Interests Flashcards
Key interest rates which apply to bank’s interaction with the central bank
Deposit facility
- interest on deposit of banks at the central bank which can become negative
Main refinancing rate
- publicly visible base rate announced by the central bank
Marginal lending rate
- allows financial institutions to borrow money from the central bank on a short-term basis, e.g. overnight
Time value of money
It is only possible to compare or combine values that refer to the same point in time
- to move cash flow forward in time, you must compound it (FV)
- to move cash flow back in time, we must discount it (PV)
the interest rate is applied to convert time values from one period to another
Standard time periods for interest rates
30/360
Actual/360
Actual/Actual
No arbitrage in perfect financial markets
Two securities that provide the same future cash flows and have the same level of risk must sell for the same price. There is “no way to make money out of nothing”
Practical application of annuity calculation
Pay in over several periods, one final payment
- saving plan
- life insurance
- building loan contract
pay-in over several periods, multiple final payments
- retirement pension
Intra-year annuities
- Annuity period = interest period
-> adapt number of periods - Annuity payments are made intra-yearly, interest payments annually
-> fictitious periodic annuity - Annuity payments are made annualy, interest payments intra-yearly
-> effective interest rate
Varying annuities with arithmetic progression
the annuity increases or decreases by a constant amount d
Redemption - payments without repayment
- No payments within the payment-free time
- During the payment free-time the loan amount increases by the interest claims - Interest payments within the payment free time
- The loan amount remains constant, however the interest claims need to be paid. The presented formulas from the repayment calculations can be applied.
Bonds and bonds price
Bonds are long-term contracts with issuers (borrowers) committing themselves to repay debt at a specified date and, if applicable, to pay coupon payments at predetermined points in time to the bond owner.
Bond price influenced through
- creditworthiness
- interest rate
- coupon
- rights
- liquidity
Zerobond
A zerobond (zero-coupon-bond) is a fixed-income security that is repaid after N years with no intermediate coupon payments
Coupon bond
A coupon bond pays regular interest payments at specified points in time. The principal amount is paid at maturity of the bond.
Categorization of bonds: price of the bond as % of nominal value
B = 100 Bond is traded at par
B < 100 Bond is traded below par (at discount)
B > 100 Bond is traded above par (at premium)
Factors influencing the pricing of coupon bond
- Coupon and redemption
- Time to maturity
- Changes in interest level
Explanation approaches for the normal yield curve
- Pure expectation hypothesis
- liquidity preference theory (preferred habitat theory)
- market segmentation theory
Interest rates with varying maturities
- Normal yield curve: the longer the capital commitment, the higher the interest which is paid
- Flat yield curve: The paid interest does not depend on the time of capital commitment
- inverse yield curve: the longer the capital commitment, the lower the interest which is paid
Risks of bonds
Three components:
- credit risk (related to the issuer of the bond)
- price risk due to changes in the interest rate level
- risk of reinvestment (of coupons)
last two risk related to changes of the market interest rate
Important: Interest rate changes have two-sided, opposite effect on the price and potential reinvestments. If the interest rate increases, the price of the bond goes down, but potential reinvestments become more attractive.
Risk of bonds (long-term vs short-term)
Long-term bond
- high price risk
- low reinvestment risk exposure
Short-term bond
- low price risk
- High reinvestment risk exposure since the face value needs to be reinvested at lower interest rates until the maturity of the long-term bond
Concept of duration
The duration represents the point in time where there is a full immunization of the portfolio against potential changes in the market interest rate. That is why the duration is called the average commitment period.
Assumptions:
- flat yield curve
- one-time change of the market interest rate instantly after the purchase of the bond
- only the level of the yield curve changes, not the slope or the curvature of the curve
- coupon payments are reinvested with the market interest rate r
Concept of duration - interest sensitivity derived from Taylor Series
Duration of specific instruments
- Duration of a zerobond equals the maturity of the bond since there are no coupon payments
- Duration of coupon bonds
-> the larger, the larger the time to maturity
-> the larger, the lower the market interest rate
-> the larger, the lower the coupon - Duration of a perpetual (this implies that with increasing time the duration converges to a limit value; the impact of the time on the duration decreases)=> 1+r / r
