Valuation Report of US Treasury Securities And Mark-to-Market Fixed-Income Portfolios
- Pankaj Maheshwari
- Apr 1, 2024
- 8 min read
Updated: 4 days ago
Introduction
US Treasury securities are debt instruments issued by the United States Department of the Treasury, the fiscal authority of the federal government. These instruments represent a contractual obligation by the federal government to repay borrowed funds to investors, either with interest or at a discount, over a specified maturity period.
The primary purpose of issuing Treasury securities is to finance the operations of the federal government, including covering budget deficits, supporting infrastructure development, funding defense and public services, and refinancing existing debt. When government expenditures exceed revenues (tax collections), the Treasury issues these securities to bridge the fiscal gap and maintain liquidity in the public accounts and support the smooth functioning of financial markets.
These securities are issued through regularly scheduled public auctions and come in a variety of instruments with different maturities and structures—ranging from short-term Treasury bills (T-Bills) to longer-dated notes, bonds, Treasury Inflation-Protected Securities (TIPS), and Floating Rate Notes (FRNs).
Project Objective
The objective of this project is to equip participants with a structured, hands-on experience with practical exposure to the end-to-end valuation of U.S. Treasury securities. The project focuses on the practical implementation of valuation methodologies using actual market data and replicates processes followed by valuation, risk, and portfolio management teams in financial institutions.
Participants will work through a step-by-step process:
Extract real-time and historical market data for Treasury securities and interest rates from official market data sources. Construct rate curves using the extracted data, applying interpolation techniques to derive missing rate points needed for valuation.
Perform valuation and revaluation of fixed-income securities using both:
Full Revaluation: Discounting Cashflow (DCF) method based on each instrument's projected cash flow and aggregated. Partial Revaluation: Sensitivity-based approximation using first-order (DV01) and second-order (Convexity) risk metrics.
Conduct Mark-to-Market (MTM) valuation and PnL attribution for the portfolio, assessing the difference between the issue/purchase price and revalued price.
Analyze interest rate risk exposure, measuring how changes in market risk factors (rates) impact valuation across short-term, medium-term, and long-term maturity buckets. Interpret results and derive insights into portfolio behavior under various market conditions (normal and stress).
This project simulates real-world responsibilities typically undertaken within treasury, valuation, or risk management functions, requiring the practical application of financial theories to real financial portfolios.
Fixed-Income Portfolio
Participants are expected to conduct a comprehensive pricing and revaluation of a U.S. Treasury fixed-income portfolio. The portfolio consists of U.S. Treasury securities across a range of maturities, from short-term T-Bills to long-dated Bonds and TIPS, each denominated in USD. These instruments fall under the fixed-income asset class, with interest rates as the primary market risk factor.
Financial Instruments: Treasury Bills, Notes, Bonds, TIPS
Instruments' Type: Zero-Coupon (T-bills), Coupon-Bearing (Notes, Bonds, TIPS)
Instruments' Asset Class: Fixed Income
Risk Asset Class: Interest Rates
Issuer Entity: US Government
Issuer Authority: US Treasury
CUSIPS: 912796Y45, 912796Y45, 91282CKB6, 91282CKD2, 91282CJZ5, 912810TX6
Denominated: USD
Face Value: $100.00
Valuation Date: 28th March 2024 (end of Quarter 1, 2024)
Coupon Frequency: Semi-Annual (if applicable)
Pricing/Valuation Model: Discounting Cash Flow (DCF), Sensitivity-Based Partial Revaluation (DV01, Convexity)
Yield Curve Construction Model: Linear Interpolation
Risk Metrics: DV01, Convexity
Day-Count Convention: Actual/360 for T-Bills, 30/360 for T-Notes, Bonds, TIPS
Portfolio Composition And Market Data
The portfolio includes six securities, diversified across tenors and structure types, with a total notional investment of $30.0 million (mn).
UST3M (912796Y45): +$1.2mn, UST26W (912796Y45): +$2.8mn, UST2Y (91282CKB6): +$1.0mn, UST5Y (91282CKD2): +$4.2mn, UST10Y (91282CJZ5): +$8.0mn | UST30Y (912810TX6): +$12.8mn
Please note, if the face value of each bond is $100 and the notional amount is $1.0 million, then the total number of bonds issued would be: $1,000,000 / $100 = 10,000 bond units.
U.S. Treasury Website: for official interest rate curves/discount rates.
Instructions
Participants are expected to conduct a detailed pricing and revaluation exercise of the above fixed-income portfolio using both full revaluation DCF and partial (sensitivity-based) revaluation methodologies. This dual-valuation approach reflects the practices followed by treasury, valuation, and market risk teams in financial institutions.
Process Workflow
Market Data: Initiate by identifying and retrieving real-time or historical market data required for pricing, including discount rates and yield curves for the valuation date (28-Mar-2024), security-specific details (CUSIP, maturity, coupon, frequency), and auction results, where applicable (for issue prices), attached. Announcements, Data, and Results
Yield Curve Construction: Proceed to construct a term structure of interest rates using linear interpolation. Interpolate missing rates across maturities to ensure proper input into the DCF model.
Security Valuation and Revaluation: for each security in the portfolio, perform:
Full Revaluation (DCF Method): Use the DCF model to revalue each security:
Project the future cash flows (coupons and principal) and discount them using appropriate rates derived from the constructed rate curve.
Calculate the present value of each security as of the valuation date: 28th March 2024.
This approach provides an accurate revaluation under both normal and stressed market conditions.
Partial Revaluation (Sensitivity-Based Approach): Implement the sensitivity-based approximate valuation methods using pre-computed sensitivities, which are especially useful for real-time risk monitoring and portfolio stress-testing.
First-Order Revaluation (DV01-based): Estimate the price change using a 1 basis point shock (DV01).
Second-Order Revaluation (DV01 + Convexity-based): Incorporate convexity to capture the non-linear effects of rate change.
These partial revaluation approaches (DV01-based, DV01 + Convexity-based) will be used in parallel with the DCF method to compare valuation accuracy, interpret model assumptions and limitations, and analyze approximation errors under different interest rate shock environments.
Mark-to-Market (MTM), and Profit and Loss Attribution: Determine whether the portfolio has experienced profits or losses by comparing revalued prices (as of 28th March 2024) with previous MTM prices (as of 27th March 2024), calculate the unrealized gains or losses (MTM PnL) for each instrument, and aggregate PnL based on maturity buckets: short-term: T-Bills (≤1Y), medium-term: T-Notes (2Y to 10Y), long-term: T-Bonds and TIPS (>10Y). Analyze the relative contribution of each maturity bucket to the overall portfolio value.
Risk Factor Analysis: Identify risk factors and associated risk sensitivities for each position, examine risk factor shocks/fluctuations (shifts in the rates curve), and assess their impact on portfolio performance.
Valuation Report Requirement
Participants are required to submit a comprehensive and professionally structured valuation report summarizing the entire end-to-end process, from data sourcing to pricing, revaluation, risk attribution, and analysis, which should include:
Executive Summary: This section must provides a concise yet comprehensive overview of the fixed-income revaluation exercise and summarizes key findings (including highlighting the validation date, describing the strcture and composition of the fixed-income portfolio, instrument types, total notional amount invested, and other relevant information), total MTM gains/losses across the portfolio, instruments with the most significant changes in the valuation and contributing to the overall gains/losses, and observations on interest rate sensitivities across maturities.
Although this section appears first in the report, it should be completed last, after all detailed analysis and calculations have been performed.
Methodology Section: This section should detail the valuation and revaluation methodologies applied to assess the fair value and interest rate sensitivity of each security within the portfolio. It should be divided into three core components:
Approaches used for portfolio revaluation:
Describe the full revaluation DCF framework used to price fixed-income securities (maybe specify the cashflow projection based on coupon schedule and maturity) and interest rate curve construction technique used to construct term structures, including the DCF valuation formula.
Explain both DV01-based and DV01+Convexity-based revaluation approaches by defining interest rate sensitivities and computation, including the assumptions involved, and how convexity adjusts for non-linear responses to large interest rate changes.
Differentiate among the three methodologies based on their approach toward revaluing instruments, accuracy, computational time, and use case. Discuss the trade-off between accuracy and speed, suitability under normal vs. stress market conditions, applicability in regulatory submissions vs. internal risk monitoring, and when each would be more appropriate.
Data Tables and Assumptions: This section should present all quantitative inputs used in the valuation exercise, along with the underlying assumptions that support the modeling and pricing framework.
Instrument-level Inputs: Provide a structured table that lists the key characteristics of each Treasury security in the portfolio, such as CUSIP, instrument type, maturity date, coupon rate and frequencies, notional amount, face value, and day-count convention.
Ensure the details align with those published in the U.S. Treasury’s auction and issuance data.
Market Data Inputs: Include tables or appendices summarizing interest rate curve data as of 27th Mar (for prior valuation) and 28th Mar 2024 (for current revaluation), interpolated spot rates used in DCF calculations, and auction results for each security (issue price, high yield, bid-to-cover ratio, etc.)
All market data should be sourced from official channels like the U.S. Treasury, FRED, or Bloomberg.
Modeling Assumptions: Justify the assumptions made in the valuation/revaluation exercise regarding day-count conventions, coupon compounding basis, rates curve construction, price approximations (DV01 or DV01+Convexity), and bond price formats.
These assumptions should be stated clearly in the report to ensure transparency and repeatability of results.
Comparative Valuation Analysis: This section should present a quantitative comparison of the results produced by the three valuation methods: Full DCF, DV01-based, and DV01 + Convexity-based. It assesses the accuracy, feasibility, and limitations of each.
Provide a side-by-side comparison for each instrument, CUSIP, valuation date, instrument prices (under DCF, DV01, DV01+Convexity as of 28th Mar. 2024), previous price (as of 27th Mar. 2024), and daily MTM PnL (under DCF, DV01, DV01+Convexity as of 28th Mar.).
Make sure to include all the securities and total portfolio-level metrics.
Accuracy Assessment: Identify where the Sensi-based approximations fail to capture non-linear behavior (deviations between DCF valuation and Sensi-based approximations), and comment on the feasibility of using partial revaluation in a real-time setting. Discuss:
Where the DV01-only approximation underestimates or overestimates price changes, and
How convexity adjustment improves accuracy, especially for longer-duration instruments.
Visualize errors via bar charts or deviation plots (optional).
Interpretation and Feasibility in Practice: Provide comments on the trade-off between computational efficiency and accuracy. If possible, run scenarios where partial revaluation may break, for example, in volatile interest rate environments (±25, ±50, ±75, and ±100bps parallel shift).
Provide recommendations on when to prefer one methodology over the other, based on your observations.
Portfolio-level Impact Analysis: This section should interpret how market risk factors (primarily changes in interest rates) impacted the portfolio valuation. It aims to identify sensitivities across maturity buckets and convexity effects, and highlight risk exposures.
MTM Gain/Loss by Maturity Bucket: Aggregate the mark-to-market revaluation results across three maturity buckets (short-term ≥1Y, medium-term 2Y to 10Y, and long-term >10Y), highlighting securities include: total notional ($), MTM PnL (DCF), MTM PnL (DV01), and MTM PnL (DV01+Convexity). Discuss which segments contributed most to portfolio gains or losses and where model differences were most significant.
Rate Sensitivities Profile:
Identify tenor buckets most sensitive to interest rate changes, typically those with higher duration and convexity. Provide modified duration and convexity metrics per tenor bucket to back your observations.
Quantify the difference between DV01-based and DV01+Convexity-based revaluations for each tenor bucket and explain why ignoring convexity in long-term instruments underestimates risk and valuation change in larger interest rate moves.
Advise how longer-dated securities amplified MTM impact (losses) due to duration/convexity, despite potentially smaller notional contribution to the overall portfolio, and discuss non-linear effects, behaviour, and their significance for real-time risk estimations.
Analyze if the portfolio is concentrated in specific maturities (heavy allocation to long bonds) or well-distributed, whether the maturity profile creates imbalanced interest rate exposure, or whether the portfolio shows risk diversification in terms of maturity buckets or duration.
Visual Representations: To ensure transparency and clarity across the report, charts and graphs should be embedded within the report wherever they help illustrate the analytical results. Each figure must be titled and sourced from the model outputs or official market data.
Yield Curve Construction: Plot actual rate curve points vs. interpolated points used in DCF valuation.
Interest Rate Shifts: Illustrate parallel or non-parallel shifts in the yield curve if comparing 27-Mar vs. 28-Mar data. Include multiple curves if analyzing scenario shifts (±25bps or ±50bps parallel shifts, flatteners/steepeners).
PnL Attribution Charts:
Per Instrument MTM Impact: Bar chart showing MTM gains/losses for each security (DCF vs. DV01 vs. DV01+Convexity).
Aggregate PnL by Maturity: Bucket stacked bar or pie chart summarizing PnL across short, medium, and long-term securities.
All visuals should include proper legends, clearly labeled axes, and concise captions explaining the takeaway message.
Draw Conclusions, Provide Recommendations, and Attach References.
Mentor’s Note:
All sections of this report must reflect the standards expected in a real-world institutional setting, as discussed during our live sessions. Your analysis should be logically structured, methodologically sound, and firmly data-driven. Use only verified market data, support all computations with mathematical precision, and document and justify every assumption applied throughout the valuation process.
Your final report should demonstrate not only your technical proficiency but also your ability to present complex valuation insights in a manner consistent with the expectations of institutional fixed-income valuation reporting and market risk documentation standards. All the best!
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