Interests

Question 1

Key interest rates which apply to bank’s interaction with the central bank

Answer 1

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

Question 2

Time value of money

Answer 2

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

Question 3

Standard time periods for interest rates

Answer 3

30/360
Actual/360
Actual/Actual

Question 4

No arbitrage in perfect financial markets

Answer 4

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”

Question 5

Practical application of annuity calculation

Answer 5

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

Question 6

Intra-year annuities

Answer 6

1. Annuity period = interest period
   -> adapt number of periods
2. Annuity payments are made intra-yearly, interest payments annually
   -> fictitious periodic annuity
3. Annuity payments are made annualy, interest payments intra-yearly
   -> effective interest rate

Question 7

Varying annuities with arithmetic progression

Answer 7

the annuity increases or decreases by a constant amount d

Question 8

Redemption - payments without repayment

Answer 8

1. No payments within the payment-free time
   - During the payment free-time the loan amount increases by the interest claims
2. 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.

Question 9

Bonds and bonds price

Answer 9

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

Question 10

Zerobond

Answer 10

A zerobond (zero-coupon-bond) is a fixed-income security that is repaid after N years with no intermediate coupon payments

Question 11

Coupon bond

Answer 11

A coupon bond pays regular interest payments at specified points in time. The principal amount is paid at maturity of the bond.

Question 12

Categorization of bonds: price of the bond as % of nominal value

Answer 12

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)

Question 13

Factors influencing the pricing of coupon bond

Answer 13

• Coupon and redemption
• Time to maturity
• Changes in interest level

Question 14

Explanation approaches for the normal yield curve

Answer 14

• Pure expectation hypothesis
• liquidity preference theory (preferred habitat theory)
• market segmentation theory

Question 15

Interest rates with varying maturities

Answer 15

• 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

Question 16

Risks of bonds

Answer 16

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.

Question 17

Risk of bonds (long-term vs short-term)

Answer 17

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

Question 18

Concept of duration

Answer 18

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

Question 19

Duration of specific instruments

Answer 19

• 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