Fixed income securities

Question 1

What is the definition of fixed income securities

Answer 1

Fixed income securities are all types of securities for which the payouts generated by the security are either perfectly predictable or determined according to a specified formula

Question 2

What is the definitions of bonds?

Answer 2

Borrowing agreement with payout scheme of a (typically semiannual) coupon and a final value (typically paid at the end of the contract).

Question 3

What is the maturity of the bond

Answer 3

The time before the contract expires

Question 4

What is the face (f) /par/nominal/principal value

Answer 4

The amount of money to be
paid at the end of the bonds “life”

Question 5

What is the Coupon rate ?

Answer 5

The per annum rate paid each period (in the form of a
coupon payment).
Note that coupons are usually paid twice a year

“essentially the interest”

Question 6

What is the “Price” of the bond?

(Defintion)

Answer 6

Price of the bond, typically stated in terms percentage of face value.
The price of the bond is the value at which a bond can be bought or sold today.

Question 7

What is the formula to calculate the price of a bond?

Answer 7

Face value (f), Annual coupon rate (C), number of periods to maturity (T) and underlying yield (y)

Question 8

What is the yield of a bond?

Answer 8

The yield of a bond is the relevant discount rate
The required internal rate of return for investors.

Question 9

YTM defintion

Yield to maturity

Answer 9

The term yield to maturity (YTM) refers to the total return anticipated on a bond if the bond is held until it matures. Yield to maturity is considered a long-term bond yield but is expressed as an annual rate. In other words, it is the internal rate of return (IRR) of an investment in a bond if the investor holds the bond until maturity, with all payments made as scheduled and reinvested at the same rate.

Question 10

YTM formula

Answer 10

Question 11

Duration

Answer 11

Duration can measure how long it takes, in years, for an investor to be repaid a bond’s price by the bond’s total cash flows.
Duration can also measure the sensitivity of a bond’s or fixed income portfolio’s price to changes in interest rates.

duration* = price change in a bond given a 1% change in interest rates.

Question 12

How do maturity and coupons affect duration

Answer 12

Time to maturity: The longer the maturity, the higher the duration, and the greater the interest rate risk. .
Coupon rate: A bond’s coupon rate is a key factor in calculation duration. If we have two bonds that are identical with the exception of their coupon rates, the bond with the higher coupon rate will pay back its original costs faster than the bond with a lower yield. The higher the coupon rate, the lower the duration, and the lower the interest rate risk.

Question 13

Convexity

Answer 13

Convexity is apparent in the relationship between bond prices and bond yields. Convexity is the curvature in the relationship between bond prices and interest rates. It reflects the rate at which the duration of a bond changes as interest rates change. Duration measures a bond’s sensitivity to changes in interest rates. It represents the expected percentage change in the price of a bond for a 1% change in interest rates.

Question 14

Immunization

Answer 14

Immunization means shielding your portfolio against interest rate risk. Especially important forpension funds (or insurance funds) because they are concerned with the future value of their portfolio; obligation to make fixed payments for number of years

Question 15

Intuitively: with higher interest rates:
- Capital loss from decrease in price (price risk)
- Reinvested coupons will grow at a faster rate (reinvestment risk)
What does this mean for the portfolio? explain both risks

Immunization

Answer 15

Capital loss: Bond prices fall as interest rates rise, potentially leading to a loss in bond value if sold before maturity.
Coupons: Reinvested coupon payments may earn higher returns due to higher market rates but could pose challenges in finding similar investment opportunities, creating income uncertainty.

For a horizon equal to the portfolio’s duration, price risk and reinvestment risk are precisely offsetting

Question 16

What is an outright duration bet

Answer 16

outperform your benchmark
our duration contribution > benchmark

Example: 2.96 contribution - bench 1.91 = 1.05

Question 17

How do you know the duration of a zero-coupon bond?

Answer 17

We know that the duration of a zero-coupon bond is equal to its maturity.

Question 18

Steps in calculating duration

Answer 18

• • PV
• • Weights
• w * T
• Sum the latter

Question 19

What is the relation between bond’s duration and it’s time to maturity? In particular, is duration increasing, flat, or decreasing with time to maturity? Does this relationship hold for all bonds selling either at par, at premium or at discount?

Answer 19

Holding the coupon rate constant, a bond’s duration generally increases with its time to maturity
(3rd duration rule). Duration always increases with maturity for bonds selling at par or at premium.
For some deep-discount bonds, duration may eventually fall with increases in maturity.

Question 20

Consider a bond with a 10% coupon and with yield to maturity = 8%. If the bond’s yield to maturity remains constant, then in 1 year, will the bond price be higher, lower, or unchanged? Briefly explain why?

Answer 20

The bond price will be lower. As time passes, the bond price, which is now above par value, will approach par.

Question 21

Answer 21

Question 22

The immunization strategy of the insurance company could lead to a surplus in the fund, how is that possible? In addition, explain that immunization is a dynamic strategy that entails constant attention of the portfolio managers.

Answer 22

Convexity of the coupon-bonds lead to deviations of the PV in the fund, if interest rates change by a large amount. PM must realign its asset duration with the duration of the obligation, rebalancing: Interest rates and therefore assets duration can change (convexity example). Asset duration changes over time regardless of interest rate changes; maturity of bonds decreases over time hence duration decreases. Liabilities can change; people pass away, pay out insurances, new people join the insurance company.

Question 23

Answer 23

Bond C: Low yield to maturity, long maturity. Bonds with the lowest yield to maturity and the longest maturity provide the best opportunity to profit, since they are the most sensitive to changes in interest rates. In other words, low yield to maturity, long maturity bonds have the greatest duration among the four types of bonds listed here.

Question 24

When do we know if a bond is trading par value, premium or discount?

Answer 24

par value bond, Coupon rate = current yield = YTM

Premium trading bond, Coupon rate > Current yield > YTM

Discount bond, Coupon rate < current rate < YTM

Question 25

A bond has a current yield of 9 percent and an YTM of 10 percent is the bond selling above or below par value?

Answer 25

Below, if the current yield is 9 but the average yield will be 10 you will need to get a capital gain

Question 26

Price sensitivity to interest rate changes are higher when?

Answer 26

Time to maturity increase
Coupon rate decreases
Initial YTM decreases

Question 27

If the modified duration is 5 and the interest rate changes with 1 percent howmuch does the price of the bond change

Answer 27

-5%

Question 28

A firm has 100k assets with a duration of 5 years and liabilities of 100k with a duration of 8 years
If interest rate goes down is this good or bad for the firm?

Answer 28

Liabilities have a higher duration and will go up more than the assets, so it is bad for the firm

Question 29

For bonds in the short run is it better if rates go up or down?

Answer 29

Down, this will increase the price of your bond and you can sell it, if you are a long term investor up is better so you can reinvest your gains for higher return.
Price risk
Reinvestment risk