APPENDIX
METHODOLOGY FOR CALCULATING CURRENCY EXPOSURES IN BOND PORTFOLIOS AND INDEXES
Portfolio Manager
Fidelity Investments
In an unhedged global bond portfolio, currency exposures are responsible for most of the return volatility. As a result, it is worth taking the time to calculate currency exposures accurately. This Appendix provides a methodology for calculating the currency exposures in a bond portfolio as of the close of the most recent portfolio pricing date. This methodology can also be used to calculate the currency exposures in Citigroup indexes and Barclays Capital indices.
It is assumed that each currency exposure will be calculated as part of an automated overnight batch process. When calculating currency exposures, there are a number of approaches that can be used. As a result, it may be helpful to define a few guiding principles at the outset:
1. If a portfolio is structured so that it exactly replicates its index, then the portfolio and the index should have the same currency exposures. In other words, each currency exposure that one calculates for the portfolio should exactly match the corresponding currency exposure that one calculates for the index.
2. If a security is held by both the portfolio and the index, then one should use the same price for the portfolio and the index.
3. For each actual price in the bond market, there is an associated settlement date. The price and the settlement date go together; they are joined at the hip. When calculating accrued interest or analytics, one should use the settlement date that goes with the price.
4. For the portfolio, identify the most reliable source for the net assets as of the close of the most recent portfolio pricing date. Use these net assets when calculating currency exposures.
5. Intra-month, for the index, use the cash positions from the index provider. Do not calculate these cash positions for the index. (Doing so is difficult for government/credit indices, and almost impossible for aggregate bond indices.)
These five guiding principles seem reasonable enough. However, except for very simple portfolios and indexes, it is impossible to adhere to all five of them at once. As a result, when calculating currency exposures, one needs to make a few tradeoffs and arbitrary decisions, and there will likely be a few inconsistencies in the end result. The methodology described in this Appendix was designed to adhere as closely as possible to these five guiding principles, minimize operational risk, and produce extremely accurate results.
A brief word on scope: In order to provide a fully defined methodology in a reasonable number of pages, it is assumed that the portfolios:
1. Invest only in the types of securities that are constituents of investment-grade global bond indexes, such as the Citigroup World Government Bond Index (WGBI) and the Barclays Capital Global Aggregate Bond Index.
2. Execute standard FX trades.
3. Maintain cash balances in foreign currencies.
Thus, derivatives, TBAs, and many other instruments are out of scope. In addition, FX forward outrights with more than one year from the most recent portfolio pricing date to the value date are out of scope. Finally, no adjustments for “bad days” are made in the discussion below. A bad day occurs when a security is scheduled to make a principal or interest payment on a weekend or holiday.
MAIN FORMULA FOR BOND PORTFOLIOS
The following formula can be used to calculate a bond portfolio’s exposure to a single currency:
Currency Exposure (A) =
Market Value of Securities (B)
+ Cash Balance (C)
+ Unsettled Sells of Securities (D)
– Unsettled Buys of Securities (E)
+ Unsettled Buys of Currency (F)
– Unsettled Sells of Currency (G)
+ Coupon Payments for Gilt Holdings (H)
+ Coupon Payments for Unsettled Sells of Gilts (I)
– Coupon Payments for Unsettled Buys of Gilts (J)
+ Coupon Payments for Unsettled Sells of Non-Gilts (K)
– Coupon Payments for Unsettled Buys of Non-Gilts (L)
+ Interest Payments for Agency MBS Holdings (M)
+ Principal Payments for Agency MBS Holdings (N)
+ Interest Payments for Unsettled Sells of Agency MBS (O)
+ Principal Payments for Unsettled Sells of Agency MBS (P)
– Interest Payments for Unsettled Buys of Agency MBS (Q)
– Principal Payments for Unsettled Buys of Agency MBS (R)
Currency Exposure (A) is the portfolio’s exposure to a single currency as of the close of the most recent portfolio pricing date. This currency exposure is expressed in the local currency. It has not been converted to the base currency of the portfolio. This main formula for bond portfolios can also be used to calculate a portfolio’s exposure to the base currency of the portfolio.
There are 17 inputs that are needed in order to calculate this currency exposure. All of the 17 inputs should be expressed in the local currency. In other words, they should not be converted into the base currency of the portfolio.
For the Unsettled Buys of Currency (F) and the Unsettled Sells of Currency (G), one needs to calculate their present values before using them as inputs to the main formula for bond portfolios.
The inputs are defined below and other definitions are provided in Exhibit A–1.
EXHIBIT A–1
Defined Terms for Bond Portfolios
Accrued Interest: For non-factoring securities:
Accrued Interest = Par Amount × (Accrued Interest Factor/100)
For factoring securities:
Accrued Interest = Current Face × (Accrued Interest Factor/100)
Accrued Interest Factor: The accrued interest factor is used to calculate the accrued interest and the market value for each of the securities held by the portfolio.
• For a U.S. Treasury bond, the accrued interest factor for a specific settlement date is the accrued interest for a hypothetical trade that was executed with a par amount of USD 100.00.
• For a gilt, the accrued interest factor for a specific settlement date is the accrued interest for a hypothetical trade that was executed with a par amount of GBP 100.00.
For each of the securities held by the portfolio, use the following hierarchy in order to determine the accrued interest factor:
• In-house quantitative models
• Bloomberg
Adjusted Net Assets: Two minor adjustments to net assets should be made:
Adjusted Net Assets = Net Assets + Shareholder Activity + Dividend Payable
Analytics: Metrics such as yield to worst, modified duration, option adjusted spread, option adjusted duration, option adjusted convexity, and key rate durations are all examples of analytics.
Base Currency of the Portfolio: For a mutual fund, this is the currency in which the net asset value is denominated.
Bond Trades: Bond trades are trades involving the types of instruments that are included in the securities held by the portfolio when calculating Market Value of Securities (B) for a portfolio. (See the definition of “Securities Held by the Portfolio.”)
Books and Records: The official record of the portfolio’s holdings and net assets. For most mutual funds, the same entity that is responsible for maintaining the books and records is also responsible for calculating the fund’s net asset value on each day that the fund is open.
Compounding Frequency: All analytics (including yield to worst) should be calculated assuming semiannual compounding.
Cross-Currency FX Trades: An FX trade where the base currency of the portfolio is not one of the currencies in the currency pair.
Currency Exposure: This is a portfolio’s exposure to a single currency. The currency exposure, by definition, is always calculated and expressed in the local currency. (Later on in the overnight batch process, the currency exposure can be converted to the base currency of the portfolio and called something else.)
Dividend Payable: For those mutual funds that declare daily dividends and pay them monthly, this is the month-to-date sum of these daily dividends.
Exchange Rates—Closing Spot Rates: The following hierarchy should be used in order to determine the closing spot rates for the portfolio:
• Books and records
• Index provider (for the index that is used as the benchmark for this portfolio)
• WM/Reuters
• Bloomberg
Exchange Rates—Closing Forward Rates: The following hierarchy should be used in order to determine the closing forward rates for the portfolio:
• Books and records
• Index provider (for the index that is used as the benchmark for this portfolio)
• WM/Reuters
• Bloomberg
Ex-Coupon Date: Gilts go ex-coupon (or ex-dividend) seven business days before each coupon payment date. This means that if the settlement date of a trade involving a gilt falls after the seventh business day before a coupon payment date, the seller will receive the entire coupon payment. As a result, if the settlement date of a trade involving a gilt falls after the seventh business day before a coupon payment date and falls before this coupon payment date, then the trade will settle with a negative accrued interest. This negative accrued interest will be subtracted from the bond’s clean price. (The one exception is the 3.5% War Loan, which is a perpetual and goes ex-coupon 10 business days before its coupon payment dates on June 1 and December 1. This gilt is not in the WGBI.)
Factoring Securities: These securities include:
• Asset-backed securities (ABS)
• U.S. agency mortgage-backed passthrough securities
• Commercial mortgage-backed securities (CMBS)
• Enhanced equipment trust certificates (EETC)
Foreign Currencies: Any currency that is not the base currency of the portfolio.
Index Pricing Date: The date on which the index was priced by the index provider. The index pricing date should be the same as the most recent portfolio pricing date.
Local Currency: The currency in which a security or a cash balance is denominated.
Market Value: Throughout this Appendix, this value is always assumed to include accrued interest. In order to calculate the market value for each of the securities held by the portfolio, use the following formulas:
Market Value = Principal + Accrued Interest
Principal = Par Amount × (Price/100)
Accrued Interest = Par Amount × (Accrued Interest Factor/100)
Most Recent Portfolio Pricing Date: For a mutual fund, this is the most recent day on which a net asset value was calculated.
Net Assets: The market value of the portfolio as of the close on the most recent portfolio pricing date. In other words, if the entire portfolio were liquidated, this is the amount of money that would be returned to the shareholders and clients. For a mutual fund,
Net Assets = Number of Shares Outstanding × Net Asset Value per Share
Non-Factoring Securities: These securities include the following types of bonds:
• Treasury
• Government-related
• Corporate
Par Amount: For non-factoring securities, use the par amount from the books and records for the portfolio. For factoring securities, use the current face from the books and records for the portfolio.
Present Value: Calculated for each unsettled FX trade where there are more than four business days between the most recent portfolio pricing date and the value date for the unsettled FX trade. For each unsettled FX trade, take both currencies in the currency pair into account and calculate the present value of the currency amount for each one separately. In order to calculate the present value of the currency amount, use the following formula:
PV = C/(1 + R/100 × N/B)
PV = Present value of the currency amount
C = Currency amount on the value date
R = Interest rate expressed as a percentage per annum
N = Actual number of days from the most recent portfolio pricing date to the value date
B = Day count basis (usually either 360 or 365, depending on the currency)
• Using four business days as the cutoff is admittedly arbitrary. For most trades involving securities, regular settlement is T + 4 business days or shorter. As a result, using four business days as the cutoff will allow one to avoid calculating present values for unsettled FX trades that were executed to fund the settlement of these securities trades. This in turn will simplify things and reduce operational risk, while having a de minimus impact on the calculated currency exposures.
• For most currencies, for the interest rate, one should use the Eurodeposit rate for funds deposited in that currency. These Eurodeposit rates are provided by Citigroup. In addition, these Eurodeposit rates can be obtained from market data services such as Bloomberg and Reuters. See Citigroup Global Fixed-Income Index Catalog, 2011 Edition (February 8, 2011); the Reuters Instrument Codes (RICs) used to obtain monthly yields (bid) for Eurodeposits are provided for 18 currencies on page 61.
Price: Price is expressed as a percentage of the par amount (or current face). For each of the securities held by the portfolio, use the following hierarchy in order to determine the price:
• Books and records
• Index provider (for the index that is used as the benchmark for this portfolio)
• Bloomberg
For each of the securities held by the portfolio, the same price that is used to calculate the principal and the market value should also be used to calculate all of the analytics.
Principal: For non-factoring securities:
Principal = Par Amount × (Price/100)
For factoring securities:
Principal = Current Face × (Price/100)
Securities Held by the Portfolio: These are all of the portfolio positions that should be included when calculating the Market Value of Securities (B) for all of the currency exposures in the portfolio. These portfolio positions should be based on the trade date holdings (not the “settlement date holdings”) as of the close on the most recent portfolio pricing date. These portfolio positions should include:
• Factoring securities
• Non-factoring securities
These portfolio positions should exclude the following:
• Items “C” through “R” in the main formula for bond portfolios
Settlement Date: For each of the securities held by the portfolio, calculate two accrued interest factors:
• Calculate the first accrued interest factor using the most recent portfolio pricing date as the settlement date. Use this accrued interest factor (and the resulting market value including accrued interest) when calculating Market Value of Securities (B).
• Calculate the second accrued interest factor, and all analytics, using the settlement date convention of the index for this portfolio. Use this accrued interest factor (and the resulting market value including accrued interest) when calculating metrics such as the average duration of the portfolio.
Settlement Date Holdings: If a portfolio buys a security on trade date “T” for settlement in T + 3 business days, then this position is not included among the settlement date holdings for this portfolio as of the close on portfolio pricing date “T.” This position is not included among the settlement date holdings for this portfolio until the close on the portfolio pricing date that corresponds to T + 3 business days.
Standard FX Trades: These include the following trades:
1. Spot FX Trade: Trade where the value date is zero to two business days after the trade date and the base currency of the portfolio (for example, USD) is one of the two currencies in the currency pair.
2. Cross-Currency Spot FX Trade: Trade where the value date is zero to two business days after the trade date and the base currency of the portfolio (for example, USD) is not one of the two currencies in the currency pair.
3. FX Forward Outright: Trade where the value date is more than two business days after the trade date and the base currency of the portfolio (for example, USD) is one of the two currencies in the currency pair.
4. Cross-Currency FX Forward Outright: Trade where the value date is more than two business days after the trade date and the base currency of the portfolio (for example, USD) is not one of the two currencies in the currency pair.
5. FX Swap: Trade where a trader negotiates and simultaneously executes a spot FX trade and an FX forward outright with the same dealer and the base currency of the portfolio (for example, USD) is one of the two currencies in the currency pair. (This swap never involves more than two currencies. The non–base currency in the short leg is always the same as the non-base currency in the long leg.)
6. Cross-Currency FX Swap: Trade where a trader negotiates and simultaneously executes a spot FX trade and an FX forward outright with the same dealer and the base currency of the portfolio (for example, USD) is not one of the two currencies in the currency pair. (This swap never involves more than two currencies. The currency pair in the short leg is always the same as the currency pair in the long leg. Whichever currency is bought in the short leg is always sold in the long leg. Similarly, whichever currency is sold in the short leg is always bought in the long leg.)
As of March 31, 2011, there were 14 currencies in the WGBI. Spot settlement for the Canadian dollar (CAD) is T + 1 business day. Spot settlement for the remaining 13 currencies is T + 2 business days.
Trade Date Holdings: If a portfolio buys a security on Trade Date “T” for settlement in T + 3 business days, then this position is included among the trade date holdings for this portfolio as of the close on portfolio pricing date “T.”
Unsettled Bond Trades: These trades include all unsettled trades involving the types of instruments that are included in the securities held by the portfolio when calculating Market Value of Securities (B) for a portfolio.
Unsettled FX Trades: These trades include all of the unsettled standard FX trades.
Unsettled Trades: These trades include:
• Unsettled bond trades
• Unsettled FX trades
Inputs to the Main Formula for Bond Portfolios
Market Value of Securities (B)
In order to calculate this input, first calculate the market value (including accrued interest) for each of the securities held by the portfolio that is denominated in the single currency for which one is calculating the Currency Exposure (A). Then sum the resulting market values. The sum is the Market Value of Securities (B).
Cash Balance (C)
This is the cash balance in the single currency for which one is calculating the Currency Exposure (A). If the cash balance is not denominated in the base currency of the portfolio, then use the following formula:
Cash Balance = Contractual End of Day Cash Balance on the Most Recent Portfolio Pricing Date
This cash balance should include all of the principal and interest payments that were scheduled to be received by the portfolio on or before the portfolio pricing date (whether or not they were actually received by the portfolio’s custodial bank and credited to the portfolio). As a general rule, when the accrued interest included in the Market Value of Securities (B) drops to reflect a coupon payment (and the duration extends), then that coupon payment should be included in the Cash Balance (C) at the same point in time. (One exception is bonds that go ex-coupon.)
This cash balance should also reflect all of the bond trades and FX trades that were scheduled to settle on or before the portfolio pricing date (whether or not the bond trades and FX trades actually settled).
If the cash balance is denominated in the base currency of the portfolio, then use the following formula:
Cash Balance in the Base Currency = Adjusted Net Assets
– (first calculate the Currency Exposure (A) for each
non-base currency, then convert the resulting local
currency amount to the base currency of the portfolio,
and then sum the resulting base-currency amounts) – (Market Value
of Securities (B) for the base currency of the portfolio)
– (the sum of “D” through “R” for the base currency of the portfolio)
Thus, the cash balance in the base currency is a “plug” that can be calculated only after all of the other inputs have been calculated. This plug is useful for a number of reasons. For example, it causes the Currency Exposures (A), when converted to the base currency of the portfolio and then summed, to equal the net assets of the portfolio. In addition, the portfolio’s exposure to each currency expressed as a percentage of net assets (i.e., as a percentage of the portfolio’s overall market value) can be calculated. Summing the percentage of the market value for all of the currencies, they will sum to 100%. As a result, the currency exposures have the “portfolio property.” (Contribution to duration is another example of a risk measure that has the portfolio property: Summing the contribution to duration made by each holding in a portfolio, the sum equals the average option adjusted duration for the overall portfolio.)
Unsettled Sells of Securities (D)
Identify all of the unsettled sells of securities that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then sum the total proceeds for all of these trades. The resulting sum will be the Unsettled Sells of Securities (D). These unsettled sells of securities should include all bond trades (as opposed to FX trades) where the scheduled settlement date is after the portfolio pricing date. (If a trade was supposed to settle on or before the portfolio pricing date, but it “failed” to settle, then do not include that trade when summing the total proceeds.)
Unsettled Buys of Securities (E)
Identify all of the unsettled buys of securities that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then sum the total proceeds for all of these trades. The resulting sum will be the Unsettled Buys of Securities (E). These unsettled buys of securities should include all bond trades (as opposed to FX trades) where the scheduled settlement date is after the portfolio pricing date. (If a trade was supposed to settle on or before the portfolio pricing date, but it “failed” to settle, then do not include that trade when summing the total proceeds.)
Unsettled Buys of Currency (F)
Identify all of the unsettled buys of currency that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then calculate the present value of the currency amount on the value date for each FX trade. Then sum the present values for all of these trades. The resulting sum will be the Unsettled Buys of Currency (F). These unsettled buys of currency should include all of the FX trades (including spot FX trades, FX forward outrights, and FX swaps) where the scheduled value date is after the portfolio pricing date. (If a trade was supposed to settle on or before the portfolio pricing date, but it “failed” to settle, then do not include that trade when summing the present values.)
When calculating the present value, use the currency amount on the value date for each FX trade, which is the currency amount that the portfolio will receive from the counterparty when the FX trade settles. In order to calculate the present value of the currency amount on the value date, see the definition for present value in Exhibit A–1.
Unsettled Sells of Currency (G)
Identify all of the unsettled sells of currency that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then calculate the present value of the currency amount on the value date for each FX trade. Then sum the present values for all of these trades. The resulting sum will be the Unsettled Sells of Currency (G). These unsettled sells of currency should include all of the FX trades (including spot FX trades, FX forward outrights, and FX swaps) where the scheduled value date is after the portfolio pricing date. (If a trade was supposed to settle on or before the portfolio pricing date, but it “failed” to settle, then do not include that trade when summing the present values.)
When calculating the present value, use the currency amount on the value date for each FX trade, which is the currency amount that the portfolio will pay to the counterparty when the FX trade settles. In order to calculate the present value of the currency amount on the value date, see the definition for present value in Exhibit A–1.
Coupon Payments for Gilt Holdings (H)
Review the securities held by the portfolio and identify all of the interest-bearing gilt positions (and positions in other securities that go ex-coupon and thus can settle with a negative accrued interest). Then, among these positions, identify the positions that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then, among these positions, identify the positions where the most recent portfolio pricing date falls after the ex-coupon date and before that coupon payment date. Calculate the payment amount (in the local currency) for each of these coupon payments. Sum these coupon payment amounts. The resulting sum will be the Coupon Payments for Gilt Holdings (H). (The sovereign debt securities of the United Kingdom are called “gilts.” In this Appendix the term “gilts” is a short-hand way of referring to all securities that go ex-coupon and trade with a negative accrued interest.)
Coupon Payments for Unsettled Sells of Gilts (I)
Review the unsettled bond trades and identify all of the sells of interest-bearing gilts (and sells of other securities that go ex-coupon and thus can settle with a negative accrued interest). Then, among these sells, identify the sells that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then, among these sells, identify the sells where the most recent portfolio pricing date falls before a coupon payment date and the sell has a settlement date that falls after the excoupon date for that coupon payment date. Calculate the payment amount (in the local currency) for each of these coupon payments. Sum these coupon payment amounts. The resulting sum will be the Coupon Payments for Unsettled Sells of Gilts (I).
Coupon Payments for Unsettled Buys of Gilts (J)
Review the unsettled bond trades and identify all of the buys of interest-bearing gilts (and buys of other securities that go ex-coupon and thus can settle with a negative accrued interest). Then, among these buys, identify the buys that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then, among these buys, identify the buys where the most recent portfolio pricing date falls before a coupon payment date and the buy has a settlement date that falls after the ex-coupon date for that coupon payment date. Calculate the payment amount (in the local currency) for each of these coupon payments. Sum these coupon payment amounts. The resulting sum will be the Coupon Payments for Unsettled Buys of Gilts (J).
Coupon Payments for Unsettled Sells of Non-Gilts (K)
Review the unsettled bond trades and identify all of the sells of interest-bearing securities that are not gilts (and that are not other securities that go ex-coupon and thus can settle with a negative accrued interest) and that are not Agency MBS (and that are not other securities that make delayed principal or interest payments). Then, among these sells, identify the sells that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then, among these sells, identify the sells where the most recent portfolio pricing date falls before a coupon payment date and the sell has a settlement date that falls on or after that coupon payment date. Calculate the payment amount (in the local currency) for each of these coupon payments (and the accompanying principal payment, if there is one). Sum these payment amounts. The resulting sum will be the Coupon Payments for Unsettled Sells of Non-Gilts (K).
Coupon Payments for Unsettled Buys of Non-Gilts (L)
Review the unsettled bond trades and identify all of the buys of interest-bearing securities that are not gilts (and that are not other securities that go ex-coupon and thus can settle with a negative accrued interest) and that are not Agency MBS (and that are not other securities that make delayed principal or interest payments). Then, among these buys, identify the buys that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then, among these buys, identify the buys where the most recent portfolio pricing date falls before a coupon payment date and the buy has a settlement date that falls on or after that coupon payment date. Calculate the payment amount (in the local currency) for each of these coupon payments (and the accompanying principal payment, if there is one). Sum these payment amounts. The resulting sum will be the Coupon Payments for Unsettled Buys of Non-Gilts (L).
Interest Payments for Agency MBS Holdings (M)
Review the securities held by the portfolio and identify all of the U.S. agency mortgage-backed passthrough securities (“Agency MBS”). These are pools issued by Ginnie Mae, Fannie Mae, and Freddie Mac. Then, among these positions, identify the positions that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then, among these positions, identify the positions where the most recent portfolio pricing date falls after an ex-coupon date (which is the last calendar day of a month) and before the corresponding interest payment date. Calculate the payment amount (in the local currency) for each of these interest payments. Sum these interest payment amounts. The resulting sum will be the Interest Payments for Agency MBS Holdings (M). (Use a similar approach for other securities that make delayed interest payments.)
Principal Payments for Agency MBS Holdings (N)
Review the securities held by the portfolio and identify all of the Agency MBS. Then, among these positions, identify the positions that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then, among these positions, identify the positions where the most recent portfolio pricing date falls on or after the day on which factors and paydowns are processed for the portfolio and before the corresponding principal payment date. Calculate the payment amount (in the local currency) for each of these principal payments. Sum these principal payment amounts. The resulting sum will be the Principal Payments for Agency MBS Holdings (N). (Use a similar approach for other securities that make delayed principal payments.)
Interest Payments for Unsettled Sells of Agency MBS (O)
Review the unsettled bond trades and identify all of the sells of Agency MBS. Then, among these sells, identify the sells that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then, among these sells, identify the sells where the most recent portfolio pricing date falls before an interest payment date and the sell has a settlement date that falls after the ex- coupon date for that interest payment date. Calculate the payment amount (in the local currency) for each of these interest payments. Sum these interest payment amounts. The resulting sum will be the Interest Payments for Unsettled Sells of Agency MBS (O). (Use a similar approach for other securities that make delayed interest payments.)
Principal Payments for Unsettled Sells of Agency MBS (P)
Review the unsettled bond trades and identify all of the sells of Agency MBS. Then, among these sells, identify the sells that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then, among these sells, identify the sells where the most recent portfolio pricing date falls on or after the day on which factors and paydowns are processed for the portfolio and before the corresponding principal payment date. Calculate the payment amount (in the local currency) for each of these principal payments. Sum these principal payment amounts. The resulting sum will be the Principal Payments for Unsettled Sells of Agency MBS (P). (Use a similar approach for other securities that make delayed principal payments.)
Interest Payments for Unsettled Buys of Agency MBS (Q)
Review the unsettled bond trades and identify all of the buys of Agency MBS. Then, among these buys, identify the buys that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then, among these buys, identify the buys where the most recent portfolio pricing date falls before an interest payment date and the buy has a settlement date that falls after the ex-coupon date for that interest payment date. Calculate the payment amount (in the local currency) for each of these interest payments. Sum these interest payment amounts. The resulting sum will be the Interest Payments for Unsettled Buys of Agency MBS (Q). (Use a similar approach for other securities that make delayed interest payments.)
Principal Payments for Unsettled Buys of Agency MBS (R)
Review the unsettled bond trades and identify all of the buys of Agency MBS. Then, among these buys, identify the buys that are denominated in the single currency for which one is calculating the Currency Exposure (A). Then, among these buys, identify the buys where the most recent portfolio pricing date falls on or after the day on which factors and paydowns are processed for the portfolio and before the corresponding principal payment date. Calculate the payment amount (in the local currency) for each of these principal payments. Sum these principal payment amounts. The resulting sum will be the Principal Payments for Unsettled Buys of Agency MBS (R). (Use a similar approach for other securities that make delayed principal payments.)
MAIN FORMULA FOR CITIGROUP INDEXES
The following formula can be used to calculate the exposure to a single currency in a Citigroup multi-currency bond index:
Currency Exposure (A) =
Market Value of Securities (B)
+ Cash Balance (C)
– FX Forward Outright Sell (D)
+ FX Forward Outright Buy (E)
Currency Exposure (A)
This is the exposure that a Citigroup index has to a single currency as of the close on the index pricing date. This currency exposure is expressed in the local currency. It has not been converted to the base currency of the index. This main formula for Citigroup indexes can also be used to calculate the exposure to the base currency of the index.
There are four inputs that are needed in order to calculate this currency exposure. All of the four inputs should be expressed in the local currency. In other words, they should not be converted into the base currency of the index.
For the last two of these four inputs, one needs to calculate their present values before using them as inputs to the main formula for Citigroup indexes.
Inputs to the Main Formula for Citigroup Indexes
Market Value of Securities (B)
In general, one should use the same approach for indexes that one uses for portfolios. However, a few things will be different. For example, the securities in the index will be the securities that are in the current returns universe for the index. This data set should come directly from Citigroup. It should be updated each evening, in order to capture intra-month principal and interest payments that have been made by index constituents. Principal and interest payments will increase the cash balances in the current returns universe. Principal payments will lower the par amounts (or current faces) of the securities in the current returns universe.
In order to calculate this input, first calculate the market value (including accrued interest) for each of the securities in the index that is denominated in the single currency for which one is calculating the Currency Exposure (A). Then sum the resulting market values. The sum is the Market Value of Securities (B).
Cash Balance (C)
Citigroup will provide the cash balances for each currency. The Cash Balance (C) will be the cash balance in the single currency for which one is calculating the Currency Exposure (A); it will be the sum of the principal and interest payments received by the index on or after the first calendar day of the month and on or before the index settlement date used by Citigroup.
These cash balances should come directly from Citigroup. They should be updated each evening, in order to capture intra-month principal and interest payments that have been made by index constituents. Principal and interest payments will increase the cash balances in the current returns universe. Principal payments will lower the par amounts (or current faces) of the securities in the current returns universe. Note that as of the close on the last business day of a month, there is no cash in the returns universe for the coming month.
FX Forward Outright Sell (D)
Unhedged indexes do not contain any FX forward outright sells. As a result, for an unhedged index, set FX Forward Outright Sell (D) equal to zero, and move on.
The returns universe for a hedged version of a Citigroup index contains one FX forward outright sell for each foreign currency in the index. For each of these FX forward outright sells, Citigroup calculates the currency amount on the value date. Citigroup does this once a month at the beginning of the month, and provides this information to their clients via automated downloads. Citigroup has published two documents that together do a nice job of describing the hedging methodology used for the hedged versions of the Citigroup indexes; the first one is entitled SSB Fixed Income Indices: Currency Hedging Methodology (March 6, 2003) and the second one is entitled Change in Spot Settlement Convention in the Currency Hedging Methodology (January 6, 2011). Using the currency amount on the value date that Citigroup provides, one needs to calculate the present value of the currency amount. In order to do this, see the definition for present value in Exhibit A–2.
EXHIBIT A–2
Defined Terms for Citigroup Indexes
Accrued Interest: Always use the accrued interest provided by Citigroup.
Compounding Frequency: All analytics (including yield to worst) should be calculated assuming semiannual compounding. As of December 31, 2010, 75.3% of the securities in the WGBI (based on market value) paid coupons semiannually.
Exchange Rates—Closing Spot Rates: Use the following hierarchy in order to determine the closing spot rates for the Citigroup indexes:
• Books and records
• Citigroup
• WM/Reuters
• Bloomberg
Exchange Rates—Closing Forward Rates: Use the following hierarchy in order to determine the closing forward rates for the Citigroup indexes:
• Citigroup
• WM/Reuters
• Bloomberg
Ex-Coupon: When a security in a Citigroup index goes ex-coupon and starts trading with a negative accrued interest, Citigroup adds the coupon payment to the Cash Balance (C). However, there is no reinvestment return until the coupon payment is actually made on the coupon payment date. There were 23 countries in the WGBI as of March 1, 2011. Of these, the sovereign debt securities of the following six countries go ex-coupon and then trade with a negative accrued interest:
1. Australia
2. Norway
3. Poland
4. Singapore
5. Sweden
6. United Kingdom
When these securities go ex-coupon, Bloomberg displays a negative accrued interest on BXT. There is one exception: when Poland’s sovereign debt securities go ex-coupon, Bloomberg displays a zero accrued interest on BXT. However, Bloomberg takes the ex-coupon date into account when calculating price given yield.
Index Pricing Date: In general, one should always use the most recent index pricing date, because the most recent index pricing date will usually be the same date as the most recent portfolio pricing date. However, if the most recent index pricing date is a different date than the most recent portfolio pricing date, then there are two possibilities:
1. The most recent index pricing date is more recent than the most recent portfolio pricing date. In this case, if there is a previous index pricing date that falls on the same date as the most recent portfolio pricing date, then use that previous index pricing date. If not, then use the most recent index pricing date and remove books and records from the hierarchies used to determine the prices and exchange rates for the index.
2. The most recent index pricing date is older than the most recent portfolio pricing date. In this case, use the most recent index pricing date and remove books and records from the hierarchies used to determine the prices and exchange rates for the index.
Index Settlement Date: Use the following index settlement dates for the Citigroup indexes:
For all of the securities in the index, the index settlement date is T + 0 (except for the last business day of the month, when the index settlement date is the last calendar day of that month).
Note that T + 0 is always the index pricing date.
For each of the securities in a Citigroup index, use the index settlement date to calculate all of the analytics.
Market Value: In order to calculate the market value for each of the securities in the index, use the following formulas:
Market Value = Principal + Accrued Interest
Principal = Par Amount × (Price/100)
Par Amount: For non-factoring securities, always use the par amount provided by Citigroup. For factoring securities, always use the current face provided by Citigroup.
Present Value: Calculate the present value for each unsettled FX trade where there are more than four business days between the index pricing date and the value date for the unsettled FX trade. For each unsettled FX trade, take both currencies in the currency pair into account and calculate the present value of the currency amount for each one separately. In order to calculate the present value of the currency amount, use the following formula:
PV = C/(1* R/100 × N/B)
PV = Present value of the currency amount
C = Currency amount on the value date
R = Interest rate expressed as a percentage per annum
N = Actual number of days from the index pricing date to the value date
B = Day count basis (usually either 360 or 365, depending on the currency)
For most currencies, for the interest rate, one should use the Eurodeposit rate for funds deposited in that currency. These Eurodeposit rates are provided by Citigroup. In addition, these Eurodeposit rates can be obtained from market data services such as Bloomberg and Reuters. See Citigroup Global Fixed-Income Index Catalog, 2011 Edition (February 8, 2011); the Reuters Instrument Codes (RICs) used to obtain monthly yields (bid) for Eurodeposits are provided for 18 currencies on page 61.
Price: For each of the securities in the index (except U.S. agency mortgage-backed passthrough securities), use the following hierarchy in order to determine the price:
• Books and records
• Citigroup
• Bloomberg
For each of the securities in the index, the same price that is used to calculate the principal and market value should also be used to calculate all of the analytics. For the U.S. agency mortgage-backed passthrough securities in the index, use the price provided by Citigroup.
Securities in the Index: These are the securities that are in the current returns universe for the index. This data set should come directly from Citigroup. It should be updated each evening, in order to capture intra-month principal and interest payments that have been made by index constituents. Principal and interest payments will increase the cash balances in the current returns universe. Principal payments will lower the par amounts (or current faces) of the securities in the current returns universe.
FX Forward Outright Buy (E)
Unhedged indexes do not contain any FX forward outright buys. As a result, for an unhedged index, set FX Forward Outright Buy (E) equal to zero, and move on.
The returns universe for a hedged version of a Citigroup index will contain one FX forward outright buy for the base currency of the index (for example, USD). Citigroup will provide this information. Using the currency amount on the value date that Citigroup provides, one needs to calculate the present value of the currency amount. In order to do this, see the definition for present value in Exhibit A–2.
MAIN FORMULA FOR BARCLAYS CAPITAL INDICES
The following formula can be used to calculate the exposure to a single currency in a Barclays Capital multi-currency bond index:
Currency Exposure (A) =
Market Value of Securities (B)
+ Cash Balance (C)
– FX Forward Outright Sell (D)
+ FX Forward Outright Buy (E)
Currency Exposure (A)
This is the exposure that a Barclays Capital index has to a single currency as of the close on the index pricing date. This currency exposure is expressed in the local currency. It has not been converted to the base currency of the index. This main formula for Barclays Capital indices can also be used to calculate the exposure to the base currency of the index.
There are four inputs that are needed in order to calculate this currency exposure. All of the four inputs should be expressed in the local currency. In other words, they should not be converted into the base currency of the index.
For the last two of these four inputs, one needs to calculate their present values before using them as inputs to the main formula for Barclays Capital indices.
Inputs to the Main Formula for Barclays Capital Indices
Market Value of Securities (B)
In general, one should use the same approach for indices that one uses for portfolios. However, a few things will be different. For example, the securities in the index will be the securities that are in the current returns universe for the index. This data set should come directly from Barclays Capital. It should be updated each evening, in order to capture intra-month principal and interest payments that have been made by index constituents. Principal and interest payments will increase the cash balances in the current returns universe. Principal payments will lower the par amounts (or current faces) of the securities in the current returns universe.
In order to calculate this input, first calculate the market value (including accrued interest) for each of the securities in the index that is denominated in the single currency for which one is calculating the Currency Exposure (A). Then sum the resulting market values. The sum is the Market Value of Securities (B).
Cash Balance (C)
Barclays Capital will provide the cash balances for each currency. The Cash Balance (C) will be the cash balance in the single currency for which one is calculating the Currency Exposure (A); it will be the sum of the principal and interest payments received by the index on or after the second calendar day of the month and on or before the index settlement date used by Barclays Capital. There is one exception: estimated principal and interest payments generated by U.S. agency mortgage-backed passthrough securities are added to the USD cash balance at the close on the first calendar day of the month.
These cash balances should come directly from Barclays Capital. They should be updated each evening in order to capture intra-month principal and interest payments that have been made by index constituents. Principal and interest payments will increase the cash balances in the current returns universe. Principal payments will lower the par amounts (or current faces) of the securities in the current returns universe. Note that as of the close on the last business day of a month, there is no cash in the statistics universe (which is the returns universe for the coming month).
FX Forward Outright Sell (D)
Unhedged indices do not contain any FX forward outright sells. As a result, for an unhedged index, set FX Forward Outright Sell (D) equal to zero, and move on.
Hedged indices contain one FX forward outright sell for each foreign currency in the index. Today, it is not possible to download these FX forward outright sells from Barclays Capital POINT, nor is it possible to see them on any screen, nor are they provided in any published reports. As a result, you need to calculate these amounts yourself. More specifically, you need to calculate the currency amount on the value date for each of the two currencies in each FX forward outright sell in each returns universe. You only have to do this once a month at the beginning of the month. A document entitled A Guide to the Lehman Brothers Global Family of Indices (March 2008) does a nice job of describing the hedging methodology used for the hedged versions of the Barclays Capital indices (pages 121–127). However, in order to exactly replicate the FX forward outright sells in each returns universe, one should ask the index group at Barclays Capital for specific guidance, as there are a number of nuances. Once you have calculated the currency amount on the value date for each of the two currencies in an FX forward outright sell, you need to calculate the present value of the currency amount for each of these two currencies. In order to do this, see the definition for present value in Exhibit A–3.
EXHIBIT A–3
Defined Terms for Barclays Capital Indices
Accrued Interest: Always use the accrued interest provided by Barclays Capital.
Compounding Frequency: All analytics (including yield to worst) should be calculated assuming semiannual compounding.
Exchange Rates—Closing Spot Rates: Use the following hierarchy in order to determine the closing spot rates for the Barclays Capital indices:
• Books and records
• Barclays Capital
• WM/Reuters
• Bloomberg
Exchange Rates—Closing Forward Rates: Use the following hierarchy in order to determine the closing forward rates for the Barclays Capital indices:
• Barclays Capital
• WM/Reuters
• Bloomberg
Ex-Coupon: When a security in a Barclays Capital index goes ex-coupon and starts trading with a negative accrued interest, Barclays Capital adds the coupon payment to the Cash Balance (C). The coupon payment is not reinvested until month end.
Index Pricing Date: In general, one should always use the most recent index pricing date, because the most recent index pricing date will usually be the same date as the most recent portfolio pricing date. However, if the most recent index pricing date is a different date than the most recent portfolio pricing date, then there are two possibilities:
1. The most recent index pricing date is more recent than the most recent portfolio pricing date. In this case, if there is a previous index pricing date that falls on the same date as the most recent portfolio pricing date, then use that previous index pricing date. If not, then use the most recent index pricing date and remove books and records from the hierarchies used to determine the prices and exchange rates for the index.
2. The most recent index pricing date is older than the most recent portfolio pricing date. In this case, use the most recent index pricing date and remove books and records from the hierarchies used to determine the prices and exchange rates for the index.
Index Settlement Date: Use the following index settlement dates for the Barclays Capital indices:
• For U.S. agency mortgage-backed passthrough securities, the index settlement date is T + 0 (except for the last business day of the month, when the index settlement date is the last calendar day of that month).
• For all securities other than U.S. agency mortgage-backed passthrough securities, the index settlement date is T + 1 calendar day (except for the last business day of the month, when the index settlement date is the first calendar day of the next month).
Note that T + 0 is always the index pricing date.
For each of the securities in the index, use the index settlement date to calculate all of the analytics.
Market Value: In order to calculate the market value for each of the securities in the index, use the following formulas:
Market Value = Principal + Accrued Interest
Principal = Par Amount × (Price/100)
Par Amount: For non-factoring securities, always use the par amount provided by Barclays Capital. For factoring securities, always use the current face provided by Barclays Capital.
Present Value: Calculate the present value for each unsettled FX trade where there are more than four business days between the index pricing date and the value date for the unsettled FX trade. For each unsettled FX trade, take both currencies in the currency pair into account and calculate the present value of the currency amount for each one separately. In order to calculate the present value of the currency amount, use the following formula:
PV = Present value of the currency amount
C = Currency amount on the value date
R = Interest rate expressed as a percentage per annum
N = Actual number of days from the index pricing date to the value date
B = Day count basis (usually either 360 or 365, depending on the currency)
For most currencies, for the interest rate, one should use the Eurodeposit rate for funds deposited in that currency. These Eurodeposit rates are provided by Citigroup. In addition, these Eurodeposit rates can be obtained from market data services such as Bloomberg and Reuters. See Citigroup Global Fixed-Income Index Catalog, 2011 Edition (February 8, 2011); the Reuters Instrument Codes (RICs) used to obtain monthly yields (bid) for Eurodeposits are provided for 18 currencies on page 61.
Price: For each of the securities in the index (except U.S. agency mortgage-backed passthrough securities), use the following hierarchy in order to determine the price:
• Books and records
• Barclays Capital
• Bloomberg
For each of the securities in the index, the same price that is used to calculate the principal and market value should also be used to calculate all of the analytics. For the U.S. agency mortgage-backed passthrough securities in the index, use the price provided by Barclays Capital.
Securities in the Index: These are the securities that are in the current returns universe for the index. This data set should come directly from Barclays Capital. It should be updated each evening, in order to capture intra-month principal and interest payments that have been made by index constituents. Principal and interest payments will increase the cash balances in the current returns universe. Principal payments will lower the par amounts (or current faces) of the securities in the current returns universe.
FX Forward Outright Buy (E)
Unhedged indices do not contain any FX forward outright buys. As a result, for an unhedged index, set FX Forward Outright Buy (E) equal to zero, and move on.
Hedged indices contain one FX forward outright sell for each foreign currency in the index. The second currency in each of these FX forward outright sells is the base currency of the index, which the index is always buying one month forward. In order to calculate the FX Forward Outright Buy (E), first calculate the currency amount on the value date for each of the foreign currencies in the index (see FX Forward Outright Sell (D) above). Then use one-month forward exchange rates (POINT displays these) to calculate the currency amount on the value date for the base currency of the index. Then sum these currency amounts on the value date for the base currency of the index. Finally, calculate the present value of this summed currency amount. In order to do this, see the definition for present value in Exhibit A–3.