Fixed Income Securities and Interest Rates Flashcards
What is a fixed income security?
Financial claims with promised cashflows of a fixed amount of money paid at fixed dates (also known as long term debt instruments)
What is collateral?
What the issuer of an indenture must put up to secure the debt
What happens to the collateral if the issuer defaults?
They may seize the collateral to recoup the principal
Define yield
Market required rate of return on a fixed income investment
Is the stock market more or less efficient than the bond market and why?
More efficient because there is more disclosure
What is a spot rate?
current interest rate
What is a forward rate?
Interest rate at a future period
Define interest rate
amount of money the borrower is obligated to pay the lender
What does size of interest rate depend on?
Chance that the borrower will default on their promise to repay the principal and fixed rate agreed within the lender agreement (CREDIT RISK)
What is a common assumption about the government in terms of defaulting?
They are less likely to default, but that is a bad assumption
Because of this assumption, treasury rates are much lower than any other and are referred to as risk free rates
Would bonds with longer time to maturity have higher or lower yield?
Higher yield, which is associated with higher risk since we are uncertain what will happen in the distant future
Describe a risk free assets return
It doesn’t fluctuate a lot over the life of the bond
What does LIBOR stand for and what is it?
London Interbank Offered Rate, and it is the interest rate at which banks are prepared to make large wholesale deposits with other banks
What does LIBID stand for and what is it?
London Interbank Bid Rate, and it is the rate at which banks will accept deposits from other banks
How big is the difference between LIBOR and LIBID, and which is higher?
Small spread, LIBOR is higher
What is equity?
Stocks and shares
Give the formula for rate of return and define all terms
r1 = (Mi + IP - M0) / M0
mi = time period i=1,...,n M0 = initial investment IP = intermittent payments
In the formula for rate of return, what would be the capital gains part?
(mi-m0) / m0
How much is one basis point?
One-hundreth of a percent
If an interest rate of 10% increases by 50 basis points, what is the new interest rate?
10.5%
Give the holding rate of return of an investment for two periods
r_0,2 = (m2 - m0) / m0
Give the formula for the average annualised rate of return
(1 + r_0,i) = (1 + ri)^i
where ri is the annualised rate of return
What happens to a bonds cashflow if interest rates rise?
The PV of the remaining cashflow decreases - vice versa is also true
What is the valuation of a bond affected by?
- inflation fluctuation
- liquidity of the bond market/bond itself
- currency and exchange rate fluctuation
- credit risk
What is a liquid bond market?
Lots of buyers and sellers of that bond
What is yield to maturity of a bond, and what is it also known as?
Interest rate required in the market on a bond
also known as the bond’s yield
What is the term structure of interest rates?
Relationship between yield and maturity of the bond
If YTM = coupon rate, what is the relationship between the price of the bond and the principal payment?
Price of bond (B0) = principal payment
If YTM > coupon rate, what is the relationship between the price of the bond and the principal payment?
price of bond < principal payment
If YTM < coupon rate, what is the relationship between the price of the bond and the principal payment?
price of bond > principal payment
Are nominal interest adjusted for inflation?
No
Are real interest rates adjusted for inflation?
Yes
What is TSoIR in terms of nominal interest rates?
Relationship between nominal interest rates on default free, pure discount securities and time to maturity
Explain each part of “pure discount securities”
pure - means no coupon payments (zero-coupon bond)
discount - discounting future cashflows
What is a pure discount security?
Have lower price compared to other bonds, normally price = £1
What is spot interest rate rt?
rt is annualised interest for maturity date t
- rt is for payments on period t
- rt is rate of interest from now and period t
- rt different for each differrent period t
How is TSoIR derived?
Set of different spot rates for different maturity rates, i.e plotting spot rates as a function of maturities
Draw upwards and downwards term structures
DRAW
What do central banks use TSoIR for?
Informing monetary policy decisions
Describe a discount bond
- maturity date t, only pays £1 at time t
- referred to as STRIPs in US
- provide info about spot interest rates, hence TSoIR can be referred to as zero-coupon yield curve
Give the formula relating current price of a zero-coupon bond (Bt) and spot interest rates (rt)
Bt = 1 / (1 + rt)^t
What is yield to maturity?
market interest rate required to find the current market value of a bond
Formula to find PV or current market price (and define terms)
PV = sum(t=1 to T) Ct / (1+y)^t + P / (1+y)^T
Ct is coupon payment at time t
P is principal
y = YTM
t is counter of periods, T maturity
Give formula for approximate YTM
Approx YTM = [coupon + { (principal - current price of bond) / number of periods to maturity } ] / [ (principal + current price) /2 ]
When do yield curves change?
- monetary policy - tightening MP slows economy and flattens/inverts yield curve (tightening means increased interest rates)
- investor expectations
How do investor expectations change yield curves?
- expectation of future short-term interest rates are related to future real demand for credit and to future inflation
- increase in short-term interest rates are related to future slowdown in economic activity and demand for credit, therefore downwards pressure of future real interest rates
- expected declines in short term rates would tend to reduce current long term rates and flatten yield curve
what is a forward transaction?
borrowing money from the future
Outline how a forward transaction works
- terms of transaction agreed at t0
- receive loan at t1
- repay loan at t2
Give two formulae for forward interest rate
ft = [B(t-1) / Bt] - 1 ft = [(1 + rt)^t / (1 + rt)^(t-1) ] - 1
Explain expectations theory
- forward rates predict future spot rates that is ft = E (r1(t))
- expectations of
rising short-term interest rates are what create a positive yield curve and visa versa - this means the slope of the yeild curve reflects the market’s expectations of future short term interest rates
Give a flaw of expectation theory
It assumes that bonds of different maturities are perfect substitutes
State liquidity preference theory
- investors believe that long-term bonds are far more risky than short-term bonds
- in other words, investors prefer higher liquidity of short term debt, and therefore any deviance from a positive yield curve will only be temporary
What are the implications of liquidity preference theory?
- bonds with longer maturities will always have higher yields
- forward rates will, on average, over predict future spot rates
- yield curve will reflect the expectations of future interest rates and risk premiums demanded by investors to hold long term bonds
State segmentation theory
- different investors confine themselves to certain maturity segments (different maturity terms)
- makes the yield curve a reflection of prevailing investment policies
Give an assumption of segmentation theory
different maturities of debt cannot be substantiated for each other
what are the implications of segmentation theory?
- bonds with different maturities are part of separate markets
- results in separate demand-supply relationships for short-term and long-term debt
What is simple maturity?
Time left to maturity on a bond
What does longer time to maturity mean?
The bond is more sensitive to changes in the required rate of return
What is a bond’s duration?
Weighted average of the maturity of the individual cashflows, t, with the weights being proportional to the PV of these cashflows
Give the formula for duration, defining all terms
D = sum(t=1 to T) wt * t
where: wt = [ Ct / (1+y)^t ] / B Ct cashflow at time t B is bond price y is YTM
What does duration measure?
the average time taken by a bond, on a discounted basis, to pay back the initial investment
When are coupons of Treasury notes payed?
Semi-annually
What must you do to duration if coupon is payed semi-annually?
divide it by 2
What does modified duration measure?
- volatility (interest rate risk) of a bond
- effectively how small changes in ytm affect the price of the bond
Give the formula for modified duration
MD = D / (1 + y)
What is the difference between maturity and duration?
- maturity considers zero-coupon bonds whereas duration uses coupon paying bonds
What is the difference between duration and modified duration?
MD measures volatiliy of interest rates etc
What is convexity?
Shows full relationship between bond price and yield
Give the formula for convexity
CX = 1/(1+y)^2 * sum(t=1 to T) ( [ {Ct / (1+y)^t} / B] * t * (t+1) )
What does convexity correct and what for?
Modified duration because it understates true price of the bond
Give price change of a bond formula
ΔB = (-MD * ΔY) = (0.5 * CX * (ΔY)^2)
Is the effect of an increase in YTM symmetric?
No
What immunisation in fixed income finance?
Investors want zero exposure to interest rate risk
What is the value of a portfolio?
xaBa + xbBb
What is the value of the portfolio when interest rates change?
xaΔBa + xbΔBb
In terms of modified duration, what is the value of a portfolio when interest rates change?
- (xaBaMDa + xbBbMDb) Δy
What is the modified duration of a portfolio?
[xaBaMDa/(xaBa + xbBb)] + [xbBbMDb/(xaBa + xbBb)]
Give the hedge ratio formula for an x-year bond and a y year bond
MDx + δMDy = 0
δ is the hedge ratio
