fimmda valuation methodology for slr and non-slr

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FIXED INCOME MONEY MARKET AND DERIVATIVES ASSOCIATION OF INDIA

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FIMMDA VALUATION METHODOLOGY FOR SLR AND NON-SLR

SECURITIES

Introduction FIMMDA has entered into an agreement with Bloomberg to provide fair value prices of all outstanding SLR bonds on a daily basis. The exercise is carried out by Bloomberg as per methodology prescribed by FIMMDA. The fair value prices are determined by a polled process of active market participants and the Bloomberg propreitory model is used for interpolating data collected from the market. The procedure and methodology is detailed below: Polling for prices On the first of each month FIMMDA valuation committee classifies all outstanding SLR bonds into the following groups: 1) Benchmark Bonds – The most well traded bonds in a given maturity 2) Other Bonds – Bonds which are not benchmark bonds but trading on the

benchmark curve. 3) Semi-liquid bonds – Bonds which are traded but not actively 4) Illiquid bonds – Bonds with minimum or no trading turnover 5) Floating rate Bonds 6) Special Bonds – UTI and Oil bonds The basis of classification is actual market turnover of these securities for the previous month as per the daily SGL data published by RBI. The Bloomberg polls for rates for the benchmark bonds from 23 contributors assigned by FIMMDA (Annexure i). These rates are polled between 2pm - 4pm daily. Of the 23 contributors there are a few contributors who update directly to Bloomberg through a facility provided on their Bloomberg terminal. Apart from above, Bloomberg receives government bond pricing from around 52 contributors across most bond maturities. These prices are stored contributor wise historically on the Bloomberg terminal.


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Calculation of prices There are 4 different pricing sources that get calculated by Bloomberg on a daily basis. They are BGN (Bloomberg Generic Price), BFV (Bloomberg Fair Value Price), BFMD (Bloomberg- FIMMDA price) and FIMD (FIMMDA day end valuation price). The same is explained below. At around 4.17pm daily, the Bloomberg system generates a BGN (Bloomberg Generic) price. Liquidity is the main criteria for a BGN price to be generated. BGN is a market consensus price for government bonds. They are calculated using prices contributed to Bloomberg through the polling process. The goal of the methodology is to produce "consensus" pricing. Since all bonds don’t have a BGN price due to not being quoted often in the market, Bloomberg derives a fair market price for it (BFV). BFV establishes a bond's theoretical value, based on where similar bonds are trading, taking into account the value of any call or put feature. This value is not based on market price. BFV incorporates OAS methodology in deriving the theoretical value. The BFV prices are represented via a par coupon yield curve graph on the Bloomberg system, which all Bloomberg users rely on. For India, the curve is updated by 4.35pm. {CURV123 <GO>}. See (Annexure ii) for Bloomberg Methodology for Fair Market Curves. Using the BFV price and the spreads obtained from the market, Bloomberg created a special pricing source called BFMD (Bloomberg-FIMMDA). This price gets generated at 4.50pm. This was specially setup to generate prices for "illiquid" securities in the Indian market. BFMD price = Bloomberg Fair Value (BFV) + Spread The spread is polled once a week on Monday from 20 contributors. These contributors provide a spread for various maturity buckets. The same spread is used for the entire week. The spreads are stored on the Bloomberg as indices. {ALLX BFMD <GO>} Bunching the prices as per category Once there is a price for all government bonds, all of it is collated into an excel sheet. The excel sheet is sorted as per maturity. The prices are shown as per their category as defined by FIMMDA.


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1) Benchmark bonds Bloomberg provides their BGN price to FIMMDA for all benchmark bonds and bonds trading on the benchmark. 2) Special bonds These are the Oil and UTI bonds. Our BGN price is provided for these bonds, as they are fairly liquid. On days BGN is not generated, Bloomberg does not provide a price. 3) Semi-liquid bonds Yield = (Avg.3 day SGL price) - (Avg.3 day BFV price) + (Today's BFV price) Once the yield is arrived, based on Bloomberg's calculator the price is derived. 4) Illiquid bonds BFMD prices are used for all illiquid bonds. 5) Floating Rate Bonds (FRB's) The coupon is the yield. The price is not provided by Bloomberg for the same. The excel sheet containing all the prices and yields, are then uploaded on the FIMMDA website. FIMMDA in turn verifies the prices. Once the verification is done, the file is available for all to see on their website. (www.fimmda.org). Note: The final prices are also available on the Bloomberg terminal by typing {FIMD <GO>}. PCS source FIMD can be used to run historical analytics on all Indian Government Bonds. In addition to above prices, Bloomberg also provides zero coupon yield curve points for maturities 1 year, 2 year, 3 year, 4 year, 5 year, 7 year & 10 year points. These are derived from FWCV.

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Verification of data Once Bloomberg uploads the file, FIMMDA independently carries out the following checks on a daily basis (for month end valuation the checks are more elaborate and done by the FIMMDA valuation committee as described in (Annexure iii))

1. The prices as per the Bloomberg valuation sheet are compared with the NDS prices (T+0)

2. In case any security as thrown up by the model shows significant deviation from

traded data the traded price is substituted.

3. If the prices as per Point 2 are changed then the corresponding yields are also changed.

4. If Bloomberg does not generate prices for Floating Rate Bonds (FRBs) (lack of

trading) the prices of FRBs are calculated by FIMMDA as per (Annexure iv) Valuation of Non-SLR securities / Corporate bonds A corporate bond Matrix of credit spreads across various tenors and ratings is generated by CRISIL on a fortnightly basis. The spread when added to the Benchmark Gsec yield for the relative tenor gives the yield to be applied for the corporate bond. On a daily basis only the underlying base yield curve is changed with the spreads remaining constant during the fortnight. The semi-annual base yield curve (YTM) is provided in the daily FIMMDA valuation file. This is required to be annualized while valuing the Non-SLR bonds. (Annexure v) gives the detailed procedure for valuing corporate bonds.


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(Annexure i) Contributors that Bloomberg polls rates/prices/spreads from on a daily basis • ABN Amro Bank • ABN Amro Securities • American Express Bank • Andhra Bank • Bank of Baroda • Central Bank of India • Corporation Bank • HDFC Bank • HSBC • ICICI Bank • ICICI Securities • IDBI Bank • IDBI Capital • Industrial Development Bank of India • ING Vysya Bank • J.P. Morgan • PNB Gilts • Securities Trading Corporation of India • Standard Chartered Bank • SBI-DFHI • State Bank of India • Syndicate Bank • Union Bank of India • UTI Bank


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(Annexure ii) Bloomberg Methodology for Fair Market Curves Bloomberg generates fair market curves, or best fit curves, for many bond sectors. These fair market curves are used to generate a fair value (BFV) for unpriced bonds in that particular sector. The Fair Market Curves are generated by a proprietary optimization model, which encompasses the following process: 1. Generation of a bond map 2. Generation of term structures 3. Optimization of term structure

a) Generation of zero coupon curves b) Calculation of option adjusted spreads c) Curve selection and fixing

1. Generation of a Bond Map

Bonds having Bloomberg Generic prices (BGN) are mapped on a yield-maturity phase space. A bond has a Bloomberg Generic price when there are at least five price contributors to a particular bond. The BGN price for a bond is statistically generated by truncating the extremes and averaging the remaining quotes. See Figure 1, where BGN priced bonds are simply mapped onto a yield-maturity diagram.

Figure 1


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2. Generation of Term Structures The vertical lines on Figure 1 are standard maturity points on the yield-maturity diagram. A line passing through all the vertical lines would represent a term structure, and the points of intersection of this line with the vertical line would represent par coupon yields for the corresponding maturities. How many term structures can be drawn in this phase space? As can be seen, infinite term structures can be generated. We need a term structure which best describes the BGN bond data that is populating the space, that is we need a term structure which will generate a bond price/yield as closely as possibly, and which can thus ascertain a fair value for a bond as reliably as possible. Thus from this family of infinite term structures, we need to home in on a term structure that serves this purpose. This takes us to the optimization model, which is an algorithm for generating the fair market curve.

3. Optimization of Term Structure

The Optimization model firstly narrows down the term structure curve space to a bandwidth area, which is the zone where the curve is most likely to exist. The model then generates term structure curves by iteration. For every curve generated, the following process is done: a) Generation of Zero Coupon Curves:

For every term structure curve is generated, it is converted into a spot curve by bootstrapping. In bootstrapping spot rates are computed from coupon rates by computing implied forward rates. For example, if one knows the 6-month spot rate and the 1-year coupon rate, one can compute the 6 month implied forward rate 6 month hence. From this one can then calculate the 1-year spot rate.

b) Calculation of option-adjusted spreads (OAS):

Once the spot curve, or zero coupon curve, is available we proceed to compute the option adjusted spread of each bond on the map. For each bond, each cash flow is discounted at the appropriate discount rate, and the present value of the bond is calculated. If the bond was exactly on the generated term structure curve, the present value would equal the BGN price of the bond and one can say the OAS of the bond is zero. However, if the bond were not the curve, one would need to add some spread to each discount rate, such that the present value would equal the BGN price. This spread is the OAS of the bond.


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For every curve generated we calculate the standard deviation of OAS of all the bonds. c) Selection of Best-Fit Curve: The model then tries to find the curve that satisfies Min (�OAS). That is, it selects that curve for which the standard deviation of the bond OASs is at a minimum. See figure below, where bonds are plotted on an OAS Duration vs. OAS chart. The line of best fit at the center satisfies Min (�OAS). That is, for this term structure, the standard deviation of the OAS of the bonds is at a minimum.

Thus this process is employed for the generation of Fair Market Curves across numerous bond sectors across many countries. The method provides an excellent fit as verified by the BFV-BGN statistics for all bond sectors. Bond Fair Values are then determined by linearly interpolating off adjacent maturity points. The mathematical treatment for the process is elegant yet simple and provides a sound, robust, and highly reliable method for consistently generating with minimum error a fair valuation basis for bonds. Modifications to the methodology for the valuation of non-benchmark securities The objective of any valuation model should be to achieve as close a fit as possible with actual traded prices in the market. The Bloomberg methodology has a high in-sample accuracy i.e. it can correctly value Benchmark bonds. The benchmark securities are assumed to be perfectly liquid. It is assumed that there is no illiquidity premium built into the yields of these securities. However, it does not take into account the factor of illiquidity, which is observed in the Indian Markets for other securities. Non-Benchmark Securities are classified into the following categories:

1. Semi-liquid or thinly traded securities, which are traded securities which belong to the same bucket as a particular benchmark, but are not traded as


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actively as the benchmark. Hence traded price data is available for these securities.

2. Illiquid securities, which are rarely traded and hence there are very little traded price data available.

The methodologies for valuation for Semi-Liquid and Illiquid securities are different. 1. Semi-liquid securities For a semi liquid security, we have a yield from the Bloomberg model called the BFV. Let us call this Yb. Assume that the actual traded yield on these securities is Ya. The actual traded yield for a particular day will be available from SGL prices released by the RBI (for the same value date) the next day. The relationship between the traded yield and the Bloomberg fair value is as follows: Ya = Yb +� Where ��is an error term. Since traded prices are available the next day, we have a series Ya(t-1) = Yb(t-1) +��(1) Ya(t-2) = Yb(t-2) +� (2) Ya(t-3) = Yb(t-3) +� (3) Where t denotes the current date, for which valuation has to be done. For the current date Ya (t) is not available because the SGL data is released one day late. However, Yb(t) is available because it is a model output. Hence Ya(t) is estimated in the following manner. Ya(t)(est) = Yb(t) +(� (1)+ � (2)+ � (3))/3 To state it simply, we estimate the actual yield of a semi-liquid security by correcting the Bloomberg Yield for the average of observed errors between the Bloomberg Yield and the actual yield for the last three days. The time for which the error is averaged (currently three days) is reviewed from time to time. In times of high volatility, this error changes and hence there is little point in taking older data for estimation.


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The three days over which the average is taken are the most recent days in a seven-day period. If a trade is observed, the spread between the traded yield and the observed yield is accordingly incorporated in the estimation. If no trades are observed for seven days, the security is treated as an illiquid security. The semi-liquid securities are set at the same time as the benchmarks. They are established on the criteria of volume and number of trades. However, the exact criteria are left to the judgment of the valuation group. 2. Illiquid Securities Illiquid securities are those for which trades are rare, if ever, observed. Hence there is no mathematical way of estimating the illiquid premium in these securities. The illiquid premium in a security is expected to be dependent on the following factors 1. Maturity: Depending on which maturity buckets in the market are active, the illiquid premiums will change. Maturity is one of the most important factors affecting the illiquid premium. 2. Coupon rate: Higher coupon securities tend to be more illiquid. 3. Issue Size: Lesser the issue size, lower will be the quantum of security in the market and hence it will be traded at lower price or a higher yield. 4. Distribution amongst various market participants: If large and inactive market participants hold a particular security to maturity, that security will be illiquid and will not trade. It is not possible to accurately model the effect of factors two, three and four on the illiquidity premium. In the FIMMDA Bloomberg method, various market participants poll the illiquidity premiums for different maturity buckets. These illiquidity premiums are then added to the BFV curve or the liquid yield curve and thus the illiquid yield curve is established. All illiquid securities in the market are valued off the illiquid yield curve.


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(Annexure iii) Month-end valuation process for SLR securities The month-end valuation is done on the first working day of the subsequent month. The day-end valuation file as on the last working day of the previous month is considered and the following process is carried out.

1. The valuation committee of FIMMDA looks at the Bloomberg model price and compares it to the SGL traded data of every bond. The committee is empowered to substitute the model price with the traded data if it is convinced that the model price is not giving the correct results. The prices can be substituted by the SGL prices for only those securities which have recorded 5 trades and 25 crores volume. The securities, which are substituted, are marked in bold and a note is also put below the valuation sheet that these security prices have been substituted using SGL prices. The deals, which are taken in the SGL, should have the trade date and value date as on the valuation date. The deals, which are “value free transfers”, are deleted from the SGL file as they distort the prices.

2. The committee decides the Benchmark, Semi-liquid, illiquid securities and

other securities for the following month after viewing the total traded volumes of the securities in the previous month.

3. The committee vets the corporate credit spreads and approves the matrix for

valuing corporate bonds. Valuation of State Government securities

1. The state government securities or SDLs are valued after adding 25 bps (specified by RBI) over the central government securities yield curve as provided by FIMMDA.

2. For valuing the SDLs, FIMMDA also supplies its members with a “state

government calculator” which is available on FIMMDA’s website (www.fimmda.org). The input fields in the calculator are the valuation date,


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maturity date and the coupon of the security. The calculator gives the “price”, “YTM” and “residual maturity” as the output.

The calculator uses the simple linear interpolation methodology for valuation of a security with residual maturity falling between the available yield curve points. (Annexure iv) Methodology for valuation of Floating Rate Central Government securities (FRBs) Introduction Floating Rate Bonds are instruments where the coupon rate is variable and is calculated using a certain predetermined methodology. Crucial to the concept of a floating rate bond is the “Benchmark Rate”, which is a market determined interest rate used for the computation of the coupon rate from time to time. The frequency at which the coupon rate is reset is called the reset frequency, while the frequency at which coupon payment takes place is the coupon payment frequency. Conventional Methods of Valuation of Floating Rate Bonds The standard method of valuation of a bond is to discount all the cash flows of the bond at a rate based on the yield available on a comparable instrument in the market. Consider a floating rate bond where the benchmark and the coupon are the same. Further the coupon payment frequency and the resetting frequency are the same. For instance, a floating rate bond that pays the 3-month FIMMDA NSE MIBOR every three months. The risk of the cash flows and the benchmark rate are the same. In such a case, since the coupon will always be discounted at the benchmark rate, the bond will be at par on the coupon reset date. To explain this mathematically, we will set the notation that we will use

1. The series tn = {0, t1, t2, t3… tN} denotes the coupon payment dates, where N is the last coupon payment.

2. The series Tm = {0, T1, T2… TM} denotes the coupon reset dates, where M is the last coupon reset.

3. r(t1, t2) denotes the interest rate in the market applicable from time t1 to t2 . 4. C(t) denotes the expected value of the coupon payment at time t. 4. P(t1, t2) denotes the price of the bond at time t2 expected at time t1. The face

value of the bond is 1. 5. C(tn ,tm) denotes the coupon payment at tm expected at tn


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With a notation such as above, the problem statement for valuation of a floating rate bond can be defined as finding the expected price of the bond at time 0 i.e. P(0,0). Case 1 Consider the case of the simple floating rate bond that satisfies the following conditions:

a. Benchmark rate and the coupon rate are the same b. Reset Dates and Coupon Payment dates are the same.

Mathematically, these conditions can be stated as follows:

1. tn = Tm 2. C (tn) = r (tm-1, tm) 3. P(0, tN) = 1; where tN is the maturity

The bond pricing equation is as follows: P(0, tn-1) = (P (0, tn) + C(tn)) -----------------------

(1+r(tm-1, tm))

In other words, the expected price of a bond on any coupon reset date is the sum of the expected price on the next coupon reset date and the coupon expected on that date, discounted at the rate expected from that date to the next coupon reset date. Using the identities established above, P(0, tn-1) = (1 + r(tm-1, tm)) -------------------

(1 + r(tm-1, tm)) Hence P (0, tn-1) = 1 It can be subsequently established that P (0, ti) = 1 for all i = {1,2, 3..,n} Hence such a bond will reset to par. Sovereign Floating Rate Bonds in India


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The Government of India has issued a series of floating rate bonds. The floating rate bonds issued by the Government of India (GOI) have the following structure:

1. Maturity : various from 2006 to 2017

2. Coupon Payment Frequency : Semi-Annual 3. Coupon Reset Frequency : Semi-Annual/Annual 4. Benchmark Rate : Average of the cut-off yields in the previous six/three auctions of 364 day T-

Bills, conducted by the RBI plus a markup determined in the auction of the floater

Mathematical results Before going into the methodology for valuing the GOI floating rate bonds, we shall consider the pricing of the following simplified structure:

1. Maturity : 6 years 2. Coupon Payment Frequency : Semi Annual 3. Coupon Reset Frequency : Semi Annual 4. Benchmark Rate : 364 day Treasury bill yield prevailing in

The market on the date of the coupon reset + markup determined in the auction.

The only difference between this structure and the previous structure is that we are ignoring the “averaging out” of T-Bill auctions. Mathematically this can be written as follows:

1. {tn}={Tm} 2. tn – tn-1 = 0.5 years 3. C (tm) = (r (tm-1, tm+1) + s) /2, where “s” is the spread (the spread is assumed to

be 0 for the purpose of the examples).

The bond pricing equation for this Bond can also be, recursively, arrived at as follows: P (0,tn-1) = (P (0,tn) + C (tn) ----------------------

(1+r (tn-1, tn))0.5


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= (P (0, tn) + r (tn-1, tn+1) / 2) --------------------------------

(1+r (tn-1, tn)) 0.5

Case 1: Flat Yield Curve Consider the case where interest rates in the market are not expected to move in the future. This also implies a flat yield curve. This can be, mathematically, written as: r (tn-1, tn+1) = r (tn-1, tn) = r The Bond Pricing Equation can be written as: P(0, tn-1) = (P(0,tn) + r/2) ------------------

(1+r)0.5

It can be proven, mathematically, that for a given level of interest rates, P (0, tn-1) > P (0, tn)1. This leads us to the following conclusions:

1. The bond will always reset above par. 2. Ceteris Paribus, the bonds value increases as its maturity increases. 3. At inception, since the bond should be at par value, there should be a

negative spread in the numerator i.e. the bond should always be issued at 1 year T-bill yield – “x” basis points.

Case 2: Upward Sloping Yield Curve Consider the case where the 1-year T-Bill yield is expected to be above the 6 month T-Bill yields. In such a case, if we denote the prices of the bond as P’(0, tn) , it can be

1 One can inductively start from the period tn-1 knowing that the P(0,tn) =1. The rigorous proof has been discussed outside of this methodology review.


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shown that for every tn =0,0.5, 1, 1.5…., P’(0,tn)( upward sloping yield curve) > P(0,tn)(flat yield curve). Since the “expectations hypothesis” implies that a continuously upward sloping curve means that expected values of 1 year forward rates are above the expected values of the six month forward rate, it can be concluded that in a continuously upward sloping curve, the value of the bonds will be higher than that assuming a flat curve. However, because of the recursive nature of the bond pricing equation, the spread cannot be computed analytically. Methodology for computation of the price The theoretical method for computation of the price can be broken down into two steps:

1. Estimation of the price of the bond on the next reset date 2. Computation of the current dirty price of the bond

Estimation of the “Next-reset” Price Since the immediately next coupon is known, the first problem is to estimate the price that will prevail on the next coupon-reset date. This price along with the coupon can then be discounted at the zero coupon rate till the next reset date. Subtracting the accrued interest for the current period gives the clean price of the bond. Computation of the “next-reset” price involves the following two steps:

a. Estimation of expected cash flows: The estimation of expected cash flows is done by computing the forward 1-year rates for each of the coupon reset dates. These forward rates are computed from the zero coupon rates prevailing in the market at the time the bond is being valued. Since there is no standard accepted zero-coupon curve in the market, we bootstrap the yield to maturity curve given by FIMMDA-PDAI to arrive at a zero coupon curve. The rates for intermediate periods are computed by linear interpolation. Estimated cash flows are derived adding or subtracting the relevant spread established at the time of the auction. For the purpose of simplicity, we ignore the “averaging out” effect i.e. the one year forward rate on the date of the coupon reset is considered for cash flow estimation. In theory, a convexity and a timing adjustment should be


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applied to these estimated cash flows2. These require an estimate of forward rate volatilities. In the absence of firm estimates for these volatilities, there is no firm fix on the adjustments to be made. Also for reasons explained in the Annexure, we ignore them for the purposes of this computation.

b. Estimation of the discounting rates: The discounting rate to be used for the computation of the next reset price should be the zero coupon rate from the next reset date to the respective cash flow date. This is thus a forward rate from the next reset date to respective future cash flow dates. This is also computed from the zero coupon curve as on the date of valuation. Estimation of Price on the value date The clean price on the value date is arrived at by discounting the total cash flow at the next reset date (the sum of the next coupon payment and the “next reset” price). This gives the dirty price of the bond. The discounting rate used is the zero coupon rate from the value date to the next coupon date. The accrued interest is removed from the dirty price and thus we arrive at a clean price for the bond. Results We value the bond maturing on 6th December 2009 using this method under various scenarios. Flat yield curve We assume that the yield curve is completely flat and all future interest rates are given by the current 6-month yield. This implies that the value of all zero coupon rates and forward rates is given by today’s 6-month yield. The price computed according to the above method is Rs. 100.49 at a yield of 6.35%. This is the intrinsic value of the bond that arises due to the fact that an annualized rate (the T-Bill Yield) is being paid semi-annually. Hence, it can be re-invested for the remaining six months. When we add the timing and convexity adjustments (assuming forward rate volatilities to be constant at 20% and an 80% correlation between the 6 month and 1 year yield, this intrinsic value increase to Rs. 100.66 because of the fact that for this bond, the convexity adjustment for most of its early life is greater than the timing adjustment.

2 Refer Appendix 1


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Upward sloping yield curve With an upward sloping curve prevalent currently, the unadjusted value comes to Rs. 101.31 while the adjusted value is Rs. 101.58. This additional value arises because of the fact that for most of its life, the forward one-year rates will be greater than the forward six-month rates. Since in the bond pricing formula shown above, the price of the bond increases as we go away from maturity and the markdown in the bond is insufficient to negate this effect, the bond is significantly above par. Appendix 1 Convexity and Timing Adjustments Let BT denote the bond price at time T, yT denote its yield. If the relationship between yt and BT is BT = G(yt), the convexity adjustment “C” is given by C = -0.5 y02 σF2 T G”(y0) / G’(y0) Where G’ and G” denote the first and second partial derivatives of G. Timing Adjustment If EI(v1) is the expected forward value of a variable v without timing adjustment, the time-adjusted forward yield E2(v) is given by E1(v)e[(- (ρσFσRR0T1 (T2-T1)/(1+ R0/m)]

Where: v1 = value of v at time T1 F = forward value of v for a contract maturing at time T1 R = forward interest rate from time T1 to T2,

with a compounding frequency of m. R0 = value of R today σF = volatility of F=V1 σR = volatility of R=V2 ρ = correlation between F and R.


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Example of Convexity and Timing Adjustments The table shows how the timing and convexity adjustment cancel each other out. Calculation of convexity and timing adjustments Value Date 25-Jul-02 25-Jul-02 Auction date 23-Nov-02 23-Nov-15 T1 (years) 0.33 13.33 T2 (years) 1.00 1.00 Unadjusted forward 8.00% 8.50% Yield = y0 G''(y0)/G'(y0) = -2/(1+y0) -1.852 -1.843 V1 20% 20% V2 20% 20% Convexity adjustment 0.01% 0.35% R 7.50% 8.00% Ρ 90.00% 90.00% Time Adjusted Value of y0 8.00% 8.23% Value with both convexity and timingadjustment 8.00% 8.58% We assume values of 20% respectively for both the volatilities and a correlation of 0.80. Since we are estimating cash flows from the forward rates, an error in the latter years is more acceptable because in present value terms, a 1 bps error occurring at the 15-year point causes an error of Rs 0.003 in the price. Further, in the interest of a conservative valuation, we ignore the adjustment terms since they are positive.




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(Annexure v) Valuation of Non-SLR bonds/Corporate bonds FIMMDA publishes the credit spreads in the form of a Corporate Bond Matrix calculated by CRISIL for the valuation of corporate bonds. The spreads published are for exact maturity tenors beginning from the 1st year till the 10th year. The methodology currently followed by CRISIL for generation of Corporate bond Matrix for FIMMDA is given below: 1. DATA SOURCES FOR CRISIL CRISIL maintains a daily debt database of traded levels for corporate bonds. The traded data from the below mentioned sources is monitored daily for verification of levels across different tenors and rating categories. The different sources are as follows

NSE Traded Data - A file containing details of corporate bond trades is received daily at 7.00pm

Off market deals - Deal logs from brokers are received daily. Trades by Mutual Funds - Custodian files of SEBI mandated proprietary data of

deals contracted by Mutual Funds is received daily. Although the Mutual Fund traded data is privy only to CRISIL and CRISIL has non-disclosure agreements on the same, such traded levels could be used by CRISIL to arrive at realizable yield levels in the market using this information, without disclosing the trade details. 2. POLLING PROCESS CRISIL is currently undertaking a rigorous polling process on corporate bonds on a fortnightly basis to cross verify with traded levels to arrive at a realizable yield level for the matrix for FIMMDA. Both PSU as well as private banks form part of the polling group. The polls include both spread across rating categories and tenor buckets as well as two-way quotes on a small set of corporate bonds. Some of the banks, which are polled, are

o State Bank of India o IDBI Bank o Andhra Bank o Canara bank




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o Standard Chartered Bank o ICICI Bank o HDFC Bank o UTI Bank

3. VERIFICATION OF DATA

Verification of traded levels across different tenors and rating categories is done. Outliers if any are identified and removed. The current rating of individual bonds that are traded is also checked. Yields across tenor and rating categories are checked as well for the general

bond logic of higher return for higher risk. Any yield inversions are noted and cross checked for market reality and the

same are highlighted. 4. MATRIX CONSTRUCTION Using the actual dealt levels and quotes of polled banks we actually fill in the matrix levels for each bucket. After removing the outliers, CRISIL analyses the data, combines it with the traded data and the off-market deals to arrive at market realisable yield levels. The matrix construction process involves the following steps

a. Yield levels - Yields levels are determined by giving the effect of yield movements for government securities as well as in the respective tenor buckets and rating categories. CRISIL would average the yield levels and arrive at a single yield for each rating category and each tenor bucket.

b. Once the yield levels are determined, CRISIL does a cross check with traded data to ensure that the yield level arrived at is a fair representative level for all the bonds falling in that rating category and tenor.

c. Spread Check - A further spread check over FIMMDA's Gsec levels as well as inter bucket spreads across rating categories is also done to smoothen any irregularities.

d. The matrix is generated by CRISIL on a fortnightly basis. However, only month end valuations are currently being used by the banking sector.

e. All the analysis done by CRISIL would be available for any clarification by FIMMDA and any clarification sought by any of the members would be given by CRISIL to FIMMDA. This would bring greater transparency in the price discovery mechanism besides enabling a standardised approach.




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5. FINAL DECISION BY THE FIMMDA VALUATION COMMITTEE The FIMMDA Valuation Committee would examine the matrix worked out by CRISIL and the actual traded spreads as reported on the Corporate Bond Trade Reporting Platforms, and finalize the spreads to be used for the month–end valuations of Corporate Bonds. CRISIL may be called in for discussions over the polycom conference call in case of wide variations between CRISIL's matrix and the Valuation Committee's matrix. 6. VALUATION OF BONDS AND DEBENTURES, OTHER THAN

GOVERNMENT SECURITIES GENERAL 1. FIMMDA will publish the Annualised Base Yield Curve and a matrix of credit

spreads across maturities and credit ratings. 2. Yield and credit spreads for intermediate tenors for each curve may be arrived

by linear interpolation. 3. The spreads must be added to the base yield corresponding to the residual

maturity and not the original maturity. 4. Bonds with a remaining maturity of less than six months are valued on the 6-

month base yield curve plus the relative credit spread. 5. FIMMDA may from time to time stipulate different spreads for any specific

category if warranted. * * Currently the following spreads will apply:

Supra-national ADB Bonds would be valued at zero spread over the respective annualised gilt yield.

BONDS AND DEBENTURES, WHICH ARE RATED BY A RATING AGENCY

1. The rated bond is to be valued by adding the credit spreads to the Base Yield Curve (corresponding to the coupon frequency).

2. Where the issuer under consideration has two or more different ratings, from different rating agencies, the lowest of the ratings shall be applicable.

3. A rating is considered as valid only if it is not more than 12 months old. (In this connection please also see Annexure IV to Para 1.2.11 of RBI Master Circular dated 2nd July 2007)

UNRATED BONDS / BOND MIGRATED TO ‘UNRATED’ CATEGORY DURING ITS TENOR:




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Bonds and debentures, which are NOT rated by a rating agency or have become ‘unrated’ during their tenor, but a corresponding rated bond of the issuer exists, then:

1. The unrated bonds will be valued by marking up the credit spread by a minimum of 20 % over the equivalent rated bond of similar tenure.

2. For the above purpose, “corresponding” would mean, if the unrated bond has a maturity of ‘t’ years, the rated bond should have a maturity not less than t - 0.5 years. For example, if the unrated bond has a residual maturity of 3 years, then the rated bond to be treated as corresponding should have a maturity of at least 2.5 years.

BONDS AND DEBENTURES, WHICH ARE NOT RATED BY A RATING AGENCY, AND NO CORRESPONDING RATED BOND OF THE ISSUER EXISTS Anyone of the two methods, mentioned below, may be adopted. Method I

1. A quick rating can be obtained from the authorized credit rating agencies. 2. The credit spread to be added to the annualized yield curve for this notional

rating will then be marked up by 25%. Method II

1. The spread over the sovereign risk free yield curve, at the time of issue, marked up by 25% will be the applicable credit spread.

2. The credit spreads thus arrived at OR the current credit spreads of AAA bond of similar residual tenor, whichever is higher, should be taken and applied over the above base yield curve for valuation.

3. SGL Data available from 1st January 1996 at the RBI’s website (www.rbi.org.in) should be used for arriving at the credit spreads at the time of issue.

4. In case of issues prior to January 1, 1996 the bonds will be valued at cost.

Bonds and debentures, which have become ‘unrated’ during its tenor, and NO corresponding rated bond of the issuer exists. In such a case highest amongst the following three spreads should be taken as the credit spreads:

1. Compute the spread over the sovereign yield curve, at the time of issue, marked up by 25%.

2. Compute the spread for the last known rating of the bond from the current spread matrix.

3. The current spread for AAA bond of similar tenor. The value, thus arrived should be applied over the base yield curve for valuation. BONDS / DEBENTURES HAVING SPECIAL FEATURES




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1. Floating Rate Bonds

Floating Rate Bonds are instruments where the coupon rate is variable and is calculated using a certain predetermined methodology. Crucial to the concept of a floating rate bond is the “Benchmark Rate”, which is a market determined interest rate, used for the computation of the coupon rate from time to time. The frequency at which the coupon rate is reset is called the reset frequency, while the frequency at which coupon payment takes place is the coupon payment frequency.

Method of Valuation of Floating Rate Bonds 1) Compute the forward benchmark rate for each reset date. 2) Using the same find the coupon (benchmark plus markup, if any) and the cash

flows on the interest payment dates. 3) Discount these cash flows by any one of the following methods:

i. Discount each cash flow using the Zero-Coupon Yields for that cash flow adjusted for the credit spread corresponding to the rating of the bond.

ii. Discount all cash flows by the G-Sec YTM for the full maturity of the bond adjusted for the credit spread corresponding to the rating of the bond.

The zero-coupon rates may be arrived at using any recognized source viz. CCIL, FIMMDA - Bloomberg, etc. Computation of the forward rate

here, rate for time T1,

(T2-T1) at time T1

hile the above formula is most accurate, an approximation may be made as follows:

. Bonds with Call and Put Options: ll and put options (on the same day) and there

( ) ( ) ( ) 21212

)(1 111 TTTT RFR +=+×+ −

WR1 = zeroR2 = zero rate for time T2, F = forward rate for period WF = (R2×T2 – R1×T1)/ (T2 – T1) 2

Where bonds have simultaneous caare several such call & put options in the life of the bond, the nearest date should be taken for Price/YTM calculation. a. Only Callable Bonds: Bonds, which are only callable by the issuer, will be valued

b. at yield-to- worst basis. Only Puttable Bonds: Bonds puttable by the investor should be valued at yield- to- best basis.




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3. For bonds linked to MIBOR, the Overnight Index Swap (OIS) market quotes will be

sed to convert MIBOR into fixed rate for the outstanding tenor. The spread over nal terms of the issue) will be added to arrive at the notional

4.

a Collar spread of 25 basis points or less will be valued like a fixed coupon bond with the coupon being the average of the cap and floor. Bonds with

valued like floating rate bonds. (Rationale: If the Collar

5.

actor equal to the income tax rate applicable for the holder and the bond will be valued as per Para 3.7.1 of RBI Master circular

. As per rules governing tax-free bonds, to get tax-free status,

6. BI Master Circular (for

anks) mentioned above.

tment indicated in Para 5 above (for Tax free bonds) will e applied with the proviso that the Preference share is not valued above its

7.

Sector Undertakings should be valued as a corporate ‘AAA’ rated paper.

8. arket-borrowing

rogramme may be valued as follows: ve, at the time of issue, will be

if the issue is more than 12 months old.

MIBOR linked Bonds:

uMIBOR (as per the origifixed coupon. Then the bond will be valued similar to a fixed coupon bond and the valuation methodology given above for corporate bonds/debentures should be followed.

Bonds with Floor and Cap: Bonds with

higher collar spread will be spread is small the likelihood of the bond hitting the cap or the floor is higher and the bond would behave like a fixed coupon bond)

Tax-Free Bonds: The coupon will be grossed up by a f

mentioned abovethese bonds are to be registered in the name of the holder claiming the tax break. Merely holding the bond with the transfer form and/or post-dated cheques/warrant will not entitle the holder, tax-free status. Preference Shares Preference shares should be valued as per Para 3.7.3 of the Rb However since dividend on Preference shares is Tax free in the hands of the investor, the valuation treabredemption value. (Ref Para 3.7.3 (f) of the RBI Master Circular for banks)

Priority Sector Bonds: Priority sector bonds issued by Financial Institutions and Public

Unrated Government guaranteed Non-SLR bonds They are those bonds that are issued outside the approved mpa. Spreads over the sovereign risk free yield curapplicable. b. The spread shall be marked up by 15%




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c. SGL data, available from January 1, 1996 at RBI website (www.rbi.org.in), should be used for arriving at the credit spreads at the time of issue. In case of

9. d

orporate Bond spread relative to the Weighted Average Maturity of the paper.

10.

Such instruments will be valued as per Net Asset Value (NAV) given by the issuing

11.

at yield to worst basis where the final maturity of the bonds will be taken to be the longest point on the Base

ead would be that which is available for the longest

12.

Deposits of tenor less than one year should be valued at carrying cost.

13. To be valued as per RBI Circular BP.BC.27/21.01/002/2006-07 dated 23rd August

2006.

A publishes the following benchmarks on a daily basis. i. FIMMDA-NSE MIBID / MIBOR

MIFOR

i

cial Paper y Bill

W re for swap transactions, the same will be used for v in

b.

e of entering into the swap transaction.

debenture/ bond issued prior to January 1, 1996 the bonds will be valued at cost. Valuation of Securitised Paper All Securitized papers would be valued on the basis of the Base Yield Curve anC

Valuation of Security Receipts / Pass through Certificates issued by Reconstruction Company / Securitisation Company

Reconstruction Company / Securitisation Company.

Valuation of Perpetual Bonds Perpetual Bonds issued by Banks should be valued

Yield Curve. The applicable sprtenor for the corresponding rating.

Valuation of Commercial Paper / Certificate of Deposits Commercial Papers/Certificate of

Valuation of Venture Capital Funds

VALUATION OF SWAPS a. FIMMD

ii. FIMMDA-Reutersiii. FIMMDA-Reuters MITOR v. FIMMDA-Reuters MIOIS v. FIMMDA-Reuters MIOCS

vi. FIMMDA-Reuters Commervii. FIMMDA-Reuters Treasur

he these benchmarks are usedalu g the swap.

In respect of the others, the same should be valued at the same benchmarks that were used at the tim

fimmda valuation methodology for slr and non-slr

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