Why Scenario Design Requires More Than a List of Shocks
A market scenario is useful only if its assumptions are clear enough that another analyst can reproduce them. “Rates rise, equities fall, and spreads widen” gives directions, but not shock sizes, affected maturities, currency conventions, or a common valuation horizon. Those omissions can lead two analysts to construct different scenarios from the same description.
A factor-based scenario specifies changes to defined market variables, such as benchmark yields, equity prices, exchange rates, and credit spreads. It is a description of a possible market state, not by itself a probability statement or a portfolio valuation. The scenario should distinguish what is shocked from what is held fixed, and should state whether the shocks are absolute changes, relative changes, or changes to a quoted level.
The starting levels matter. A 50-basis-point increase in a yield is an absolute change of 0.50 percentage points, while a 10% increase in an equity index is a relative change. An exchange-rate shock also depends on the quote convention. A scenario must not leave these distinctions implicit.
A Consistent Specification
Begin by defining the factors and their units. For example, a yield may be stated in percent, a credit spread in basis points, an equity index as a price or percentage return, and an exchange rate as units of one currency per unit of another. Then identify the common horizon and state which market variables move together in the scenario.
Record the valuation date, starting factor levels, and horizon. State whether the shocks are instantaneous or accumulated over a period.
Use a precise tenor for rates, a clear index or asset-price basis for equities, an explicit currency quote for FX, and a defined benchmark for spreads.
For an absolute shock, add the change to the initial level. For a relative shock, multiply the initial level by one plus the percentage change.
Specify assumptions such as no change in the benchmark definition, no currency-quote reversal, and no additional factor movement beyond those listed.
For yields and spreads, one basis point is 0.01 percentage points. Thus, an increase of 35 basis points is an increase of 0.35 percentage points, not an increase of 35%. For an equity price or exchange rate shocked by a percentage, the new level is the initial level multiplied by the relevant growth factor.
A scenario described as internally consistent has a coherent set of factor changes, units, and assumptions. That does not mean that the shocks must be statistically likely or that the scenario uniquely describes an economic event. It means the individual instructions can be applied together without contradictory definitions or hidden changes in convention.
Worked Example: Specifying a Nonparallel Interest-Rate Scenario
A hypothetical insurer records benchmark yields of 3.20% at 2 years, 3.65% at 5 years, and 4.00% at 10 years. Design an instantaneous scenario in which yields fall by 40, 25, and 10 basis points, respectively. Find the shocked yields and the change in the 10-year-minus-2-year slope. Assume all other valuation inputs are held fixed.
Method. Convert each basis-point shock to a percentage-point change, apply it to the matching tenor, and compare the curve slope before and after. This avoids treating a nonparallel scenario as if one uniform shock applied to every maturity.
At 2 years, a fall of 40 basis points is a change of \(-0.40\) percentage points. The shocked yield is \(3.20\%-0.40\%=2.80\%\).
At 5 years, a fall of 25 basis points is a change of \(-0.25\) percentage points. The shocked yield is \(3.65\%-0.25\%=3.40\%\).
At 10 years, a fall of 10 basis points is a change of \(-0.10\) percentage points. The shocked yield is \(4.00\%-0.10\%=3.90\%\).
The initial 10-year-minus-2-year slope is \(4.00\%-3.20\%=0.80\) percentage points. The shocked slope is \(3.90\%-2.80\%=1.10\) percentage points. The slope therefore increases by \(1.10-0.80=0.30\) percentage points, or 30 basis points; the curve steepens between these two tenors.
Valuation assumptions. This is an instantaneous market-factor scenario from the stated starting curve. The three tenor shocks are specified explicitly; interpolation at other maturities is not prescribed here. No passage of time, carry, or other market-factor movement is included.
Check and trap avoided. Each shocked yield is below its starting yield, as required by the stated downward shocks. A common error is to apply the 40-basis-point 2-year shock to the whole curve. That would give the wrong 5- and 10-year levels and conceal the intended change in slope.
Joint Shocks and Currency Conventions
A scenario may shock more than one factor at once. When an asset is denominated in a foreign currency, its home-currency value depends on both the asset’s local-currency value and the exchange rate. The quote convention must be explicit. Let \(q\) denote units of the home currency per one unit of foreign currency. If the foreign asset return is \(r_F\) and the exchange-rate percentage change is \(r_q\), the home-currency value changes by the product of the two growth factors:
This relation follows by writing the initial home-currency value as \(V_0^{H}=V_0^{F}q_0\). After the shocks, \(V_1^{F}=V_0^{F}(1+r_F)\) and \(q_1=q_0(1+r_q)\), so \(V_1^{H}=V_0^{F}q_0(1+r_F)(1+r_q)\). Dividing by \(V_0^{H}\) gives the stated result. The product includes an interaction term; simply adding the two percentage changes omits it.
Worked Example: Combining a Foreign Equity Shock With FX
A hypothetical U.S. insurer holds a euro-denominated equity investment worth €8.00 million. The exchange rate is quoted as U.S. dollars per euro, initially $1.10 per €1. In a one-period scenario, the equity falls 15% in euros and the euro weakens by 8% against the U.S. dollar. Calculate the ending euro value, ending exchange rate, ending U.S.-dollar value, and total U.S.-dollar return. Assume both percentage changes apply over the same period.
Method. Apply the equity shock to the local-currency asset value and the FX shock to the stated USD-per-EUR quote. Then multiply the two ending levels to obtain the home-currency value.
The ending equity value is \(€8.00\text{ million}\times(1-0.15)=€6.80\text{ million}\).
A weakening of the euro means fewer U.S. dollars per euro under the stated quote. The ending exchange rate is \($1.10\times(1-0.08)=$1.012\) per euro.
The initial U.S.-dollar value is \(€8.00\text{ million}\times$1.10/€=$8.80\text{ million}\). The ending value is \(€6.80\text{ million}\times$1.012/€=$6.8816\text{ million}\).
The U.S.-dollar change is \($6.8816\text{ million}-$8.80\text{ million}=-$1.9184\text{ million}\). The corresponding return is \($6.8816/$8.80)-1=0.782-1=-0.218\), or a loss of 21.8%.
Check and trap avoided. The joint growth factor is \(0.85\times0.92=0.782\), matching the ending-value ratio \($6.8816/$8.80=0.782\). Adding the shocks would suggest a 23% loss, but the correct loss is 21.8%; the product includes the positive interaction term \((-0.15)(-0.08)=0.012\). Reversing the exchange-rate quote would also reverse the interpretation of the euro’s weakening.
Separating Benchmark Rates and Credit Spreads
For a credit instrument whose yield is expressed as a benchmark yield plus a spread, the two factors should be specified separately. The spread is the yield increment over the stated reference rate. If both factors change, the total yield change is the sum of their absolute changes, provided the benchmark and spread definitions remain the same.
The relationship is an accounting identity under this quoted-yield convention: the instrument’s total yield consists of the reference yield and the additional spread. A scenario that changes both components must update each one before adding them. This identity does not, by itself, determine a price change; price valuation also requires the instrument’s cash flows and an appropriate valuation method.
Worked Example: Combining a Reference-Rate Shock With Spread Widening
A hypothetical credit instrument has a reference yield of 4.10% and a spread of 1.40%. A scenario raises the reference yield by 35 basis points and widens the spread by 65 basis points. Find the initial total yield, each shocked component, the post-shock total yield, and the total-yield change. Assume the reference-rate and spread definitions do not change.
Method. Convert both shocks from basis points to percentage points, update the components separately, and then add them. This avoids confusing the spread change with the total-yield change.
The initial total yield is \(4.10\%+1.40\%=5.50\%\).
The shocked reference yield is \(4.10\%+0.35\%=4.45\%\). The shocked spread is \(1.40\%+0.65\%=2.05\%\).
The post-shock total yield is \(4.45\%+2.05\%=6.50\%\). Its change is \(6.50\%-5.50\%=1.00\) percentage point, or 100 basis points. This also equals the sum of the component changes: \(35+65=100\) basis points.
Check and trap avoided. The total yield rises from 5.50% to 6.50%, consistent with both specified upward shocks. A common error is to add only one component’s shock or to state an inconsistent post-shock total. In particular, 4.45% plus 2.05% is 6.50%, not 5.50%.
Valuation assumptions. The example specifies yield factors, not a bond-price calculation. It assumes a constant reference-rate definition and a spread measured over that reference. It makes no separate assumption about defaults, cash flows, or price sensitivity.
Scenario Documentation and Common Traps
A scenario table makes the instructions auditable. It should show the starting level, shock, resulting level, and unit for every factor. For a curve, list the affected tenors or state a precise rule for how the shock varies by tenor. For FX, write the currency pair and quote direction. For credit, identify the reference rate and the spread convention.
| Factor | Specify | Typical ambiguity to remove |
|---|---|---|
| Interest rate | Benchmark, tenor, starting yield, and change in basis points | Whether the shock is parallel or varies by maturity |
| Equity | Index or asset, starting level, and percentage change | Whether the change is a percentage return or a point change |
| Foreign exchange | Currency pair, quote direction, starting rate, and percentage change | Which currency strengthens under the stated quote |
| Credit spread | Reference rate, spread starting level, and basis-point change | Whether the spread change is separate from the reference-rate change |
Before using a scenario, check that all shocks refer to the same horizon and that none has been counted twice. For example, if a total yield shock is supplied directly, do not add separate benchmark and spread shocks unless the scenario explicitly intends that decomposition. If the reference rate and spread shocks are supplied separately, calculate the total change from both.
A deterministic scenario is not automatically a forecast, a probability estimate, or a measure of portfolio risk. Its purpose is to define a set of factor conditions clearly. Any subsequent portfolio analysis must apply its own valuation assumptions; scenario design alone does not specify how instruments are repriced.
Check Your Understanding
For each problem, write the factor changes with the stated units and check that the resulting levels agree with the scenario directions.
- A hypothetical benchmark curve has 3-year and 7-year yields of 2.85% and 3.55%. A scenario raises the 3-year yield by 20 basis points and lowers the 7-year yield by 15 basis points. What are the two shocked yields, and how does the 7-year-minus-3-year slope change? (Answer: 3-year yield 3.05%; 7-year yield 3.40%; slope falls from 0.70 to 0.35 percentage points, a 35-basis-point flattening.)
- A foreign equity position is worth £5.00 million, and the exchange rate is quoted as U.S. dollars per pound at $1.25 per £1. The equity rises 6% in pounds while the pound weakens 4% in U.S. dollars. Find the ending exchange rate and U.S.-dollar return. (Answer: $1.20 per £1; \(1.06\times0.96-1=1.76\%\).)
- A hypothetical bond’s reference yield is 3.75%, and its spread is 1.10%. The reference yield falls 20 basis points while the spread widens 45 basis points. Find the initial and post-shock total yields and the change. (Answer: initial 4.85%; post-shock reference 3.55%, spread 1.55%, total 5.10%; increase 0.25 percentage points, or 25 basis points.)
- An equity index starts at 2,400 and falls 9%. A currency quote, stated as Canadian dollars per U.S. dollar, starts at 1.36 and rises 3%. Find both ending factor levels and state which currency strengthened under this quote. (Answer: index 2,184; quote 1.4008 Canadian dollars per U.S. dollar; the U.S. dollar strengthened against the Canadian dollar.)
- A scenario specifies a 30-basis-point rise in a benchmark yield and a 50-basis-point spread widening for an instrument initially yielding 6.20% in total. Find the total-yield change and post-shock yield. (Answer: total-yield increase 80 basis points, or 0.80 percentage points; post-shock yield 7.00%.)