**Francesca Brusa (Oxford)
Tarun Ramadorai (Oxford and CEPR)
Adrien Verdelhan (MIT Sloan and NBER)**

*March 2015*

- Large increase in financial integration over the past 30 years.
- Aggregate foreign equity holdings, as a % of global GDP: from 3% in the 1980s to approximately 30% in 2011.
- Foreign equity holdings of the U.S.: $6 trillion.

**What are the expected returns on those foreign equity holdings?**- Finance logic:
- If an asset’s return tends to be low in bad times, the asset is risky. Its expected return should be above the risk-free rate.

- Finance logic:
- How to measure bad times?
- I Capital Asset Pricing Model (CAPM): Aggregate market return

- How to compare returns?
- Foreign equity returns are in foreign currencies

- Exchange rate risk should matter. . .
- When investors invest abroad, but consume at home, and domestic and foreign purchasing powers differ.

- Yet, empirical evidence is diffcult to obtain.
- International CAPM of Dumas and Solnik (1995): world stock market return + three bilateral exchange rates (Yen, Mark, and Pound).

- Recent findings: Two risk factors account for a large share of systematic changes in bilateral exchange rates
**Idea:**Instead of using raw bilateral exchange rates, use currency risk factors that summarize their systematic variation.

- 1. Three factors describe the time-series of foreign equity benchmark returns
- Smaller difference between expected and realized returns than in the competitors’ models (World CAPM, International CAPM, and Fama-French factors)

- 2. Those three factors account for a large share of foreign equity mutual funds’ and macro/emerging hedge funds’ returns
- 3. A simple reduced-form model to study the interaction between currency and equity risk

- World CAPM:
- Sharpe (1964) and Lintner (1965) to Stehle (1977), Solnik (1974), . . .
- Korajczyk and Viallet (1989), Harvey (1991), Chan, Karolyi and Stulz (1992), Bekaert and Harvey (1995), Karolyi and Stulz (1996).

- International CAPM:
- Solnik (1974), Sercu (1980), Stulz (1981), Adler and Dumas (1983), . . .
- Bekaert and Hodrick (1992), Ferson and Harvey (1993), Ferson and Harvey (1994), Bekaert (1995, 1996), Dumas and Solnik (1995), De Santis and Gerard (1998), Harvey, Solnik, and Zhou (2002)

- New equity factors and frictions:
- Chaieb and Errunza (2007), Bekaert, Harvey and Lundblad (2007); Hou, Karolyi, and Kho (2011), Karolyi, Lee and van Dijk (2012), Karolyi and Wu (2014), Malkhozov, Mueller, Vedolin, and Venter (2014)

- Currency drivers:
- order

ows (e.g., Evans and Lyons, 2002, and Froot and Ramadorai, 2005) and risk factors (e.g., Lustig, Roussanov and Verdelhan, 2011, 2014, Menkhoff, Sarno, Scheming, and Schrimpf, 2012, Maggiori, 2012, Lettau, Maggiori, and Weber, 2013, and Verdelhan, 2014)

- order

- Empirical evidence:
- Equity benchmark indices
- Hedge funds and mutual funds

- Theoretical framework:
- Intuition
- Replication in a reduced-form model

- Conclusion

- Test assets: from 46 developed and emerging countries, spanning value, growth, and country index returns from

1/1976 to 12/2013. - Risk factors: global equity factor (built from local currency equity returns) and two currency factors: Dollar and Carry
- Estimation: time-varying betas obtained on rolling windows

- Other comparisons of the pricing errors:
- Histograms and kernel density estimates of rolling alphas
- Rolling mean absolute alphas

- Even if the market prices of risk are estimated (Fama-McBeth procedure), the CAPM Redux still compares favorably:
- the market prices of risk are positive and significant for our three factors
- equity risk is priced for the CAPM, International CAPM, and FF models, but not the other factors (except GBP); the prices of risk appear further removed from the mean of the risk factors.

- Subsamples:
- time-windows (increasing sizes starting from 1976 or backwards from 2013)
- test assets (country aggregates, developed vs emerging markets)
- length of the rolling windows

- Assume that financial markets are complete (thus log changes in exchange rates are differences in log SDF)
- Start from the law of motion of each SDF, which depends on country-specific and global shocks
- Assume that each country-aggregate dividend growth ratedepends on the same shocks as the SDF
- Two key assumptions:
- Prices of risk are time-varying (time-varying currency risk premia)
- One global shock affects all SDF in the same way (role for a pure equity risk factor)

- Simple and tractable reduced-form model:
- Interest rates, exchange rates, and price-dividend ratios in closed-forms, as well as realized and expected equity and currency excess returns, and equity and currency risk factors.

- Implications:
- The world stock market return in U.S. dollars depends on all global shocks.
- No role for bilateral exchange rates in theory
- But in the model the market price of global equity risk depends on several state variables.
- Those state variables are unknown to the econometrician.
- Quantities and market prices of risk evolve at different frequencies.

- Role for currency factors in practice, even in simulated data

- Three factors (Global Equity, Dollar, and Carry) describe the time-series of foreign equity benchmark returns.
- Predicted and realized equity excess returns are closer than in the competitors’ models.

- Currency risk matters for foreign equity mutual fund and \macro/emerging” hedge fund returns.
- Interaction between currency and equity risk in a simple reduced-form model:
- Time-variation in quantities and prices of risk is key.