Profit And Loss Explained

Profit and loss explained analysis and reporting has become a required tool for the middle and front office. Brian Shydlo, a Managing Principal at Essentia Advisory Partners, an EPAM Company, looks at what needs to be considered when designing and developing P&L Explained reporting systems and considers some exciting potential uses for it.

Profit and loss explained analysis is a powerful tool for the risk manager and trader if implemented and used optimally. However, its true depth and complexity are often underappreciated. While P&L explained reports have been around for over a decade, it is only since 2003, with the rise of sophisticated investment banks and hedge funds with proprietary energy trading desks, that this tool has gained popularity and become a requirement.

This article aims to raise awareness of the potential and complexity of P&L explained analysis. It also provides guidelines for designing and developing effective P&L Explained reporting solutions.  The final section evaluates the current landscape of information technology solutions, dispels some common myths, and explores future developments.

For those considering a P&L explained project, having clarity, and understanding from the outset is crucial, as making design changes later can be costly.  Consequently, many companies involve experts in the initial stages to help accelerate their progress toward achieving their goals.

PROFIT’S ROOT CAUSE

A P&L explained analysis attributes the daily change in the value – e.g., the mark-to-market (MTM) – of a portfolio of deals to its root causes. Risk managers use this knowledge of the source of trading profits to act more effectively. For example, if they discover that an options desk’s profits are primarily due to changes in commodity prices rather than volatility changes, they will investigate further.  Traders use this report as a diagnostic tool to reconcile their end-of-day hand-calculated P&L estimates with the values produced by their trading system.

Items that influence P&L include changes to deal attributes (volume and trade price), market data (commodity prices), and, for options, the number of days to expiration. Ideally, the sum of these explanatory factors for a given analysis should equal P&L, which is taken as a given. However, they are often close, but not equal, resulting in a residual labeled “unexplained” or “variance” on reports (see Figure 1).

Figure 1) General Formula for P&L Explained

A typical report layout has columns for total P&L, unexplained P&L, new deal P&L, and any other explanatory factors that have had an impact. For example, profit and loss due to commodity price changes would appear in a column headed ‘Impact of Prices’. There is typically one summary report with rows per portfolio, trade type, or commodity, and a detailed per trade report.

Two different methodologies are used in P&L Explained reporting: the sensitivities method and the revaluation method. The sensitivities method, which utilizes sensitivities known as the Greeks, is the most common because most firms already compute these values, making this method relatively easier.  For example, the ‘Impact of Delta’ uses the Greek that shows the first-order sensitivity to market price changes to explain P&L.  The formula is:

(Today’s Price – Yesterday’s Price) * Delta per tick / tick size

Where Delta is the profit from a one-tick move, and tick size is usually $0.01.

The revaluation method, on the other hand, derives explanatory factors by repeatedly recalculating MTM using the actual inputs from the current and prior day, swapping them out one at a time while keeping the other inputs unchanged.  This method can be relatively more accurate than the basic sensitivities approach.  For example, the delta sensitivities of spread options and swaptions are not additive as they are for vanilla options, a phenomenon known as the cross-gamma effect.  The revaluation method effortlessly handles this effect, whereas it is often ignored when using the sensitivities approach because it requires an additional complicated formula.  Each approach has several other pros and cons.

DESIGN REQUIREMENTS

All organizations have three core requirements for a basic end-of-day P&L explained report (see Table 1).

Table 1) Core Requirements

1

The numbers are correct

2

The numbers are in the correct buckets/columns

3

The presentation of the report is suitable

The first core requirement is accuracy, ensuring that the explanatory factors fully account for the P&L without any residual P&L due to unknown causes.  However, few P&L explained reports meet this critical requirement.  This is because different deal types possess distinct features and operational characteristics, and not all reports contain the necessary logic to describe these features and operational characteristics, and not all reports contain the necessary logic to describe these features adequately and prevent unexplained P&L.

The second requirement is that each component of P&L must be attributed to its correct cause, ensuring that every ‘Impact of’ column on the report reflects the appropriate value. While coding a report to accurately capture all circumstances, such as P&L due to deal amendments, can be challenging, the main obstacle for software vendors in creating an off-the-shelf solution stems from the unique preferences of each trading organization.

For example, some firms may prefer to display P&L due to new trades as a single value, while others may opt to split new trade P&L and related broker fees into separate columns. Another allocation decision arises when a firm’s volatility formula depends on market prices.  Market price changes directly affect an option’s MTM with a secondary effect on the MTM due to revised volatility.  Some firms interpret this second effect as ‘Impact of Volatilities’, while others classify it as ‘Impact of Prices’.

The final requirement is that the presentation of the report is suitable, encompassing both the formatting of the report and the technology used. Report output solutions can vary widely, ranging from a simple text file to a visually appealing report created using a report writer tool.  They can employ an Excel pivot table front end or a web-based datamart.

Firms may also desire additional features such as:

  • Charts and graphs
  • Drill-down capability
  • Ability to run intra-day and not just at end-of-day
  • Interactive grouping, summing, and filtering
  • Alternate reporting views, one focusing on attribution by deal and another by net position.
SUGGESTIONS & CONSIDERATIONS

To improve usability, consolidating explanatory factors into a two-level hierarchy can provide a clearer overview. The top-level groups would encompass multiple bottom-level contributors to P&L, allowing for a more concise display of summary columns. Users can expand or collapse each group to view detailed columns, offering a streamlined approach. This hierarchical solution has the potential to condense several dozen detail-level columns into typically nine columns, although firms may have the flexibility to opt for alternative groupings (see Figure 2).

Figure 2) Hierarchy of P&L Explanatory Factors (Assumes Sensitivities Method)

Another suggestion is to incorporate both the actual unexplained and the absolute value of the unexplained. When summing the unexplained at the portfolio level, the positives and negatives of the original per-deal unexplained may cancel out, resulting in a misleadingly low net unexplained. Addressing this issue by examining the sum of the absolute values can provide a more accurate assessment.

Considerations for explaining P&L arise when deciding whether to attribute it to market data inputs or outputs. For instance, natural gas forward prices are based on inputs (Nymex price and a basis spread) and result in an output (all-in price). Similarly, a volatility formula with multiple inputs (at-the-money volatility, curve flatness factor, strike price, and forward price) yields a single output: volatility. While attributing P&L to the inputs aligns with traders’ perspective, using market data outputs can be more straightforward to implement, especially when inputs are only available in a separate system.

Designing drill-down by time, such as the ability to view month-by-month data for multi-month deals, requires careful consideration. Generating consistent numbers for deal types with different levels of granularity (monthly, daily, hourly) poses challenges. Some companies address this by creating a single monthly report that accommodates all deals, although this may involve manipulating the numbers to fit the format. Additionally, they may create separate reports for daily or hourly exposures tailored to specific subsets of deals.

CURRENT ENVIRONMENT, MYTHS, AND THE FUTURE

Providers of energy trading and risk management software currently offer out-of-the-box P&L explained reports. However, no off-the-shelf P&L explained solution meets 100% of the three primary requirements described above all of the time. A typical scenario occurs when a firm starts by using a vendor-provided report and then enhances it either to meet their custom allocation requirements or to reduce unexplained. For example, some organizations set formal unexplained thresholds which if exceeded compels them to seek a resolution. In some cases, usually after one too many enhancement iterations with a vendor-supplied report, a firm will decide to build their own report. This allows them to fully meet their short-term needs and gain control over how the report will work in the future (see Figure 3).

Figure 3) Goal of a Typical P&L Explained Report Enhancement Project

P&L explained reporting is the subject of two common myths. The most common myth is that the P&L number must be incorrect if, after calculating all of the known causes, there is residual P&L still unexplained. In fact, the P&L number is always considered correct in a P&L explained report, although it certainly makes risk managers uncomfortable if the value in the ‘unexplained’ column on the report is not zero. Therefore, when you do find the cause of the unexplained P&L, which is usually done manually after the fact, the total P&L number never changes due to any reallocation, even a reallocation from ‘unexplained’ to one of the explanatory columns.

The second myth is that P&L explained reporting is easy, a myth that is refuted by the many considerations described in this article. Furthermore, as demanding as it is for a firm to build a solution to meet its own limited requirements it is even more difficult for a vendor to produce a solution to suit the needs of multiple client firms.

In the coming years, we can expect software companies to consistently integrate client feedback and enhance their P&L explained reports, catering to the needs of many firms. Moreover, more advanced firms will likely persist in creating custom P&L explained solutions to fully align with their specific requirements.  It is also probably that, alongside mastering P&L explained reporting, there will be an increase in the popularity of other ‘explained’ reports, such as a VaR (Value-at-Risk) explained report, demonstrating the reasons for VaR fluctuations from one day to the next.

Email: Brian_Shydlo@epam.com

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