International Finance

International Cost of Capital: ICAPM and Currency Risk Factors

Main Issues

• Why does international asset pricing differ from domestic?
• Computing returns across currencies: the domestic investor’s perspective
• The CAPM and the tangency portfolio argument

• Why CAPM breaks internationally: which market portfolio? FX risk?
• The 2×2 ICAPM framework with worked examples
• Currency risk factors: carry, dollar, momentum, volatility

• Connection: this gives us the discount rate for APV Step 1 (Lecture 10)

This lecture answers the question Lecture 10 left open: “What discount rate should we use for the base case in APV?” We build from the domestic CAPM, show why it breaks internationally, develop the ICAPM, and then move to modern currency factor models for practical implementation.

Why International Asset Pricing?

The Open Question from Lecture 10

• Lecture 10: APV framework for cross-border valuation

• Step 1 requires the unlevered cost of equity: \(r_{project}\)
• We left this open — now we answer it

• The challenge: international projects face risks that don’t arise domestically
  • Which market portfolio should we use? US? World? Local?
  • Does exchange rate risk carry a separate premium?

Lecture 10 established the five-step APV framework. Step 1 — the branch stage — discounts operating cash flows at the unlevered cost of equity. But we never said how to compute that rate. This lecture fills that gap. The next lecture (Country Risk) fills in APV Step 4.

Two Problems with Going International

Problem 1: Which market portfolio?

• A US firm evaluating a project in India:
  • Use the S&P 500? The BSE Sensex? MSCI World?
  • The answer depends on financial market integration

Problem 2: Exchange rate risk

• Is FX risk separately priced, or is it already captured in the market factor?
• The answer depends on product market integration (PPP)

These are not just theoretical — they give different discount rates

These two questions structure the entire lecture. Problem 1 is about the market portfolio (financial integration). Problem 2 is about whether we need a second factor for FX risk (product market integration / PPP). The 2x2 framework later combines these two dimensions.

International Diversification and Home Bias

• Cross-country equity correlations are lower than within-country
  • Diversification benefits are real and well-documented

• Yet investors hold 70–80% domestic equity (the “home bias puzzle”)
  • Information asymmetries, familiarity bias, institutional constraints
  • Hedging domestic consumption risk (if PPP fails)

• This puzzle matters for asset pricing:
  • If investors are home-biased, is the world CAPM the right model?
  • If they should hold global portfolios, domestic CAPM is wrong

We keep this brief — just enough to motivate why the choice of market portfolio matters. The home bias puzzle has been documented since French and Poterba (1991). Despite some decline over time, home bias remains large, especially in emerging markets.

Returns in International Markets

Computing Returns in Domestic Currency

A US investor buying German stocks earns two components:

1. Local return (\(r_{local}\)): the DAX return in EUR
2. FX return (\(\Delta s\)): the change in EUR/USD

Exact formula: \[r_{domestic} = (1 + r_{local})(1 + \Delta s) - 1\]

Approximation (for small returns): \[r_{domestic} \approx r_{local} + \Delta s\]

Key principle: We always evaluate returns from the perspective of the domestic investor

This is foundational. Everything that follows — CAPM, ICAPM, factor models — is about pricing assets in domestic currency terms. The cross-product term is usually small but can matter for high-volatility emerging market currencies.

Example: Local Return + FX Return

Scenario A: DAX returns 8%, EUR appreciates 5% against USD. The US investor earns approximately 13%. Scenario B: Same DAX return, but EUR depreciates 12%. The US investor loses 4% despite the positive local return. The FX component dominates!

Variance of Domestic Returns

The variance of the domestic return has three components:

\[\text{Var}(r_{dom}) = \text{Var}(r_{local}) + \text{Var}(\Delta s) + 2\text{Cov}(r_{local}, \Delta s)\]

Key implication: Even a risk-free foreign bond is risky to a domestic investor!

• German 1-year T-bill: riskless for a German investor
• For a US investor: \(\text{Var}(r_{dom}) = 0 + \text{Var}(\Delta s) + 0 = \text{Var}(\Delta s)\)
• EUR/USD can move 10–15% per year — far from riskless!

Unless PPP holds perfectly (which it doesn’t — Lecture 3)

This is why exchange rate risk must enter asset pricing. Different investors see different risk profiles for the same asset. A British investor sees the US T-bill as risky (GBP/USD fluctuates), while a US investor sees it as risk-free. This violates the homogeneous expectations assumption of the standard CAPM.

Why This Matters for Asset Pricing

• Investors in different countries see different risk–return profiles for the same asset

• This violates the homogeneous expectations assumption of the CAPM
  • The US investor’s tangency portfolio differs from the German investor’s
  • They disagree on which assets are “risky”

• We need a model that accounts for this heterogeneity

Two ingredients needed:

1. Which market portfolio to use (financial integration)
2. Whether FX risk is separately priced (product market integration)

This slide sets up the logical flow for the rest of the lecture. We first review the domestic CAPM to see where the homogeneity assumptions enter, then show exactly how they break internationally.

The Domestic CAPM

Mean-Variance Optimization

The efficient frontier shows the set of portfolios that maximize expected return for a given level of risk. Adding the risk-free asset creates the Capital Market Line. Every investor holds a combination of the risk-free asset and the tangency portfolio. Under homogeneous expectations, all investors agree on the tangency portfolio, so in equilibrium it must equal the market portfolio.

Tangency Portfolio = Market Portfolio

Homogeneous opportunities: all investors face the same assets and risk-free rate

Homogeneous expectations: all investors agree on means, variances, covariances

\(\Rightarrow\) Everyone holds the same tangency portfolio as their risky allocation

Equilibrium: demand = supply

\(\Rightarrow\) Tangency portfolio (demanded) = Market portfolio (supplied)

This is the key insight of the CAPM: in equilibrium, the market portfolio is the tangency portfolio

These assumptions are strong. Internationally, they’re even harder to justify because investors in different countries face different risk-free rates and see different returns on the same assets (in their own currency). That’s where the CAPM breaks.

The CAPM Equation

Risk is measured relative to the market portfolio:

\[\beta_j = \frac{\text{Cov}({\widetilde{r}}_j, {\widetilde{r}}_M)}{\text{Var}({\widetilde{r}}_M)}\]

The CAPM:

\[E[{\widetilde{r}}_j] = r_f + \beta_j \times \underset{\color{#2E86AB}{\small\textbf{market risk premium}}}{\bbox[#dbeafe,5px,border:1px solid #2E86AB]{\;(E[{\widetilde{r}}_M] - r_f)\;}}\]

• \(\beta = 0\): earn the risk-free rate (no systematic risk)
• \(\beta = 1\): earn the market return
• \(\beta > 1\): amplified market risk, higher expected return

The CAPM says that only systematic risk (beta) is priced. Idiosyncratic risk can be diversified away. This is the workhorse model for cost of capital estimation domestically. Beta services (Bloomberg, MSCI) provide estimates for industries and firms.

CAPM: Numerical Examples

Suppose the market premium is 5% and \(r_f = 2\%\):

\(\beta\)	Expected Return	Interpretation
0	2%	Risk-free rate
1	7%	Market return
2	12%	Aggressive (amplified risk)
\(-0.5\)	\(-0.5\%\)	Hedge asset (insurance)

• In practice: beta services provide estimates for industries/firms
• But they typically assume the CAPM holds country-by-country with the domestic market
• Is this the right benchmark? \(\rightarrow\) Not always!

The negative beta case is interesting — it means the asset moves opposite to the market, so it acts as insurance. Investors are willing to accept negative expected returns for this hedge property. Gold and some currencies can have negative betas in certain periods.

Why CAPM Breaks Internationally

Problem 1: Financial Integration

A country is financially integrated if:

• Firms borrow and raise funds in international capital markets
• Investors directly invest across borders
• Cross-border capital flows are substantial

If integrated (US, UK, Germany, Japan): benchmark = world market portfolio

If segmented (some EM with capital controls): benchmark = domestic market portfolio

Practical proxy for world market: Vanguard Total World Stock ETF (VT), FTSE Global All Cap Index, expense ratio 10bp

Financial integration means that assets are priced by global investors, not just local ones. In an integrated market, a stock’s expected return depends on its covariance with the world market, not the local market. Most developed markets are integrated; many emerging markets are partially or fully segmented.

Venus and Mars: Segmented Markets

Imagine two planets with the same currency (no FX risk for now):

Parameter	Mars	Venus
Risk-free rate	5%	5%
Market volatility	30%	30%
Risk aversion (\(\gamma\))	0.45	0.65

Expected returns on domestic markets:

\[\mu_M = 5\% + 0.45 \times 0.30^2 = 9.05\%\] \[\mu_V = 5\% + 0.65 \times 0.30^2 = 10.85\%\]

Sharpe ratios: 0.135 (Mars) vs. 0.195 (Venus)

This example, from the old lecture slides, is pedagogically powerful because it removes FX risk entirely. The only question is: does financial integration matter? Same assets, same volatility, but different risk aversion leads to different prices and expected returns.

Segmented: Cost of Capital Differs!

A project on Venus with \(\beta = 0.75\):

Venus investor (uses Venus market, premium = 5.85%):

\[E[r] = 5\% + 0.75 \times 5.85\% = 9.39\%\]

Mars investor (uses Mars market, premium = 4.05%):

\[E[r] = 5\% + 0.75 \times 4.05\% = 8.04\%\]

Same project, same beta, DIFFERENT cost of capital!

\(\Rightarrow\) When markets are segmented, who you are matters

This is the key insight. Under segmentation, the same project has a different cost of capital depending on who is valuing it. The Mars investor would accept a lower return because Mars is less risk-averse. This means an investment could be profitable for a Mars firm but not for a Venus firm — purely because of where the investor is based.

Integrated: Cost of Capital Is the Same

Now open the border — markets are financially integrated:

Parameter	Integrated World
Aggregate risk aversion (\(\gamma\))	0.53
World market return	7.38%
World market volatility	21.21%

Same project on Venus, \(\beta = 0.75\):

\[E[r] = 5\% + 0.75 \times 2.38\% = 6.79\%\]

\(\Rightarrow\) Same for both investors! Who you are doesn’t matter. Only systematic risk (relative to the world) is priced.

Integration lowers the cost of capital (6.79% vs 8-9%) because diversification across planets reduces the effective risk. The world portfolio has lower volatility (21.21% vs 30%) due to imperfect correlation. This is the core argument for financial globalization reducing the cost of capital in emerging markets.

Problem 2: Exchange Rate Risk

Now add different currencies. Ignore FX risk?

• If product markets are integrated (PPP holds):
  • No real exchange rate risk \(\rightarrow\) single-factor CAPM suffices
  • Just pick the right market portfolio (world or domestic)

• If product markets are not integrated (PPP fails):
  • Investors see different real returns on the same asset
  • A UK investor sees the US T-bill as risky; a US investor sees it as risk-free
  • \(\rightarrow\) Violation of homogeneous expectations

\(\Rightarrow\) Need an additional factor for FX risk

This is where Lecture 3 (PPP) feeds in. We showed that PPP fails dramatically in the short and medium run. Large and persistent deviations from PPP mean that real exchange rate risk is substantial. This is the second dimension of the 2x2 framework.

The Two-Factor International CAPM

When PPP fails and financial markets are integrated:

\[E[{\widetilde{r}} - r] = \underset{\color{#2E86AB}{\small\textbf{world market risk}}}{\bbox[#dbeafe,5px,border:1px solid #2E86AB]{\;\beta_W \times (E[{\widetilde{r}}_W] - r)\;}} \;+\; \underset{\color{#D45500}{\small\textbf{exchange rate risk}}}{\bbox[#fce7d6,5px,border:1px solid #D45500]{\;\beta_s \times (E[{\widetilde{s}}] + r^{FC} - r)\;}}\]

where:

• \(\beta_W = \frac{\text{Cov}(\widetilde{r}, {\widetilde{r}}_W)}{\text{Var}({\widetilde{r}}_W)}\) — world market beta
• \(\beta_s = \frac{\text{Cov}(\widetilde{r}, \widetilde{s})}{\text{Var}(\widetilde{s})}\) — exchange rate beta

\(\Rightarrow\) Two sources of systematic risk, two risk premia

This is the Adler-Dumas (1983) International CAPM. The first term is the standard global market factor. The second term captures the premium for bearing exchange rate risk. In principle, with N currencies, there are N exchange rate factors — but in practice we focus on the most relevant bilateral rate or use factor models (Part 6 of this lecture).

The 2×2 ICAPM Framework

Three Key Questions

Before applying the 2×2 framework, consider:

Q1: What if UIP holds (\(E[{\widetilde{s}}] + r^{FC} - r = 0\))?

• FX risk premium is zero \(\rightarrow\) \(\beta_s\) drops out; single-factor CAPM suffices

Q2: What if the carry trade is profitable?

• FX risk premium \(\neq 0\) \(\rightarrow\) \(\beta_s\) matters; sign depends on FX correlation

Q3: What if the firm hedges all its currency exposure?

• \(\beta_s = 0\) by construction \(\rightarrow\) FX term drops out
• Another reason hedging can be valuable (Lecture 6)

These three questions come from the video script and are very useful for building intuition. Q1: if UIP holds, there’s no compensation for bearing FX risk, so it doesn’t affect expected returns. Q2: the carry trade’s profitability is evidence that FX risk premia exist — recall Lecture 5 showed b = -0.88 on average. Q3: if the firm hedges, its equity returns are no longer correlated with FX, so beta_s becomes zero.

The Four Cases

This is the central organizing framework. The rows represent product market integration (whether PPP holds). The columns represent financial market integration (whether capital flows freely). Each cell gives a different pricing model with different inputs. Most developed-market pairs fall into Case 2 (FM integrated, PM segmented). EM pairs often fall into Case 4.

Case 1: Both Integrated (e.g., within EU)

Product markets integrated (PPP holds) + Financial markets integrated

1. Use your home currency risk-free rate
2. Use a global index as proxy for market portfolio
3. No FX risk — PPP eliminates real exchange rate risk
4. Run a univariate regression to estimate \(\beta_W\)

\[E[\widetilde{r}] = r_f + \beta_W \times (E[{\widetilde{r}}_W] - r_f)\]

This is just the standard CAPM with a global market portfolio

Case 1 is the simplest case. Within a currency union like the Eurozone, there’s no exchange rate risk and financial markets are highly integrated. The global CAPM applies. Estimate beta against a world index (MSCI World, VT ETF) and use the global equity premium.

Case 2: PM Segmented, FM Integrated (e.g., UK–US)

Product markets segmented (PPP fails) + Financial markets integrated

1. Use your home currency risk-free rate
2. Use a global index as proxy for market portfolio
3. FX risk matters — PPP deviations create real exchange rate risk
4. Run a multivariate regression for \(\beta_W\) and \(\beta_s\)

\[E[{\widetilde{r}}] = r_f + \beta_W(E[{\widetilde{r}}_W] - r_f) + \beta_s(E[{\widetilde{s}}] + r^{FC} - r_f)\]

If the company is perfectly hedged: \(\beta_s = 0\) \(\rightarrow\) reduces to Case 1

This is the most common case for developed-market cross-border projects. US-UK, US-Germany, US-Japan — all have integrated financial markets but PPP fails. You need two betas: one for the world market and one for the bilateral exchange rate. Note: if the firm hedges, the FX beta goes to zero and you’re back to the simple global CAPM.

Case 3: PM Integrated, FM Segmented (e.g., EU–Greece pre-crisis)

Product markets integrated (PPP holds) + Financial markets segmented

1. Use your home currency risk-free rate
2. Use the domestic market portfolio (financial markets are segmented)
3. No FX risk — PPP holds
4. This is just the single-country CAPM

\[E[\widetilde{r}] = r_f + \beta_M \times (E[{\widetilde{r}}_M] - r_f)\]

Back to the textbook domestic CAPM — but with a domestic benchmark

This case is less common but arises when countries share a product market (or PPP holds approximately) but capital markets are segmented. Pre-crisis Greece within the Eurozone might be an example: same currency, similar prices, but limited financial integration. The domestic market portfolio is the right benchmark.

Case 4: Both Segmented (e.g., UK–India)

Product markets segmented (PPP fails) + Financial markets segmented

1. Use your home currency risk-free rate
2. Use the domestic market portfolio (capital markets segmented)
3. FX risk matters — PPP deviations plus limited hedging options
4. Run a multivariate regression for \(\beta_M\) and \(\beta_s\)

\[E[\widetilde{r}] = r_f + \beta_M(E[{\widetilde{r}}_M] - r_f) + \beta_s(E[\widetilde{s}] + r^{FC} - r_f)\]

If the company is perfectly hedged: \(\beta_s = 0\) \(\rightarrow\) reduces to Case 3

This is the most complex case. Both product and financial markets are segmented. You need the domestic market beta (not global, because capital can’t flow freely) and the FX beta. Many emerging market pairs fall here: UK investing in India, EU investing in Latin America. Note I’m illustrating with just one exchange rate; in principle there should be one for each relevant currency.

Worked Example: Data

Country A investor valuing a project in Country B. Financial markets are segmented.

Quantity	Symbol	Value
Risk-free rate, Country A	\(r^A\)	3%
Risk-free rate, Country B	\(r^B\)	5%
E[return on A market]	\(E[{\widetilde{r}}_A]\)	10%
E[return on world market]	\(E[{\widetilde{r}}_W]\)	8%
E[exchange rate return]	\(E[\widetilde{s}]\)	1%
Var(A market)	\(\text{Var}[{\widetilde{r}}_A]\)	0.0324
Cov(project, A market)	\(\text{Cov}[{\widetilde{r}}_j, {\widetilde{r}}_A]\)	0.0432
Cov(project, FX)	\(\text{Cov}[{\widetilde{r}}_j, \widetilde{s}]\)	0.004
Var(FX)	\(\text{Var}[\widetilde{s}]\)	0.02

This is adapted from the old slides. The student needs to first determine which case applies, then compute the correct cost of capital. Financial markets are given as segmented. The question is: are product markets integrated or segmented?

Testing Product Market Integration

We estimate a PPP regression:

\[\ln\left(\frac{S_{t+1}}{S_t}\right) = -0.06 + 0.89 \times (I^A_{t,t+1} - I^B_{t,t+1})\]

• The slope coefficient (0.89) is not significantly different from 1
• The constant (\(-0.06\)) is not significantly different from 0
• \(\Rightarrow\) Cannot reject Relative PPP

Conclusion: Product markets are integrated

Financial markets segmented + Product markets integrated = Case 3

This is a key empirical step. To apply the 2x2 framework, you need to determine which case applies. Here we test PPP using the relative PPP regression. If the slope is close to 1 and the intercept close to 0, PPP holds and product markets are integrated. In this example, we cannot reject PPP, so we’re in Case 3.

Worked Example: Solution

Case 3: Domestic CAPM (FM segmented, PM integrated)

\[E[r_j] = r^A + \beta_A \times (E[{\widetilde{r}}_A] - r^A)\]

Compute beta against the domestic (A) market:

\[\beta_A = \frac{\text{Cov}[{\widetilde{r}}_j, {\widetilde{r}}_A]}{\text{Var}[{\widetilde{r}}_A]} = \frac{0.0432}{0.0324} = 1.333\]

Expected return:

\[E[r_j] = 0.03 + 1.333 \times (0.10 - 0.03) = 0.03 + 0.0933 = \mathbf{12.33\%}\]

Note: we used the domestic market premium, not the world market premium, even though we’re valuing a foreign project!

This is the punch line. Because financial markets are segmented, the relevant benchmark is the domestic market, not the world market. The investor’s own shareholders are the ones who need to be compensated, and they can only diversify domestically. If we had incorrectly used the world market (Case 1), we would have gotten a different answer.

Currency Risk Factors

The Practical Problem with Bilateral Betas

The 2×2 framework uses \(\beta_s\) for one bilateral exchange rate

But a multinational faces MANY currencies:

• A European firm with subsidiaries in the US, Japan, UK, Brazil…
• Cannot reliably estimate \(N\) separate bilateral betas

Solution: Factor models

• Identify common risk factors in currency markets
• Just as Fama-French replaced single-beta CAPM in equities
• A firm’s currency exposure can be decomposed into factor loadings

\(\Rightarrow\) From bilateral \(\beta_s\) to systematic factor exposures

This is the transition from theory to practice. The 2x2 framework is theoretically elegant but practically limited when firms face many currencies. Factor models solve this by identifying the common sources of risk that drive currency returns. This parallels the move from the CAPM to multi-factor models in equities.

From UIP Failure to Risk Factors

Recall from Lecture 5: UIP fails dramatically

• 75+ studies: average slope \(b = -0.88\) (should be \(+1\))
• \(\Rightarrow\) FX risk premia exist and are economically large

But how are they structured?

Key insight (Lustig, Roussanov, Verdelhan, RFS 2011):

• Sort currencies by interest rate into portfolios
• This sorting reveals systematic factor structure
• High interest rate currencies earn high returns \(\rightarrow\) carry factor

The cross-section of currency returns is not random — it has structure

This connects directly to Lecture 5’s empirical findings. UIP failure means there is a risk premium in currency markets. LRV (2011) showed that this risk premium has a cross-sectional structure: it’s not random which currencies earn high or low returns. Sorting by interest rates reveals a systematic pattern, just like sorting by book-to-market reveals value in equities.

The Carry Factor (HML)

Construction: Sort currencies into 6 portfolios by interest rate

• Long highest interest rate portfolio
• Short lowest interest rate portfolio
• The difference is the HML carry factor

Key statistics (LRV 2011):

	Mean Excess Return	Std Dev	Sharpe Ratio
HML Carry	3.31%	9.56%	0.35

• Positive returns most months — but severe crashes in crises
• “Picking up pennies in front of a steamroller”

The carry factor is the most important currency factor. It earns a positive average return because high interest rate currencies tend to appreciate (violating UIP), so you earn both the interest differential and the FX appreciation. But the distribution is highly negatively skewed — the returns come from many small gains and a few very large losses.

Carry Trade: Cumulative Returns

This figure shows the cumulative return of a G10 carry trade strategy (long high interest rate currencies, short low interest rate currencies). The upward trend is clear, but note the sharp drawdowns during crisis episodes. The GFC in 2008 was particularly devastating as safe-haven currencies (JPY, CHF) surged. The dollar factor (equal-weighted) shows the average return of holding foreign currencies vs USD.

Carry Trade: Crash Risk

The drawdown chart makes the crash risk visceral. Carry trades can lose 20-30% in a few months during crises. This negative skewness is the key risk characteristic. The carry premium is compensation for bearing this crash risk. This connects to Lecture 8’s options content: the carry trade payoff resembles selling put options — you collect small premiums but face large losses in tail events.

The Dollar Factor (DOL)

Average return of all currencies against the USD

• Captures broad dollar strength/weakness
• Acts as the “level” factor (carry is the “slope”)

When global risk appetite falls:

• USD strengthens (flight to safety)
• DOL turns negative; carry also crashes (high-yield currencies fall)

\(\Rightarrow\) DOL and carry are correlated but distinct

• DOL: directional dollar bet
• Carry: cross-sectional bet (long high minus short low)

The dollar factor captures the common component of all currency returns vs USD. It’s related to global risk appetite — when investors are risk-averse, they buy USD and sell risky currencies. DOL can be thought of as a “market factor” for currencies, analogous to the equity market factor.

Momentum and Volatility Factors

Momentum:

• Past currency winners continue to outperform (3-12 month horizon)
• Similar to equity momentum, but in FX
• Sharpe ratio \(\approx\) 0.45 — higher than carry!

Volatility:

• When global FX volatility spikes, carry crashes
• A “volatility innovation” factor captures this
• Negative correlation with carry returns
• Sharpe ratio \(\approx\) 0.30

These factors capture different dimensions of currency risk

Momentum in currencies was documented by Menkhoff et al. (2012). It’s distinct from carry — you can have a high interest rate currency with negative momentum (e.g., after a crisis). The volatility factor captures the idea that carry traders are essentially selling volatility insurance. When volatility spikes, they lose. These factors are not perfectly correlated, so they capture different risk dimensions.

Factor Sharpe Ratio Comparison

This comparison puts currency factors in context. Carry and momentum have Sharpe ratios comparable to or higher than US equity. But carry has much higher crash risk (negative skewness). Momentum has the highest SR but can also reverse sharply. The dollar factor has the lowest SR but captures the most common risk in currency markets. Together, these factors explain the cross-section of currency returns — just as Fama-French factors explain equity returns.

The Modern Factor Model

Replace bilateral \(\beta_s\) with systematic factor exposures:

\[E[rx_i] = \beta_{DOL} \times \lambda_{DOL} + \beta_{HML} \times \lambda_{HML} + \beta_{MOM} \times \lambda_{MOM} + ...\]

where \(\lambda\) are factor risk premia and \(\beta\) are factor loadings

Advantages over bilateral \(\beta_s\):

• Handles multiple currencies simultaneously
• Factors are tradeable (can be hedged)
• More robust estimation (fewer parameters)

A firm’s currency exposure = its factor loadings:

• High carry loading \(\rightarrow\) exposed to crash risk \(\rightarrow\) higher cost of equity
• Can hedge specific factors selectively

This is the practical payoff of the factor model approach. Instead of estimating N bilateral betas, you estimate factor loadings on a small number of tradeable factors. This is directly analogous to using Fama-French factors instead of estimating beta against every individual stock. A firm with subsidiaries in high-carry countries has a high HML loading, which increases its cost of equity.

Three Questions Revisited with Factors

Q1: UIP holds \(\rightarrow\) all factor risk premia = 0

• No compensation for currency risk \(\rightarrow\) factors don’t matter
• But UIP fails empirically, so this case is rejected

Q2: Carry trade profitable \(\rightarrow\) \(\lambda_{HML} > 0\)

• Firms exposed to high-carry currencies face higher cost of equity
• This is compensation for bearing crash risk

Q3: Firm hedges FX \(\rightarrow\) all currency factor loadings \(\rightarrow 0\)

• Factor exposures drop out
• Another reason hedging can reduce the cost of capital

These three questions from the 2x2 framework section map directly to the factor model. The carry factor premium is the modern, empirical answer to “is FX risk priced?” — yes, it is, and the price is compensation for crash risk. Hedging eliminates factor loadings, which reduces the cost of equity. This connects back to Lecture 6’s argument that hedging can increase firm value.

Connection to Valuation

This Gives Us the APV Discount Rate

Lecture 10 established the APV framework:

\[V^{APV} = \underset{\text{Step 1: Base case}}{\sum_t \frac{E[\text{FCF}_t]}{(1 + r_{project})^t}} + \text{PV(financing)} + \text{Country risk adj.}\]

Now we can fill in \(r_{project}\):

1. Determine the integration case (2×2 framework)
2. Estimate the appropriate betas (market + FX or factor loadings)
3. Apply the correct ICAPM formula

The rest of APV (Steps 2–5) is unchanged from Lecture 10

This is the payoff. We’ve now answered the question Lecture 10 left open. The discount rate for APV Step 1 comes from the ICAPM, applied to the appropriate integration case. For most developed-market projects, this means Case 2 (global CAPM + FX factor).

EuroCorp Revisited

Recall from Lecture 10: EuroCorp (German) evaluating a US project

US–Germany: PM segmented (PPP fails), FM integrated = Case 2

\[E[r] = r_f^{EUR} + \beta_W(E[r_W] - r_f^{EUR}) + \beta_s(\text{FX premium})\]

If EuroCorp hedges its USD exposure:

• \(\beta_s = 0\) \(\rightarrow\) reduces to global CAPM
• This is how we justified the 10% unlevered cost of equity in Lecture 10

If EuroCorp does not hedge:

• USD/EUR exposure adds a risk premium (positive or negative depending on \(\beta_s\))
• Cost of equity differs from the hedged case

This closes the loop with Lecture 10. The 10% USD unlevered cost of equity we used in the EuroCorp example comes from applying the global CAPM (Case 2, hedged). If the firm doesn’t hedge, the cost of equity changes. This also connects to Lecture 6: hedging affects the cost of capital, not just cash flow volatility.

Summary

Domestic CAPM: one factor (market), homogeneous expectations

\(\rightarrow\) International CAPM: two factors (world market + FX), PPP deviations

\(\rightarrow\) Factor models: carry, dollar, momentum, volatility

Framework	When to Use	Inputs
Domestic CAPM	FM segmented, PM integrated	\(\beta_M\), domestic premium
Global CAPM	FM integrated, PM integrated	\(\beta_W\), global premium
ICAPM (2-factor)	FM integrated, PM segmented	\(\beta_W\), \(\beta_s\)
Factor model	Multi-currency exposure	Factor loadings

Next lecture: Country Risk — the other missing piece (APV Step 4)

The progression from CAPM to ICAPM to factor models reflects increasing realism. The domestic CAPM is the simplest but most restrictive. The ICAPM adds FX risk. Factor models are the most practical for multinationals. Together with Lecture 10 (valuation framework) and the next lecture (country risk), this completes the three lectures on the investment decision.

Course Connections

• Lecture 3 (PPP): PPP failure is why we need the FX factor
• Lecture 5 (UIP): UIP failure means FX risk premia exist (carry trade evidence)
• Lectures 6–8 (Hedging): Hedging eliminates \(\beta_s\) — reduces cost of capital
• Lecture 9 (Financing): Basis affects cost of debt; this lecture addresses cost of equity
• Lecture 10 (Valuation): This fills in the discount rate for APV Step 1

Next: Country Risk completes the APV framework (Step 4)

• How should country risk enter valuation?
• Adjust cash flows or discount rates?
• The “500bp fallacy” revisited

The course architecture is now visible. Lectures 1-5 built the macro/market foundations. Lectures 6-9 covered the three firm decisions (hedging, financing). Lectures 10-12 complete the investment decision: valuation framework (L10), discount rate (L11), and country risk adjustments (L12). Each lecture draws on and extends what came before.