Basic Pricing Concepts and Methodology

September 5, 2002

Discussion Topics

• Overview of Treasury Security Market

• Common Risk and Return Measures

• Characteristics of available Agency Investments

• Pricing Methodology

• Things to consider when choosing investments

Primary and Secondary Treasury Security Markets

• Treasury auctions new securities periodically to finance government deficits

• Treasury auctions its securities competitively in the “primary market”

• Once auctioned, Treasury securities are traded between investors in the “secondary market”

The Treasury Security Market• Highly-liquid primary and secondary markets

• Treasury securities are regarded as credit-risk free

• Interest-rate risk is major risk facing investors in Treasuries

• Reinvestment risk also exists

• Prices on Treasury instruments fluctuate continuously depending on the level of interest rates

• Variety of investment vehicles available to investing agencies– Overnight investments– bills – notes and bonds– inflation indexed notes and bonds– zero coupon bonds

Investment Prices and Yields• Prices and yields are inversely related

• Prices are determined by discounting the cash flow from a security to its present value using current market rate as discount

• Bid and Ask prices - narrow spreads

• Prices are quoted “flat”, w/o accrued interest, accrued interest added to settlement price

• Yield to Maturity (YTM) is standard yield measure

The Main Risk: Interest Rate Risk• As the level of interest rates change, the price of

fixed-income investments change - this is a continuous process based on economic activity

• Inverse relationship between prices and interest rates - as rates rise, prices fall and vice-versa

• Longer-maturity instruments are more price sensitive to interest rate movements

• Lower-coupon instruments are more price sensitive than Higher coupon instruments

Re-investment risk• Arises when considering investment alternatives• Must be considered if purchasing an asset that

has a maturity shorter than the liability• E.g. Investing for a liability arising in 4 years.

– Can purchase an asset with 4 years to maturity (exact maturity match - no reinvestment risk)

– Can purchase a shorter-dated maturity - e.g., a 2-yr security and reinvest in another 2-yr security when the first instrument matures (this option has some reinvestment risk)

Return Basics • Generally, three components of return on

Treasuries – coupon– price appreciation or depreciation– reinvestment of coupons (depends of reinvestment

rate)

• The sum of these three components constitute the “total return”

• TIIS have an additional return component tied to the CPI

Basic Risk-Return Rules of Thumb

• The more risk, the greater the return

• Absent credit risk, risk in fixed-income securities generally increases as the maturity of the investment increases

• Portfolio management theory prescribes that the maturity of liabilities should be matched to the maturity of assets. The greater the maturity “gap” between, assets and liabilities, the greater the risk

Categories of Market-Based Investments available to Investing Agencies

• Mirror image market-based specials– T-bills– T-notes– T-bonds– TIIS

• Additional market-based specials– O/N investments– Treasury Zeros coupon bonds

Investment Instrument Characteristics• T-Bills - short maturity - discount instruments• T-Notes and T-bonds- short to long maturity-

semi annual coupon paid• TIIS- medium to long maturity - semi annual

coupon and indexed for inflation• O/N Investments - very short maturity -

overnight• Zeros - medium to long maturity - deep

discount instruments

Treasury Bills• Issued w/ maturities of 1-, 3-, & 6-months • Identified by maturity date, e.g. “10/31/02”• Bills trade at discounts to maturity price of 100• Bills are quoted on a bank-discount rate basis BDR

= [[(100 - Price)/100] x (360/DTM)]• (Must convert to coupon equivalent (CE) to

compare to other investments• CE = [ [(100 - Price)/Price] x (365/DTM) ]• Difference between the purchase price and maturity

price represents the interest earned by bill investor

Fixed-Rate Treasury Notes and Bonds

• Issued with maturities of 2-, 5-, and 10 years.

• Notes are between 1 and 10 years; bonds are greater than 10 years. Bonds no longer issued.

• Longer dated bonds are still outstanding and available as investments ( longest maturity is 2/15/31)

• Note and bonds are Identified by coupon and maturity date, e.g. “6% of 9/30/02”

• Unlike bills, notes and bonds have a coupon associated with them and interest is paid semi-annually

• Longer-maturity notes and bonds carry significant interest rate risk

Treasury Inflation-Indexed Securities (TIIS)• TIIS are floating rate instruments designed to protect

investors from inflation.

• Principal is indexed to the CPI (nsa)

• Coupons on IIS are real-rate coupons, lower than comparable nominal rate instruments

• Indexing is based on the ratio of the current CPI divided by the CPI at issuance. (Index Ratio x Principal ) Coupon is a fixed-real coupon times indexed principal

• As inflation increases, principal increases as well as coupon

• Be aware - TIIS yields and prices quotes are based on real rates and real prices - settlement prices account for inflation and can be significantly higher

Overnight Investments

• Issued with a stated rate of interest applied to the par amount of the investment.

• Mature on business day following investment. Interest credited at maturity

• Rate determined by FRB-NY survey of O/N repurchase agreement (repo) rates.

• O/N repurchase agreements are one-day loans collateralized by Treasury securities

Zero Coupon Bonds (Zeros)• Zeros are not issued by Treasury - they are created

by market participants through STRIPs• Zeros carry no coupon - instead they are a single

payment at some future date - can be short or long maturities

• Zeros are identified by just a maturity date.• the price of a zero is the PV of the single future

payment - often quoted in market on yield basis• long zeros are extremely sensitive to interest rate

movements - carry great deal of interest-rate risk

Zero Pricing Formula

2

i + 1

2s

ri + 1

F = P

n

P = Price

F = Face value of the amount being purchased or redeemed

i = Discount rate as determined below

n = Number of full semiannual periods from the purchase dateor redemption date (as the case may be) to the maturity date

r = Number of days from the purchase date or redemption date(as the case may be) to the next semi-annual date, or zero ifthe purchase date or redemption date is on a semi-annualdate

s = Number of days in the semiannual period that ends on thesemi-annual date following the purchase date or redemptiondate (as the case may be).

Pricing Methodology• O/N Rates come from FRB-NY repo rate survey• Bills, Notes, Bonds, & IIS prices come from trading

desk at FRB-NY (survey of dealers)• Zero prices are determined by OMF - via a survey

of dealer quotes - averaged; quotes that deviate more than 1 Std Dev from average are eliminated

• Mean of the bid-ask prices are used for investments, while ask prices for investment redemptions

• Timing- Pricing occurs between 11:15 AM and 11:45 AM for O/Ns, bills, notes, bonds, and IIS and 12:00 noon for zeros.

Things to consider before investing

• Horizon: When do you need the money?

• What is the nature of the liability?

• What alternatives investment are there?

• What is the outlook for interest rates?

– Fed Policy

– Rate Forecasts (public, private, model-based)

– Inflation and Inflation Expectations

– Federal Budget Deficits and Surpluses

Sources of Investor Information• Financial Newspapers - e.g.,WSJ, Financial Times, etc.• Fixed-Income Newsletters - e.g. Wrightson, Grant’s Interest Rate Observer,

etc.

• Newswire/Analytic Services - e.g. Reuters, Bloomberg, Dow Jones Capital

Markets, etc. • Federal Reserve publications - press releases, statistical releases, economic

reports, etc. • Treasury publications - Daily Treasury Statement, Monthly Statement of

Public Debt, auction data, etc.• OMB releases - Annual Budget, Mid-Session Review• Price-yield conversion formulas along with related examples can be found in

the Uniform Offering Circular Pt 356, Appendix B at http://www.publicdebt.treas.gov/gsr/gsruocam.htm