Fixed Income Scenario Analysis

1. Calculation Name

Scenario Sensitivity (Rate and Spread Shocks)

2. Description and Mathematical Formula

Scenario analysis shocks the portfolio and benchmark using predefined rate/spread moves. For scenario \( s \):

\[ \mathrm{PnL}^P_s = \sum_{k} \mathrm{Exposure}^P_{k} \times \Delta_s z_{k}, \quad \mathrm{Active}_s = \mathrm{PnL}^P_s - \mathrm{PnL}^B_s \]

where \( \Delta_s z_{k} \) is the shock applied to factor \( k \) (e.g., key rate shift, spread change, FX move).

3. Input Sample Data

Scenario	Portfolio PnL (bps)	Benchmark PnL (bps)	Active PnL (bps)	Description
Parallel +50 bp	-420	-480	+60	Uniform +50 bp shift
Parallel -50 bp	+410	+460	-50	Uniform -50 bp shift
Steepener (+25 / -25)	-110	-140	+30	30Y +25 bp, 2Y -25 bp
Flattener (-25 / +25)	+105	+80	+25	30Y -25 bp, 2Y +25 bp
Credit +75 bp	-250	-290	+40	Corporate spreads +75 bp

4. Mathematical Solution

• Active PnL for each scenario is simply the difference between portfolio and benchmark PnL.
• Example (Parallel +50 bp): \( -420 - (-480) = +60 \) bps.
• Aggregate check: the plugin also reports the worst loss (here -420 bps) and best gain (+410 bps) for quick risk triage.

5. Sample Python and R Code

Python

import pandas as pd

scenarios = pd.DataFrame(
    {
        "scenario": [
            "Parallel +50 bp",
            "Parallel -50 bp",
            "Steepener (+25 / -25)",
            "Flattener (-25 / +25)",
            "Credit +75 bp",
        ],
        "pnl_port": [-420, 410, -110, 105, -250],
        "pnl_bench": [-480, 460, -140, 80, -290],
    }
)

scenarios["active_bps"] = scenarios["pnl_port"] - scenarios["pnl_bench"]
print(scenarios)
print("Worst-case:", scenarios["pnl_port"].min(), "bps")
print("Best-case:", scenarios["pnl_port"].max(), "bps")

R

library(dplyr)

scenarios <- tibble::tibble(
  scenario = c(
    "Parallel +50 bp",
    "Parallel -50 bp",
    "Steepener (+25 / -25)",
    "Flattener (-25 / +25)",
    "Credit +75 bp"
  ),
  pnl_port = c(-420, 410, -110, 105, -250),
  pnl_bench = c(-480, 460, -140, 80, -290)
)

scenarios <- scenarios %>%
  mutate(active_bps = pnl_port - pnl_bench)

worst_case <- min(scenarios$pnl_port)
best_case <- max(scenarios$pnl_port)
scenarios
worst_case
best_case

6. Output Table

Scenario	Active PnL (bps)	Risk Note
Parallel +50 bp	+60	Portfolio less rate-sensitive than benchmark
Parallel -50 bp	-50	Underperforms rally due to shorter duration
Steepener (+25 / -25)	+30	Beneficial overweight in long maturities
Flattener (-25 / +25)	+25	Gains from barbell positioning
Credit +75 bp	+40	Portfolio has tighter credit risk than benchmark

7. Conclusion

Scenario analytics give a forward-looking view of rate and spread risks. This template captures the essence of the FinFacts scenario plugin, helping teams document stress results alongside attribution and performance metrics.