF?
- The opportunity cost of holding money increaser
- The relative expected return of money decreases
- and therefore the quantity demanded of money decreases
52
What causes shifts in money demand in the LPF?
- Income effect
- A higher level of income causes the demand for money at each interest rate to increase and the demand curve to shift to the right
- Price-level effect
- A rise in the price level causes the demand for money at each interest rate to increase and the demand curve to shift to the right
53
What is MS in the LPF?
Controlled by the central bank
54
What is the liquidity effect?
The LKPF framework leads to the conclusion that an increase in the money supply will lower interest rates
55
What effects could occur from an increase in MS that would counteract the liquidity effect?
* Income effect
* Price-level effect
* Expected-inflation effect
56
What is the income effect in both the bond market and LPF frameworks?
- Raises interest rate in both bond market and liquidity preferences frameworks
- Increase in MS leads to increase in economic activity leads to increase in income:
- Bond Market Framework
- Increase in income leads to increase demand for bonds
- Increase in economic activity leads to increase supply of bonds
- Ambiguous outcome (assume increase i, supply shifts bigger)
- Liquidity Framework Model
- Increase in income leads to increase demand for money leads to increase interest rate
57
What is the price level effect in both the bond market and LPF frameworks?
- Raises interest rate only in the liquidity preference framework
- A one time increase in the money supply will cause prices to rise to a permanently higher level by the end of the year. The interest rate will rise via the increased prices. Price-level effect remains after prices have stopped rising
- Increase in MS leads to increase in Prices leads to increase in MD leads to increase i
58
What is the expected inflation effect in both the bond market and LPF frameworks?
- A rising price level will raise interest rates because people will expect inflation to be higher. When the price level stops rising, expectation of inflation return to 0. Expected inflation effect persists only as long as the price level continues to rise
- Bond Market Model
- Increase in MS leads to increase inflation expectation leads to increase in interest
59
What is the summary of the effect of an increase in MS on i?
- Liquidity effect: i falls
- Income effect: i rises
- Price-Level effect: i rises
- Expected-inflation effect: i rises
- No clear conclusion between MS and interest rate
- Increase in MS may increase or decrease i
- If liquidity effect > all other effects: MS and i inverse
- If liquidity effect < all other effects: MS and i positively related
60
What is the risk structure of interest rates and what are it's factors?
- The risk structure of interest rates is the relationship among interest rates on bonds that have different characteristics but the same maturity
- Factors
- Risk attributes
- Liquidity management
- Information Costs
- Taxation
61
What is default risk and how is it measured?
- Risk that the bond issuer will fail to make payments of interest or principal
- Measuring Default Risk
- The default risk premium on a bond is the different between the interest on the bond and the interest rate on a treasury bond with the same maturity
- A bond with a default risk will always have a risk premiums
- Interest rate on a bond - interest rate on treasury bond
- i.e. default risk is almost 0 on treasury bonds
62
What is a bond rating?
A bond rating is a single statistic that summarises a rating agencies views of the issuer’s likely ability to make the required payment on its bonds
63
What is the initial default risk premium if PT > PC?
- PT > PC implies iT < iC
- The initial default risk premium is the difference in yields associated with the prices PT and PC
- = iC - iT
- Investors require extra return to compensate them for a high level of risk on the C bond
- In other words, the C bond’s default risk premium must be very high
64
What happens a bonds default risk rises?
- As the default risk on corporate bonds increases, the demand for corporate bonds shifts to the left, and the demand for treasury bonds shifts to the right
- The price of corporate bonds fall, and the interest rate on them increases
- The price of treasury bonds rises, and the interest rate on them falls
65
What is the business cycle - default risk relationship?
- During recession, the default risk on corporate bonds typically increases, which can cause a flight to quality (i.e. iT falls, iC rises)
- The default premium typically rises during recessions
66
How do liquidity and information costs affect the risk structure of interest rates?
- Investors case about liquidity, so they are willing to accept a lower interest rate on more liquid investments
- Spending time and money acquiring information on a bond reduces the bond’s expected return
- A change in a bond’s liquidity or the cost of acquiring information about the bond affects its demand
- During the GFC, homeowners defaulted on many of the mortgages contained in portage-backed bonds
- Investors also had difficulty finding information about the types of mortgages in them
67
What are the types of income from bonds and how are they different?
- Interest income from coupons - taxed at the same rate as wage and salary income
- Capital gains or losses from prices on the changes on the bonds - taxes at a lower rate than interest rate, and taxes only if they are realised i.e. a bond sold at a higher price than paid for
68
For tax purposes what kinds of bonds are there?
- Corporate bonds
- Coupon payments subject to federal, state and local taxes
- Treasury Bond
- Coupon payments subject to federal taxes only
- Municipal bonds
- No tax on coupon payments
69
What is the effect of a federal tax increase on the bond market?
If the federal income tax rate increases, the demand curve for tax-exempt maniacal bonds shifts to the right, and the demand for treasury and corporate bonds shifts to the left
70
Summarise the risk structure of interest rates
- In increase in a bond’s default risk causes it’s yield to rise (through price decreasing and i increasing) because investors must be compensated for bearing additional risk
- In increase in a bond’s liquidity causes its yield to fall because investors incur lower costs in selling the bond
- In increase in a bond’s information costs’s causes its yield to rises because investors most spend more resources to evaluate the bond
- In increase in a bond’s tax liability causes its yield to rise because investors care about after-tax returns and must be compensated for paying higher taxes
71
What is the term structure of interest rates?
The relationship among the interest rates on bonds that are otherwise similar but have different maturities
72
What is the treasury yield curve and what are its variants?
- The Treasury yield curve shows the relationship among the interest rates on Treasury bonds with different maturities
- An upward-sloping yield curve occurs when short-term rates are lower than long-term rates (short-term rates < long-term rates)
- A downward sloping yield curve occurs when short-term interest rate are higher than long term interest rates (short-term rates > long-term rates)
- Co-movement occurs also
73
What theories are sued to explain the term structure of interest rates?
* Expectation Theory
* Segmented Market Theory
* Liquidity Premium or Preferred Habitiat Theory
74
What is expectation theory?
- Holds that the interest rate on a long-term bond is an average of the interest rates investors expect on short-term bonds over the lifetime of the long-term bonds
- Two key assumptions:
- Investors have the same investment obejctvies
- For a given holding period, investors view bonds of different maturities as being perfect substituted for one another
75
In expectation theory what is the expected return for holding a bond for 2 period buy and hold strategy?
the expected return for holding the two-period bond for two periods is 2i2t
76
In expectation theory what is the expected return for holding a bond for 2 period rollover strategy?
it + iet+1
77
What is a buy and hold strategy?
- Buy 1 long-term (2 (n) year) bond
- $1 spent is expected to grow to $1(1+i2t)(1+i2t)
- i2t is today’s interest rate on two year bond
78
What is a rollover strategy?
- Buy and sell 2 (n) short term (1 year) bonds
- $1 spent is expected to grow to $1(1+it)(1+iet+1)
- it is today’s interest rate on one-period bond
- iet+1 is the expected interest rate on one-period bond next period
- Need to form exception of rate on next period’s one year bone
79
What is the general equation for expected return in the expectation theory?
- int = [it + iet+1 + iet+2 + … + iet+(n-1)]/n
- int: interest rate on n period bond
- The nth period interest rate equals the average of the one-period interest rate expected to occur over the n-periof life of the bond
80
What is interest carry transfer?
- Refers to borrowing at a low short-term interest rate and using the borrowed funds to invest at a higher long-term rate
- As the yield curve is typically upward sloping, borrowing short term and investing long term seems a good investment strategy
- Average investor would struggle as gap is too small
- Institutional investors can borrow at a low short term rate and they face less default risk.
- But interest carry trade would not bring potential profits because the expectations theory holds that the average of the expected short-term interest rates should be roughly equal to the equivalent long term interest rates
- if the yield curve were inverted, and institutional investors could borrow long term and invest the funds at the higher short-term rates. This would be4 subject to reinvestment risk - the risk that the interest rate on new short-term investments will decline after they mature
81
What are the implication of expectation theory?
- An upward sloping yield curve is the result of investors expecting future short-term rates to be higher than the current short-term rate (expected future short-term rate > current short term rate)
- A flat yield curve is the result of investors expecting future short-term rates to be the same as the current short-term rates (expected future short-term rate = current short term rate)
- A downward sloping yield curve is the result of investors expecting future short-term rates to be lower than the current short term rate (expected future short-term rate < current short term rate)
82
What are the shortcomings of expectation theory?
- Explains an upward sloping yield curve as the result of investors expecting future short term rates to be higher than the current short term rate
- But if the yield curve is lyrically upward sloping, investors must be expecting short term rates to rise most of the time
- This explanation seems unlikely because at any particular time, short-term rates are about as likely to fall as to rise. We can conclude that the expectations theory is overlooking something important about the behaviour of investors in the bond market.
83
What is the segmented market theory?
- Holds that the interest rate on a bond of a particualr maturity is determined only by the demand and supply of bonds of that maturity
- Two related obsevations:
- Investors in the bond market do not all have the same objectives
- Investors do not see bonds of different maturities as being perfect substitutes
- Segmented markets means that investors in the market for bonds of one maturity do no parpiticape in markets for bonds of other maturities
- Compared to short term bonds, long term bonds are subject to greater interest rate risk, and they are often less liquid
- The yield curve is typically upward sloping because more investors are in the market for short term bonds, causing their prices to be higher, and their interest rates lower than long term bonds
- But the segmented markets theory cannot explain a downward sloping yield curve, or why interest rates of all maturities tend to rise and fall togethers
84
What is the Liquidity premium theory?
- Holds that the interest rate on a long-term bond is an average of the interest rates investors expect on short-term bonds over the lifetime of the long-term bond, plus a term premium
- Term premium is the additional interest investors require in order to be willing to buy a long term bond rather than a comparable sequence of short term bonds
- Investors have a preference for bonds of one maturity over another
- They will be willing to buy bonds of different maturities only if they earn a somewhat higher expected raturn
- Investors are likely to prefer short over long term bonds
85
What is the equation for the liquidity premium theory?
- This theory adds a term premium to the expectation theory equation
- int = [it + iet+1 + iet+2 + … + iet+(n-1)]/n + lnt
- int: interest rate on n period bond
- where lnt is the liquidity premium for the nth period at time t
- Lnt is always positive
- Rises with the term to maturity
86
What are the implication of liquidity premium theory?
- A steeply rising yield curve indicates that short term rates are expected to rise
- A moderately steep yield curve indicates that short term rates are not expected to change much
- A flat yield curve indicates that short term rates are expected to fall moderately in the future
- A downowad sloping \yield curve indica5es short term inditerest rates are expected to fall
87
In sum, how do the LPT and PHT explain the term structure of interest rates?
- Interest rates on different maturity bonds move together over time; explained by the first term in the equation
- int = ([it + iet+1 + iet+2 + … + iet+(n-1)]/n)
- Yield curves tend to slop upward when short term rates are low and to be inverted when short term rates are high; explained by the liquidity premium term in the first case and by a low expected average in the second case
- Yield curves typically slope upwards; explained by a larger liquidity premium as the term to maturity lengthens
88
What happens to interest rates during the business cycle according to liquidity preference?
During a business cycle recession, income will fall. This causes the money demand curve to shift to the left. The resulting equilibrium will be at a lower interest rate.
89
What does 'yields soar' imply?
‘Yields soar’ implies P down b/c either D down or S up
90
How can excessive G affect the bond market?
The unchecked spending by the Spanish government led to higher budget deficits, an increased supply of Spanish government bonds, and an increased risk of default on government bond payments.
91
What happens to i-LR if people start preferring SR bonds to LR bonds?
DSR increases vs DLR: PSR rises: iSR fall: iLR rise (increased risk premium)
92
What is default risk premium?
The default risk premium on a bond is the difference between the interest rate on the bond and the interest rate on a Treasury bond that has the same maturity. - the additional yield that an investor requires for holding a bond with some default risk.
93
What are the types of income an investor can earn on a bond?
Interest income from coupons: Coupon payments, when taxed, are taxed at the individual income tax rate. Coupons on corporate bonds are taxed by the federal government and may be taxed by state and local governments. Coupons on Treasury bonds are taxed only by the federal government. Coupons on municipal bonds issued by state and local governments are typically not taxed.
Capital gains or losses from price changes: Capital gains, in 2013 in the US, were taxed at a lower rate than interest income and taxed only if they are realized.
