Measuring and Managing Exchange Rate Exposure
Exchange rate risk vs. exchange rate exposure
Three types of exposure: transaction, translation, operating
The exposure regression: \(V = a + bS + u\)
Operating exposure examples and measurement
Hedging with forwards: transaction and operating exposure
Multiple FC cash flows: aggregation and hedging
Overview of hedging instruments
Lecture 6 established:
Under M&M, hedging is irrelevant
In reality, hedging adds value through: distress costs, tax convexity, agency costs, information asymmetries
But to hedge, you first need to measure what you’re exposed to.
This lecture answers: What is exposure, how do we measure it, and how do we hedge it?
Exchange rate risk = uncertainty about the future spot rate.
Exchange rate exposure = how much firm value changes per unit change in the exchange rate.
Two firms in the same country, facing the same FX risk, can have very different exposures — one may benefit from a depreciation while the other is harmed by it.
Transaction exposure: known FC-denominated contractual cash flows
Translation exposure: accounting consolidation effects
Operating (economic) exposure: how FX changes affect competitive position, margins, volumes
The exposure regression captures all three:
\[\Delta V = \alpha + \beta \cdot \Delta S + \varepsilon\]
\(\beta\) measures total exposure — regardless of whether it comes from contracts, accounting, or competitive effects.
Arises from existing contracts denominated in foreign currency:
Accounts receivable / payable in FC
FC-denominated debt service
Dividends from foreign subsidiaries
Contractual purchase or sale commitments in FC
Easy to identify (it’s in the contracts) and easy to hedge (known amount, known date).
This is what most firms think of when they think “FX exposure” — but it is only part of the picture.
Arises from consolidating foreign subsidiary financial statements into the parent’s reporting currency.
Assets and liabilities translated at current exchange rate
Income statement items at average rate over the period
Creates accounting gains/losses on the balance sheet
Key question: Does translation exposure reflect economic exposure?
Often no — it is an accounting convention, not a cash flow
Many firms do not hedge translation exposure
Brief treatment here; low conceptual payoff relative to other exposure types
How FX changes affect future operating cash flows through competitive effects:
Revenues, costs, margins, and market share all respond to FX
Often larger than transaction exposure
Much harder to measure — requires understanding competitive dynamics
Cannot always be hedged with financial instruments alone
This is the most important type of exposure for strategic decision-making.
A firm with zero transaction exposure can still have massive operating exposure.
Example: A US ski resort in Colorado.
All revenues in USD. All costs in USD. No foreign currency cash flows.
Zero transaction exposure.
But: When the USD appreciates, European ski tourists find Colorado expensive relative to the Alps. Fewer Europeans visit. Revenue falls.
Operating exposure is positive (benefits from USD depreciation)
This exposure is invisible if you only look at contracts
This is why measuring exposure properly matters
The fundamental framework:
\[\tilde{V}_T = a + b \cdot \tilde{S}_T + \tilde{u}_T\]
where:
\(V_T\) = firm value (or cash flow) at time \(T\), in home currency
\(S_T\) = spot exchange rate (HC/FC)
\(b\) = exposure (in FC units)
\(a\) = unexposed component (HC, independent of \(S\))
\(u_T\) = residual (firm-specific risk, uncorrelated with \(S\))
\[V_T = \underbrace{b \times S_T}_{\text{Exposed}} + \underbrace{a + u_T}_{\text{Unexposed}}\]
Exposed portion (\(b \times S_T\)): varies with the exchange rate. Can be hedged.
Unexposed portion (\(a + u_T\)): independent of the exchange rate. Cannot be hedged with FX instruments.
Units:
| \(V_T\) | \(a\) | \(b\) | \(S_T\) | \(u_T\) |
|---|---|---|---|---|
| HC | HC | FC | HC/FC | HC |
The exposure \(b\) is in foreign currency units — it is the FC amount you need to hedge.
\(b > 0\): firm benefits from FC appreciation (net exporter profile, long FC)
\(b < 0\): firm benefits from FC depreciation (net importer profile, short FC)
\(b = 0\): firm is not exposed to this exchange rate
Estimating \(b\) in practice:
Regression approach: regress stock returns on FX changes: \(r_{i,t} = \alpha + \beta \cdot \Delta s_t + \varepsilon_t\)
Scenario analysis: project cash flows under different FX assumptions
The regression approach captures all channels (transaction + translation + operating). But \(\beta\) may be noisy, time-varying, and affected by existing hedges.
Revenue in FC, costs in HC
HC depreciation (\(S \uparrow\)): FC revenues worth more in HC terms \(\Rightarrow\) profits rise
Exposure \(b > 0\) (long FC)
Profit function:
\[\Pi(S) = b \cdot S - C_{\text{HC}}\]
Example: European pharmaceutical company selling drugs in USD. EUR revenues are fixed costs; USD revenues increase in EUR terms when EUR depreciates.
Revenue in HC, costs in FC
HC depreciation (\(S \uparrow\)): FC costs rise in HC terms \(\Rightarrow\) profits fall
Exposure \(b < 0\) (short FC)
Profit function:
\[\Pi(S) = R_{\text{HC}} - b_{\text{cost}} \cdot S\]
Example: US retailer sourcing products from Asia. Revenues are in USD; costs increase in USD terms when USD depreciates against Asian currencies.
Both revenues AND costs in HC — no explicit FC cash flows
But: competes with foreign firms whose costs are in FC
HC appreciation (\(S \downarrow\)): foreign competitors become cheaper \(\Rightarrow\) domestic firm loses market share
Exposure \(b > 0\) even though the firm has zero transaction exposure.
Example: US steel producer competing with Korean imports. All costs and revenues in USD. But when USD appreciates, Korean steel becomes cheaper in USD, taking market share.
This is pure operating exposure — invisible if you only look at contracts.
Pricing power: Can the firm pass through FX changes to customers?
Market structure: How competitive is the industry? More competition \(\Rightarrow\) larger operating exposure.
Cost structure: Domestic vs. imported inputs
Strategic flexibility: Can the firm shift production, sourcing, or pricing?
Time horizon: Operating exposure generally grows with the horizon
Firms with high pricing power and flexible operations have lower operating exposure. Commodity-like industries with intense competition have higher operating exposure.
Setup: You will receive FC \(X\) at time \(T\).
Exposure = \(X\) (in FC)
Hedge: sell FC \(X\) forward at rate \(F_{t,T}\)
Hedged value:
\[V_T^H = X \times F_{t,T}\]
This is known today — no FX risk remains.
This is the simplest case. The forward contract exactly offsets the exposure because both the amount and the timing are known.
From the regression: exposure = \(b\) (in FC units).
Hedge: sell FC \(b\) forward at rate \(F_{t,T}\).
Hedged value:
\[V_T^H = a + b \times F_{t,T} + u_T\]
The FX risk (\(b \times S_T\)) is replaced by a known quantity (\(b \times F_{t,T}\))
Residual risk \(u_T\) remains — it cannot be hedged with FX instruments
Exposure \(b\) is estimated, not observed \(\Rightarrow\) hedge is approximate
Exposure changes over time \(\Rightarrow\) hedge needs updating (dynamic hedging)
Residual risk \(u_T\) can be substantial
Financial hedging alone may be insufficient for operating exposure
Operational hedges may be needed:
Diversify production locations (match FC costs with FC revenues)
Diversify sourcing across currencies
Build flexibility into pricing and contracts
Best practice: Use financial hedges for near-term known flows (transaction exposure) and operational hedges for longer-term competitive effects (operating exposure).
A firm may have FC cash flows at different dates:
\[X_1 \text{ at } T_1, \quad X_2 \text{ at } T_2, \quad \ldots, \quad X_n \text{ at } T_n\]
Cannot simply add them — different maturities have different present values.
Aggregate exposure = present value of all FC cash flows:
\[\text{PV}_{\text{FC}} = \sum_{k=1}^{n} \frac{X_k}{(1 + r^*_k)^{T_k}}\]
where \(r^*_k\) is the FC interest rate for maturity \(T_k\).
Approach 1: Hedge each cash flow individually
Approach 2: PV hedge with a single forward
Approach 3: Duration matching
In practice, most firms use a mix: exact hedges for large near-term flows, aggregate hedges for more distant flows.
US firm receives GBP cash flows over three years:
| Year | Cash flow (GBP M) | PV factor (at 5%) | PV (GBP M) |
|---|---|---|---|
| 1 | 10 | 0.952 | 9.52 |
| 2 | 15 | 0.907 | 13.61 |
| 3 | 20 | 0.864 | 17.28 |
| Total | 45 | 40.41 |
Duration \(= \frac{9.52 \times 1 + 13.61 \times 2 + 17.28 \times 3}{40.41} = \frac{88.58}{40.41} \approx 2.19\) years
Hedge options: (a) three separate GBP forwards, or (b) one forward for GBP 40.41M at \(\sim 2.19\) years.
Forwards (primary tool): OTC, fully customizable (amount, date, currency), no upfront cost, counterparty credit risk
Futures (exchange-traded): standardized sizes and dates, margin requirements, daily marking-to-market, no counterparty risk (clearinghouse)
Natural hedges: match FC revenues with FC costs — borrow in FC, source inputs in FC, locate production abroad
NDFs (non-deliverable forwards): for currencies with capital controls (CNY, BRL, INR, KRW). Cash-settled in USD at a reference fixing rate.
Preview: Options provide nonlinear protection — useful when exposure is uncertain or asymmetric. Full treatment in a later lecture.
| Exposure type | Primary instruments | Notes |
|---|---|---|
| Transaction | Forwards, futures | Known amount, known date |
| Operating | Forwards (for estimated \(b\)) + operational hedges | \(b\) is estimated; combine financial and strategic responses |
| Translation | Often unhedged | Accounting, not economic; if hedged: balance sheet hedges |
Key principle: The instrument should match the exposure.
Certain, near-term FC flows \(\Rightarrow\) forwards (precise hedge)
Uncertain, long-term competitive effects \(\Rightarrow\) operational hedges + partial financial hedges
Accounting effects \(\Rightarrow\) evaluate whether hedging is worth the cost
Risk \(\neq\) exposure. Risk is market-wide; exposure is firm-specific.
Three types: transaction (easy), translation (mostly ignore), operating (hardest, often largest)
The exposure regression \(V = a + bS + u\) is the unifying framework
Operating exposure can exist even with zero FC-denominated cash flows
Multiple FC cash flows: aggregate via PV, hedge with matching forwards
Next: Nonlinear exposure and FX options — when forwards are not enough.
