Day 59 in MIT Sloan Fellows Class 2023, Managerial Finance4, Bonds-1

Fixed income markets:

• • Issuers: entities that create fixed-income securities in order to raise funds (e.g.,governments, corporations, commercial banks, states, municipalities)
  • Intermediaries: entities that assist issuers in creating and selling fixed-income securities(e.g., dealers, investment banks, credit-rating agencies)
  • Investors: entities that buy fixed-income securities (governments, pension funds,insurance companies, individuals)
• Bonds: a type of fixed-income security. They are described by their
  • Maturity: the amount of time at which the last payment on a bond is due.
  • Face-value: the value of a bond that appears on its face and that will be paid to the investor by the issuer at maturity, also referred to as par value or principal.
  • Coupon: the interest charged on a bond’s face value while maturity is not reached.Bonds can have a coupon (coupon bonds) or not (zero-coupon bonds).
  • Collateral: assets that are pledged as security for payment of debt.
  • Spot interest rates: the current appropriate interest rate for discounting a cashflow at a period t, expressed as rt.

Zero coupon bonds

They are bonds  without any coupon payments,  also known  as discount  bonds. 

The price P of zero-coupon bonds provide information about "spot interest rates".

Coupon bonds

bonds  with coupon payments  before its maturity.

• Cash flows of coupon bonds  depend  only on their  maturity, face value, and  coupons.  
• A coupon bond  with maturity  date T and face value of F and scheduled  annual  coupon payments  of C t has the  following cashflows: 

Yield-to-maturity(YTM)

The yield-to-maturity  (YTM) is the discount  rate y which when  used  at all time horizons  results  in the same bond  price.

Yield curve describes set of yields that exist on bonds of different maturities. 

Expectations Hypothesis(EH)

The EH is a model which  seeks to explain variation  in the term 
structure  of interest  rates. The key idea is that the long-term interest  rate is a geometric average of current  and expected future  short-term  rates.If investors  regard long-term bonds  as riskier  than short-term  bonds, for instance due  to a lack of liquidity,  they  will require  a higher  return  (compensation  for risk). 

Duration

Duration is the weighted-average timing  of the cashflows of a bond. Changes in interest  rates introduce two potentially  offsetting effects for a long-term investor: 
 

• Price effects: increases  in interest  rates lead the value  of existing fixed income positions to decline, lowering the investor’s  wealth today, making  them worse off.
• Reinvestment  effects: Any  new investments  (e.g., as existing securities  mature  and are replaced  with new ones or new contributions  are made)  earn higher  returns.This can make investors  better  off by increasing the growth rate of future wealth. 

Duration  shortcuts: 

• The duration  of a portfolio is the weighted  average of the duration  of its components
• The duration  of a perpetuity  is: (1+y)/y
• The duration  of a zero-coupon bond  is its maturity
• The duration  of a coupon bond  is always lower than its maturity 

To set the same duration of liabilities and assets, you can avoid inflation risk.