Money Market, Bonds, Mibor

8/4/2019 Money Market, Bonds, Mibor

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MONEY MARKET

Bonds

Mibor Presented By:Group-4

Aditya Kumar Singh (81124)Amit Harshvardhan(81126)

Rahul Poswal (81166)Sumit Garg (81177)


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FinancialMarket

Money

Market

Capital

Market

Primary Secondary

Primary Secondary


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Money Market

Money Market is concerned with the buying &

selling of short -term (less than one year originalmaturity) government and corporate debtsecurities whereas capital market deals with long

term.


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Money Market Instrument

Treasury Bills

Certificates of Deposits

Commercial Papers

Inter-corporate Deposits

Ready Forwards


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Money Market Instrument (cont.)

Bills of Exchange

Bill discounting

Short Term Debentures

Fixed Deposits

Mutual Funds Scheme


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Treasury Bills

Issued By RBI.

Maturities of 14, 91, 364 days.

Issued for minimum of Rs 25,000 & its multiples.


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Certificates of Deposits

Risk Free Option like T-Bills.

Issued in denominations of 0.5 mn.

Maturity ranges from 30 days to 3 years.


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Commercial Papers

Introduced by RBI.

Issued by Financial companies with credit rating.

Issued in denominations of Rs 5 lakhs or inmultiples.

Duration of 15 days to 1 year.


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MIBOR

MIBOR-Mumbai Interbank Bid-Offer rate.

MIBOR is equivalent to daily call rate.

It is the overnight rate at which funds can be borrowed andchanges everyday

The MIBOR rate is used as a bench mark rate for majority of

deals struck for Interest Rate Swaps, Forward Agreements,Floating Rate Debentures and Term Deposits.


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MIBOR

NSE had developed and launched the NSE Mumbai

Inter-bank Offer Rate (MIBOR) for the overnight

money market on June 15, 1998

NSE launched the 14-day NSE MIBID MIBOR onNovember 10, 1998 and the longer term money marketbenchmark rates for 1 month and 3 months on December 1,1998

The exchange introduced a 3 Day FIMMDA-NSE MIBID-MIBOR on all Fridays with effect from June 6, 2008 inaddition to existing overnight rate.


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WHY MIBOR IS USED

Unbiased - The National Stock Exchange of India (NSEIL)has been trusted by the securities markets for its unbiasedindependence and professionalism

Market Representation - based on rates polled by NSE froma representative panel of 33 banks/ primary dealers.

Transparent - The reference rate is released to all the market

participants simultaneously through various media, making ittransparent

Reliable - The high level of co-relation between actual dealsand the reference rate gives an indication of its reliability.


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Dissemination of NSE MIBID MIBOR

FIMMDA-NSE MIBID MIBOR rates are broadcast throughthe NEAT-WDM trading system immediately on release

The NSE website carries the daily rates as well as the

historical data on the FIMMDA-NSE MIBID MIBOR

FIMMDA-NSE MIBID MIBOR rates are also carried by allleading financial dailies including Economic Times, FinancialExpress, Business Standard and Business Line.

MIBOR rates are released to contributors and users through E-mail.


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MIBOR Methodology

Volume weighted average (VWA) is calculated by averagingthe reported trades after weighting them with their respectivevolume.

The VWA needs price volume data of all executed deals and isa reliable measure of the market

Polling is used for obtaining reference rates by polling a few

market participants and summarizing the prices they report.

The procedure involves querying bid and offer prices fromeight market participants.


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MIBOR Methodology

Traded mean: Calculating fixed trimmed mean of thereported rates have been used by some organizations whichneed to use a reference rate.

They collect rates from individual dealers and compute areference rate as the trimmed mean is obtained after deleting"n" highest and lowest observations.

Bootstrapping: The bootstrap technique is a non-parametricmethod for computing the test statistics

Computing the reference rate as an average of the polled ratesafter an appropriate amount of trimming.


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Bonds

Bond is a debt security.

Authorized issuer owes the holders a debt and,

depending on the terms of the bond, is obligedto pay interest (the coupon) and/or to repay theprincipal at a later date, termed maturity.

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Definitions

Par or Face Value -

The amount of money that is paid to the

bondholders at maturity. It generallyrepresents the amount of money borrowedby the bond issuer.

Coupon Rate -

The coupon rate, which is generally fixed,determines the periodic coupon or interestpayments. It is expressed as a percentage

of the bond's face value. It also represents


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Definitions

Maturity Date -

The maturity date represents the date

on which the bond matures, i.e., thedate on which the face value is repaid.The last coupon payment is also paid onthe maturity date.

Yield to Maturity -

The yield to maturity is the interest ratethat brings a bond's original value,

principal payments and interest


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Definitions

Market interest rate The interest rates yieldedby any investment take into account:

The risk-free cost of capital Inflationary expectations

The level of risk in the investment

The costs of the transaction

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The basic interest rate pricing model is

I = ir + pe + rp + Ip

Whereir =is the risk-free return to capital

Pe = inflationary expectations

rp = a risk premium reflecting the length of the investment

and the likelihood the borrower will default

lp = liquidity premium

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Types of Bond

Callable bond

Convertible bond

Perpetual Bond Bonds with finite Maturity

Non zero coupon Bonds

Zero coupon Bonds

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Bond Valuation

Bonds are valued using time value of moneyconcepts.

Their coupon, or interest, payments are treatedlike an equal cash flow stream (annuity).


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Example

Assume Ram buys a 10-year bond from the KLMcorporation on January 1, 2008. The bond has a facevalue of Rs 1000 and pays an annual 10% coupon. The

current market rate of return is 12%. Calculate the priceof this bond today.

1. Draw a timeline

$100 $100$100

$100$100

$100$100

$100$100$100

$1000

+

?

?


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Perpetual Bond

V = CF/r

= 100/0.12

= 833.33

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Non zero coupon with finite maturity

First, find the value of the coupon stream PV = 100/(1+.12)1 + 100/(1+.12)2 +

100/(1+.12)3 + 100/(1+.12)4 +

100/(1+.12)5 + 100/(1+.12)6 +100/(1+.12)7 + 100/(1+.12)8 +100/(1+.12)9+ 100/(1+.12)10

PV = 565


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Find the PV of the face value

PV = MV/ (1+r)t

PV = 1000/ (1+.12)10

PV = 322

Add the two values together to get the totalPV

V = 565 + $322 = $887


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Zero coupon bond with finite Maturity

V = MV/(1+r)n

= 1000/(1.12)10

= 322

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Presented By:

Piyush Mehta (081163)Sachin Vohra (081173)


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Topics To Be Covered

Valuation of Bonds

Yield

Current Yield

Yield to Maturity (YTM) Yield Curve & Term Structure

Bootstrapping

Nelson Siegel Model (NSE- ZCYC)


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Current Yield:

Annual Coupon Receipts / Market Price of the

BondFor example,

if a 12.5% bond sells in the market for Rs.104.50, current yield will be:

= (12.5/104.50) * 100= 11.96 %

However current yield does not considertime value of money, future cash flows,reinvestment income.


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Yield to Maturity (YTM):

Discount rate which equates the price of a bond

with the PV of its expected future cash flows

nmIRR

n

kk

mIRR

kCP

1100

11

Where

n = total no. of periods ( n = mt)

m = no. of coupon payments per year

t = no. of years to maturity

C = periodic coupon rate ( C/m)

P = market price of the bond


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Example:

What is the yield to maturity of a 5% coupon 9

year Rs. 1,000 par value bond if the price is Rs.813 (annual coupons)?

We need to solve the following equation for r:

9

813 = (50/(1+r)^t)+ (1000/(1+r)^9)

t=1


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Suppose coupons are semi-annual:18

813 = (25/(1+r)^t)+ (1000/(1+r)^18)

t=1

What determines interest rates?

investor preferences(e.g. willingness to saveaffects the supply of capital)

productive opportunities(e.g. firms desire toinvest affects the demand for capital)

inflation(let idenote the expected rate ofinflation)


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inflationerodes the purchasing power of money) distinguish between nominaland realinterestrates:

1+rnominal = (1+rreal)(1+i)

rnominal = rreal + i+ i * rreal

= rreal + i

nominal rates will change whenever expectedinflation does


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Problems with Yield to Maturity

The same rate is used to discount all payments,

but what if

r1 r2 r3.. ? For example:

Bond A: 3 years, annual coupon of 5%Bond B: 3 years, annual coupon of 15%

Spot rates: r1 = :04; r2 = :048; r3 = :054Calculate the yield to maturity and PV for eachbond:


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Yield to maturity can give a misleadingimpression of return since it implicitly assumesthat all intermediate payments are reinvestedand earn the same rate of return

Yields to maturity do not add upeven if you

know the yield to maturity for A and the yield tomaturity for B, you do not know the yield tomaturity for A plus B


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Until now we have assumed that nominalinterest rates are the same for all future periods;this allowed us to use

the general PV formula:

T

PV = (Ct/(1+r)^t)

t=1 Using the same YTM rate can lead to erroneous

results because it takes all the coupons have tobe invested for all the time periods at a single

rate


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Actually there are different rates in the market

for each of the cash flows These rates are known as zero coupon rates or

spot rates

Zero Coupon Yield based Valuation


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So our new formula becomes:

T

PV = (Ct/(1+rt)^t)t=1

PV= C/(1 + r1

) + C/(1 + r2

)^2 +... (C+R)/(1 + rm) ^m


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Yield Curve

A graph of bond yields to maturity by time tomaturity is called a yield curve.

4.00%

4.50%

5.00%

5.50%

6.00%

6.50%

7.00%

3mo 6mo 1yr 2yr 3yr 5yr 10 yr 30 yr


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Yield Curve Contd

Has different shapes:

Upward Going

Inverted Flat

NSE estimates the ZCYC from the market pricesand enables the computation of appropriatediscount rates


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Zero Coupon Yield based Valuation

Each coupon bond is really a package ofsingle payment bonds.

For example, a 2-year 10% coupon bond isreally a package of five single payment

bonds:

four for the semi-annual coupon paymentsand

one for the repayment of the principal.


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Zeroes

A single payment bond is called a zero.

A coupon bond can be thought of as a

package of zeroes,one for each of the coupon payments and

one for the principal.

In principle, any coupon bond could bestripped or unbundled into its constituentzeroes.


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Spot Yields

A spot yield is the current yield to maturity on azero.

For example, the 1-year spot yield is the yield to maturity

on a 1-year zero.

The price (per dollar of corpus) of an n-year zero isrelated to the n-year spot rate by the formula:

0Pn 1

1 in2

2n

F l if th 3 1/2 t i ld i 6 05%


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For example, if the 3 1/2 year spot yield is 6.05%,then the price (per dollar of corpus) of the 3 1/2 yearzero is:

0P3.5 = 1/(1+(.0605/2))^ 7= 1/(1.03025)^ 7

= 0.811

Alternatively, we can express the n-year spot yield asa function of the price of an n-year zero:

in 2

1

0P

n

1

2n

1


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Price of a Coupon Bond

n Spot Yield Price of zero Cash flow Value

1/2 5.10% $0.98 $0.0375 $0.03661 5.49% $0.95 $0.0375 $0.0355

1 1/2 5.64% $0.92 $0.0375 $0.0345

2 5.82% $0.89 $0.0375 $0.0334

2 1/2 5.88% $0.87 $0.0375 $0.0324

3 5.95% $0.84 $0.0375 $0.0315

3 1/2 6.05% $0.81 $0.0375 $0.0304

4 6.12% $0.79 $0.0375 $0.02954 1/2 6.12% $0.76 $0.0375 $0.0286

5 6.19% $0.74 $1.0375 $0.7647

$1.0571

5- ear 7.5% cou on bond

For Example:


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Term Structure

The term structure of interest rates is thepattern of spot rates over the range of

maturities.A flat term structure means that spot yields

are equal at all maturities.

A normal term structure slopes upward

An inverted term structure slopesdownward


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Bootstrapping

Here we use rates of bonds without intermittentcoupons i.e. Zero Coupon Bonds

However, in most markets zero coupon bondsacross varying tenors dont exist and so wecould bootstrap from the zero coupon treasuriesand derive r1,r2,r3..rn of the coupon paying

bonds


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Heres yield curve information

Bootstrapping

Coupon Term (yrs) Yield Price

8.50% 1/2 5.10% $101.66

7.38% 1 5.49% $101.819.00% 1 1/2 5.63% $104.78

8.88% 2 5.81% $105.72

6.75% 2 1/2 5.86% $102.03

7.75% 3 5.93% $104.946.25% 3 1/2 6.03% $100.69

5.63% 4 6.09% $98.38

6.50% 4 1/2 6.10% $101.56

7.50% 5 6.16% $105.69


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The first bond has 1/2 year to run

Its price is $1.0166 per dollar of face value.

Therefore the 1/2 year spot rate is

i1/2 = 2((1.0425/1.0166)^1 1)

= 2(.0255)= 5.10 %

Bootstrapping


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Given the 1/2 year spot rate, we candetermine the price of the 1/2 year zero:

0P1/2 = 1/(1+i1/2/2)^1

= 1/(1+0.0510/2)

= 0.9751

Bootstrapping


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For each dollar of face value, the 1-year bondwill pay $.03690 in 6 months and $1.03690 inone year.

Its price should equal:

$ 1.0181 = $ 0.03690/(1+i1/2/2)^1 +

$1.03690/(1+i1/2)^2

Bootstrapping


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$ 1.0181 = $ 0.03690/(1+.0510/2)^1 +

$1.03690/(1+i1/2)^2

i1 = 5.49 %

Bootstrapping

Which we can solve for the 1-year spot rate as :

B t t i


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Now solving for 0P1i.e. 0P1 = C1/(1+r0.5)^0.5 + C2/(1+r1)^1

The yield curve is then drawn from these derived zero rates

Bootstrapping

Coupon Maturity Yield Price Zero Price Spot Yield

8.50% 0.5 5.10% $101.66 $97.51 5.10%

7.38% 1 5.49% $101.81 $94.73 5.49%9.00% 1.5 5.63% $104.78 $92.00 5.64%

8.88% 2 5.81% $105.72 $89.16 5.82%

6.75% 2.5 5.86% $102.03 $86.51 5.88%

7.75% 3 5.93% $104.94 $83.88 5.95%

6.25% 3.5 6.03% $100.69 $81.16 6.05%

5.63% 4 6.09% $98.38 $78.58 6.12%

6.50% 4.5 6.10% $101.56 $76.23 6.12%

7.50% 5 6.16% $105.69 $73.71 6.19%


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Spot rate function is given as:

r= 0 + (1+ 2) * [1-exp(-m/)]/(m/)- 2*

exp(-m/) Discount function is given by:

d= exp((-r * m)/100)

m= time to maturity

0,1, 2 =long run ,short run & medium runcomponents of interest rates

NSE - ZCYC (Nelson Siegel Model)


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p_est =PV arrived using discount function

pmkt = actual market prices

Pmkti= p_esti + ei Minimizing the sum of squared price errors

When m is very large, then value of

r= 0 (non zero constant)

When m tends to zero, then

r= 0+ 1

NSE-ZCYC (Nelson Siegel Model)


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Steps:

Starting values of parameters (0,1,2,)

Determine the discount function using theseparameters

Determine present values of cash flows therebyprices of the bonds

Optimize the solution that minimize the sum ofsquared price errors



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Determine the price and also spot rate for eachbond

Plot the spot rates against the maturity values



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Thank You

Documents

Money Market, Bonds, Mibor