A balanced portfolio under an equity-led shock

Define the portfolio and the joint shock

The starting inventory contains $4 million of US equities, $3 million of Treasuries, $2 million of corporate bonds and $1 million of cash. Every value is already expressed in USD, and every holding is denominated in USD. Those amounts imply capital weights of 40%, 30%, 20% and 10%. They describe this teaching portfolio, not a recommended allocation or an observed investment account.

The equity-led preset combines a 30% equity decline, a 50 basis point government-rate increase and a 150 basis point credit-spread widening. Its EUR, GBP and JPY assumptions are -8%, -10% and +3%, respectively, but none affects these USD holdings. The shocks are simultaneous valuation assumptions without an assigned horizon or probability; they are not a replay of a named crisis.

Translate assumptions into holding returns

Equity beta is one, so the equity sleeve follows the assumed market move exactly. For bonds, the engine uses local decimal return = -duration * rate change + 0.5 * convexity * rate change squared - spread duration * spread change. Convert basis points by dividing by 10,000: the two changes are 0.005 and 0.015. This is a fixed-sensitivity approximation, not cash-flow repricing.

Treasuries have duration seven, convexity 60 and zero spread duration. Their calculation is -7 * 0.005 + 0.5 * 60 * 0.005 squared = -0.03425. Corporate bonds use duration five, convexity 35 and spread duration four: -0.025 + 0.0004375 - 0.06 = -0.0845625. USD cash has zero modeled local return and no currency translation effect; interest earned is excluded.

Reconcile dollars before interpreting percentages

Adding the four P/L amounts gives -$1,471,875. Adding that signed change to the starting $10,000,000 gives $8,528,125. Dollar figures are rounded after calculation to remove floating-point residue. The full starting inventory is also the covered inventory here, so modeled contribution divided by total value and modeled-sleeve return share the same denominator and both equal -14.71875%.

Each holding's return uses its own starting value, whereas its portfolio contribution uses $10 million. Equities therefore contribute -12 percentage points, Treasuries -1.0275 points and corporate bonds -1.69125 points. Cash contributes zero. These additive contributions explain the portfolio result; adding the individual holding returns would incorrectly give each sleeve equal weight regardless of the capital invested.

Why the bond allocation does not offset this loss

This scenario explicitly raises government yields while equities fall. Both bond sleeves consequently lose value through duration, and corporate bonds also lose through wider spreads. The positive convexity adjustment contributes $2,250 for Treasuries and $875 for corporates, partially reducing their losses. It does not reverse them. FINRA's duration explainer supports the general relationship between interest-rate increases and bond-price sensitivity; it does not supply these hypothetical inputs.

The useful question is conditional: which presumed diversifiers still help under these particular shocks? A different rate assumption could change the answer. This calculation contains no estimated correlation matrix and does not establish that stocks and bonds always decline together. Cash preserves modeled nominal value, but the engine does not test inflation, deposit-counterparty risk or access to funds.

Separate arithmetic completeness from model completeness

Value coverage is 100% because all starting dollars have a supported mapping. That does not mean complete risk coverage. Fixed beta ignores changing equity exposures; duration and convexity omit curve twists, changing sensitivities and instrument optionality. Spread duration is not a default-and-recovery model. Fees, income, taxes, trading costs, financing and forced-sale effects are absent. The Basel Committee's stress-testing principles emphasize understanding assumptions and limitations; citing them does not certify this calculator.

Questions before using the result

Does a dated holdings inventory reconcile to the starting total? Are beta and bond sensitivities suitable for the actual instruments and shock size? Would collateral calls or withdrawals require cash before assets could be sold? Which alternative joint scenario would challenge the assumed offsets? Retain the inputs, engine version 1.0.0 and review decisions with the output. This is a reproducible educational sensitivity, not a forecast, maximum-loss guarantee or investment recommendation.

Review checkpoints

• Reconcile -$1,471,875 of modeled P/L to an $8,528,125 ending value.
• Use $10 million for portfolio contributions, not each sleeve's denominator.
• 100% value coverage does not mean every risk is modeled.
• Challenge sensitivities, joint shocks and funding needs separately.

Source notes

1. FINRA: Duration and bond-price sensitivity to interest rates
2. Basel Committee: Stress testing principles (2018), assumptions and limitations

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