Fixed income securities Flashcards
What is the definition of fixed income securities
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
What is the definitions of bonds?
Borrowing agreement with payout scheme of a (typically semiannual) coupon and a final value (typically paid at the end of the contract).
What is the maturity of the bond
The time before the contract expires
What is the face (f) /par/nominal/principal value
The amount of money to be
paid at the end of the bonds “life”
What is the Coupon rate ?
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”
What is the “Price” of the bond?
(Defintion)
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.
What is the formula to calculate the price of a bond?
Face value (f), Annual coupon rate (C), number of periods to maturity (T) and underlying yield (y)
What is the yield of a bond?
The yield of a bond is the relevant discount rate
The required internal rate of return for investors.
YTM defintion
Yield to maturity
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.
YTM formula
Duration
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.
How do maturity and coupons affect duration
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.
Convexity
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.
Immunization
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
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
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