Inter Bank Loans (LIBOR, SOFR, SONIA, ESTR)

 Interbank Loans are very short term loans primarily over night loans between banks

Terms are short, however transactions are huge. Hundreds of Billions of dollars.

Variety of interest rates are associated with this Markets 

Fed Funds Rate : Rate at which US Banks can borrow from each other to full fill their Fed reserve requirements. This is a primary instrument for FED's monitory policy

LIBOR : London Interbank Offer Rate, has been around for sometime. It was a benchmark rate for Fixed Income securities for decades. However, with recent abuse it is being replaced by other rates.

SOFR : Secured Overnight Financing Rate (US Markets replacement for LIBOR)

SONIA : Sterling Overnight Index Average (UK Markets Replacement for LIBOR)

ESTR: Euro Short Term Rate (Euro Zone's replacement for LIBOR)

This market is very important to us, because it sets the short term interest rates for the entire Fixed Income.

It is also the market through which the Central Banks can exercise their monitory policy on the markets.

This the market where the Central Banks have the most control over and it is the conduit through which they can transmit their monetary policy to the economy.

Through this control they set interest rates for all short term markets.

Money Markets & Repos

Money Markets are usually very short term instruments.

Debt Market is roughly divided into 2 kinds

Bond Markets -> Maturities > 1 year

Money Markets -> Maturities < 1 year

TBills are Money Markets and they mostly use actual/360 or actual/365 conventions.

Repos are another short term money market Instrument.

Repo : Repurchase Agreement

Short term contract between 2 parties to exchange cash for an asset with an agreement to reverse the exchange at a future point.

2 Parties will enter into Repo Agreement.

One Party will lend cash by take other party's security. 

Second party will agree to buy the security back at a predetermined date in the future by paying the cash + interest (Repo Rate) in the contract.

Usually Repo's are very short term and they buy back the very next day.

REPO is from the buyers perspective.

Reverse Repo is the same thing from the lenders perspective (Party who is lending cash)

Example of Repo

Suppose a bank enters into a REPO agreement with a Broker Dealer. 

On Monday March 18, Broker Dealer will purchase a $5 M US Treasury Note with a coupon rate of 4.5%. With Bond currently trading at $4.5M, Broker Dealer agreed to purchase at a price of $4.4M with a repo rate of 1.5% and both parties agreed to buy it back the next day.

Note in the above transaction, Broker dealer is buying the bond at a price (4.4M) less than its market value (4.5M). This difference below the market rate is called "Hair Cut". To protect the lender incase of a default.

Hair Cut : When the amount is lent less than the Market Value of the Security, it is called Hair Cut. Charging Hair Cut will mitigate the loss of Capital.

Overnight Repos: Repos that expire the next day are called Overnight Repos

Term Repos: Little longer term Repos than overnight are called Term Repos.

Treasuries Basics

 Government Debt is called Treasury

Treasury Bills (T-Bills) -> Govt Debt with maturity < 1 year

Treasury Notes (T-Notes) -> Govt Debt with Maturity between 1 and 10 years

Treasury Bonds (T-Bonds) -> Govt Debt with Maturity more than 10 years

Treasury Strips (T-Strips) -> Zero Coupon Bonds issues by US Govt with maturity > 1 year backed by T-Bonds and the coupons from TBonds.

UK Govt Bonds are Gilts: UK Govt Bonds with maturity between 1 -30 years.

US Notes and Bonds, Gilts pay Coupons Semi Annually

Issue Date : Date when the Bond originated.

Maturity Date for a 10 year bond will be IssueDate + Maturity Date

Accrued Interest is calculated as Actual/Actual.

Sovereign Debt is the Government Debt

German Short term Bonds (< 5 years) is called Bobls.

German Long term Bonds are called Bunds

Bonds Basics

Coupon Bonds generate Cash Flows (coupons) at Preset Intervals

cash flow c1, c2, c3, c4 etc

are generated at time intervals

time interval t1, t2, t3, t4 etc

Last cash flow is cn+face value of the bond

Face Value of the bond is also called Par or Nominal value or Principal

Maturity Date is the Date contact ends. On or about maturity date, face value of the bond is paid to the Bond Holder by the Bond Issuer

Prior to the maturity, only interest / coupon payments are made.

Vanilla Bond or Bullet Bond is bond is the bond that pays our the Principal only in the end on the maturity date along with last coupon. No amortization.

If coupon is paid several times (k times) a year, the actual coupon that is being paid out at each interval is c/k

Most common coupon frequencies are 1 (Annually) and 2 Semi Annual

Zero Coupon Bonds : are special case that make exactly one payment on the Maturity Date. (Principal + Coupon Amount)

Bond Price is a measure of its economic value

Yield : Yield is a return measure for an investment over a set period of time, expressed as a percentage

Bond Yield or Yield to Maturity of the bond has a direct relationship with Bond Price.

​Price=t−1∑T​(1+YTM)tCash Flowst​​where:YTM= Yield to maturity​


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Yield is inversely proportional to Bond Price

The more the yield the less will be Bond Price

Bond Price vs Nominal Value 

Bond Price > Nominal Value -> Bond is trading at Premium

Bond Price < Nominal Value -> Bond is trading at Discount

Bond Price = Nominal Value -> Bond is at Par

Yield < Coupon Rate -> Premium Bond

Yield = Coupon Rate -> On Par

Yield > Coupon Rate -> Discount Bond

Bond's Dirty Price

A dirty price is a bond pricing quote, which refers to the cost of a bond that includes accrued interest based on the coupon rate.

Remove Accrued Interest from the Dirty Price we have clean Price.

If you're pricing/selling the bond in between coupon dates,  Accrued interest from last coupon to the sale date belongs to the seller and from sale date to next coupon belongs to the buyer.

Day Conventions 

Actual /Actual (Assumes all days in the year 28 or 29 or 30 or 31 days a year)

30/ 360 (Assumes every month has 30 days and 360 days in the year)

30/365 (Assumes every month has 30 days and 365 days in a year)

Financial Analytics - Interest Rate calculation

Interest Rate calculation

Simple Interest = PtR/100 

P= Principal

t=Time Period

R = Rate of Interest

Compound Interest over T :

A = P(1 + r/n)nt

• A = Accrued amount (principal + interest)
• P = Principal amount
• r = Annual nominal interest rate as a decimal
• R = Annual nominal interest rate as a percent
• r = R/100
• n = number of compounding periods per unit of time
• t = time in decimal years; e.g., 6 months is calculated as 0.5 years. Divide your partial year number of months by 12 to get the decimal years.
• I = Interest amount
• ln = natural logarithm, used in formulas below

Continuous Compounding :

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P&L = V(T) - V(0)

Gross Return = V(T)/V(0)

Return = P&L/V(0)

Return = Gross Return -1

Annualized Return (Average of Returns over a period T)

(1+Row) Pow T = V(T)/V(0)

Row = (V(T)/V(0))Pow 1/T -1