REPO

Anatomy of REPO -

Security Details
Security Name (GOI - Govt of India)	9.40% GOI 2012
Coupon Rate (per annum)	9.40%
Maturity Date	11-Sep-12
Last Coupon Date	11-Sep-10
Next Coupon Date	11-Mar-11

1)

REPO Details
Face Value (INR)	500,000,000
Repo Rate (% per annum)	5.75%
Repo Tenor (Days)	7
Clean Price (for Face value of 100)	103.83
Trade Date	23-Oct-10
Value after (Days)	1
Settlement Date (Trade Date + Value after days)	24-Oct-10

2)

Principal amount received by borrower on :	24-Oct-10
Clean Price per Bond	103.83
Last Coupan till date (Number of Days)	43
Add:Accrued Interest per Bond	1.1228
Loan proceeds per bond - DIRTY PRICE	104.9528
Total Loan proceeds (Rs)	524,763,889
Total Interest Paid	578,677.99

· Here, Number of days calculated in Last coupon till date is as follows – From Sep 11 to Sep 30 = 20 days & From Oct 1 to Oct 23 = 23 Days.

· In accrued interest per bond, days as per market convention for Government bond = 12*30 = 360 Days

· Accrued Interest = Coupon Rate * Last coupon till date * FV / 360

· Dirty Price = Clean Price + Loan Proceeds

· Total Loan proceeds (INR) = 500,000*104.9528/100

· Total Interest Paid = 5.75%*7(days)*total loan proceeds/365

3)

Transaction Reversal on Due Date
Transaction due date	31-Oct-10
Total repayment proceeds (Rs)	525,342,567
Repayment proceeds per bond	105.07
Last coupan Till date (Number of Days)	50
Less : Accrued Interest per bond	1.31
Reversal price per bond - Derived Figure = CLEAN PRICE	103.76

· Transaction Due Date = Settlement Date + Repo Tenor

· Total Repayment = Total Loan Proceeds + Total Interest Paid

· Repayment proceeds per bond = Total Repayment*FV per Bond (100) / Total FV of bonds (500,000,000)

· Last coupon till date = 43+7 = 50 days

· Accrued Interest (for 360 days) = Coupon Rate * 50(days) *FV (100) / 360

· Reversal price per bond = Repayment proceeds per bond – Accrued Interest

Class 1B

Class 1 – Derivatives Notes

YTM – ROI anticipated / return made on the bond if it is held till maturity.

Assumption in the YTM calculation – Every coupon will be reinvested at the same interest rate.

Accrued Interest –

· From last payment of coupon till today, some days have passed. In case, I sell my bond now, I should get interest for this period. This is called accrued interest.

· Accrued interest is that which has been earned since the last coupon payment. Because the bond hasn't expired or the next payment is not yet due, the owner of the bond hasn't officially received the money. If he or she sells the bond, accrued interest is added to the sale price

YearFrac – A formula of excel denoting fraction of year.

If the interest rate falls on 31^st May of the month, then number of days for American is 31 and European is 30.

100 basis points = 1% = 0.01. Hence, 1 Basis Point = 0.0001

Duration (excluding convexity)–

Impact on the price of a bond for a given change in the Interest rate in market

= dp / dr (1st derivative or 1st level of sensitivity)

Where,

p = Price of Bond (Current)

R = YTM

Delta = Change in bond price wrt change in interest rate

For duration, Delta = (p) * (-D) * (δ r) / (1+ YTM/ m), where,

· m = number of compounding

· p = Price of Bond

· δ r = Change in Interest Rate

For modified duration, Delta = P * (-MD) * (δ r), where,

· Modified Duration, (-MD) = (-D) / (1+ YTM/ m)

For dollar duration, Delta = (-$D) * (δ r), where,

· Dollar Duration, (-$D) = P * (-MD)

Delta (including convexity)

(P) * (-D) * (δ r) / (1+ YTM/ m) ……………. It is called cushion (can be +ve or -ve)

+

(P) * (0.5) * (Convexity) * (δ r)^2 …………. It is always +ve (Better push)

Notional bond - The same is not trading in the market

Deliverable Bonds - For delivery, any bond with maturity not less than 6.5 years & more than 10 years becomes a deliverable bond. Mechanism must exist to equate bond to be delivered to the notinal bond being traded.

Bond Futures - It is a contractual obligation for the contract holder to purchase / sell a bond on a specified date at a predetermined price.

Price paid by buyer to seller = Settlement Price of Bond = Invoice Price

= Future Contract Price * Conversion factor of the bond that you deliver + Accrued Interest from last coupon date to date of delivery of the bond that you deliver.

Cheapest to Deliver - Always get delivered if I wait till maturity

Class 1-A

Currency Forward Rates

1 Tick = 1 Basis point (Increment/decrement will be in this multiple), Interest rates changes by 1 tick.

For a contract period of 3 months,

Principle / Contract Amount	1,000,000
Rate (1 basis point); Interest Rate goes up by 1 basis point	0.01%
Time (3 months in year)	1/4
Net payout (Principle * Rate * Time)	25

Euro-Dollar ($ trading market outside US)

http://www.cmegroup.com/trading/interest-rates/stir/eurodollar.html

For 1 month forward interest rate, take Rate of January, 2011 (w.r.t December, 2010)

Last Price (Go to CME Group » Interest Rates » Eurodollar)	99.675	%
Euro-Dollar Interest Rate (I borrow from Euro Dollar) = 100 - Last price	0.325	%
Libor Rate (1 month Forward) (means I lend to Libor)	0.5	%
Gain = Euro Dollar Interest Rate - Libor Rate	0.175	%

Bonds

Bond Price of Forwards -

Short Term Market Borrowing Interest Rate (Bond is bought by taking loan from the market)	5%
Face Value (FV)	100
Coupon Rate	7.00%
Settlement Date (The date bond is bought from the market)	10-Jul-10
Frequency (per year) – Semi-Annual	2
Previous Coupon Date	24-Feb-10
Price of Bond (Current / Spot Price)	98.35
Accrued Interest = FV * Coupon % *YEARFRAC(Previous Coupon, Settlement Date, Basis=4)	2.64
Dirty Price (Outflow, when bond was bought by borrowing money from the market @ 5%)	100.99
Next Coupon Date = EDATE(Previous coupon Date,6 - it is semi-annual)	24-Aug-10
Forward Date (The date bond is going to be sold / 3 Month forward date)	10-Oct-10
Coupon on 24-Aug-2010 (Inflow)	3.50
Accrued Interest [Inflow - From 24 Aug (when coupon is paid) to 10 Oct (is the forward contract date)]	0.89
Borrowing Cost [Outflow - Borrowed Dirty price from market @ 5%]	1.26
Net Outflow [Outflow - This is the forward price to be quoted today for selling the bond (Finding bond price)]	97.86

Class 1

Derivatives – Prof Ramesh Laxman

YTM calculation from 1st Principal (Bonds)

Day Count Conversion

Basis	In Excel
30/360, American	Default / 0
Actual/Actual	1
Actual/360	2
Actual/365	3
30/360, European; Indian Govt Bond Market	4

Calculation – All marked in yellow is given in the question. All marked in purple / colorless are calculated.

Face Value	100
Coupon Rate	7.99%
Settlement Date	24-Oct-11
Maturity Date	9-Jul-17
Frequency (per year)	2
Previous Coupon	9-Jul-11
Price of Bond (Current)	99.99
Accrued Interest	2.33
Dirty Price	102.32

Next Coupon Date

9-Jan-12

Formula used for the above calculation is as follows -

· Settlement Date = Today()

· Previous Coupon = COUPPCD(Settlement Date, Maturity Date, Frequency, basis = 4)

· Accrued Interest = YEARFRAC(Previous Coupon Date, Settlement Date, Basis = 4)

· Next Coupon Date = EDATE(Previous Coupan Date, Number of Months after previous coupon which is 6 months here). Similarly, EOMONTH = Gives month end date, used by bankers to calculate FDs.

Coupan Date	Outflow	PV
9-Jan-12	3.995	3.9303
9-Jul-12	3.995	3.7793
9-Jan-13	3.995	3.6342
9-Jul-13	3.995	3.4946
9-Jan-14	3.995	3.3603
9-Jul-14	3.995	3.2312
9-Jan-15	3.995	3.1071
9-Jul-15	3.995	2.9878
9-Jan-16	3.995	2.8730
9-Jul-16	3.995	2.7626
9-Jan-17	3.995	2.6565
9-Jul-17	3.995	2.5545
9-Jan-18	3.995	2.4563
9-Jul-18	103.995	61.4851
Sum	155.9300	102.3128

In the above calculation, formula used is as follows -

· 1^st Coupon Date = EDATE(Previous Coupan Date, Number of Months after previous coupon) = EDATE(9-Jul-11, 6) = 9-Jan-12

· Outflow = Face Value * Coupon rate / Frequency (per annum)

· PV = Outflow / (1+Yield%/Frequency per annum)^(Frequency per annum*YEARFRAC(Settlement Date, Current Coupon Date, Basis=4))

Duration Calculation

Duration(Settlement Date, Maturity Date, Coupon, Yield, Frequency per annum, Basis=4 here)

= 4.589762

Yield = 7.99%

Sum of PVs = Dirty Price

Hence, use Goal seek to make Sum of PVs = Dirty Price by changing / finding the value of yield.