Theory Lecture 3 Flashcards
Firms operating outside of home market are exposed to exchange rate changes. What are the risks associated with it?
A. Transaction risk: gains/losses when monetary transactions are settled in foreign currency
B. Translation risk: a bookkeeping issue related to own currency value of A/L
• Both risks have consequences for the value of the multinational firm!
FX vs. equity from risk prospective
Equity prices are roughly log-normal (constant volatility, smooth changes in prices w/o
jumps).
• None of this is true about FX rates.
• Non-constant volatility and frequent jumps make the extreme outcomes more likely in
FX rates than in other assets.
• This makes FX rates notoriously hard to predict.
• FX returns display well-known anomalies such as forward discount bias.
Basic model of FX returns. How do we set it up?
• We set up a strategy by shorting a (riskless) domestic currency deposit (at 𝑖𝑡) and
invest (long) into (riskless) FX deposit (at 𝑖𝑡∗) to earn the return 𝑟𝑡
𝑓𝑥 =𝑠𝑡+1𝑒 −𝑠𝑡 − 𝑖𝑡 −𝑖𝑡∗ (in logs)
• With risk-neutral investors and efficient speculative FX market (𝑟𝑡 𝑓𝑥 =0), Uncovered
interest parity (UIP) holds
If we also cover FX risk by forward FX contract, Covered interest parity (CIP) holds :
𝒇𝒕 −𝒔𝒕 =𝒊𝒕 −𝒊𝒕
On what does the FX risk premium depend on?
➢The FX risk premium depends on the difference between the expected ratio of the SDFs and the ratio of their expectations
➢The FX risk premium depends on the conditional covariance of SDF across countries.
Key implication of EMH of FX market:
If the forward rate is an unbiased predictor of the future exchange rate (𝑠𝑡+1𝑒 =𝑓𝑡), then CIP holds and foreign exchange returns earn zero profits on average.
Is it possible that CIP and UIP deviates?
Theoretically, the deviations from the CIP,UIP are possible due to the non-rationality of market expectations, risk aversion of investors (when there 𝑖𝑡and/or 𝑖𝑡∗ are not risk-free), existence of transaction costs, market frictions, government interventions, and limits to speculation (excess return per unit of risk is large enough)
Tests of EMH involve a joint hypothesis. Why
Due to assumptions that:
FX market participants are, on average,
a) have rational expectations (by which 𝑆𝑡+1 =𝑆𝑡+1𝑒 +𝑢𝑡+1and the forecast error 𝑢𝑡+1 is
independent of the information at time t, 𝐸(𝑢𝑡+1 𝐼𝑡+1 =0) and
b) risk-neutral.
What is “Forward discount bias“?
Many studies (starting from Fama ’84 JME) find 𝛽1 typically close to minus unity.
Why the forward discount bias is an anomaly
• Intuitively , the result 𝑠𝑡+𝑘 −𝑠𝑡 =∆𝑠𝑡+𝑘=−1 𝑓𝑡 −𝑠𝑡 implies that the forward premium
𝑓𝑡 −𝑠𝑡 mispredicts the direction of the subsequent change in the spot rate ∆𝑠𝑡+𝑘.
• It also means that the vol of FX return is larger than vol of ER changes!
Empirical tests of EMH in FX market based on arbitrage/CIP found:
➢A negative relationship between the forward premia and future ER.
➢The FX risk premia are more volatile than the changes in ER.
➢The FX risk premia change signs over time.
• We need models that account for these findings!
Typically we see the vol of consumption stable and approx. 20X smaller than vol of the FX risk premia (Mark ’85 JME). Models need to generate high vol in SDF.
FX returns need to generate the following empirical regularities:
➢A negative relationship between the forward premia and future ER.
➢The FX risk premia are more volatile than the changes in ER.
➢The FX risk premia change signs over time.
Conceptually, the models need to achieve high variability in the marginal utility of
consumption (SDF is a function of consumption; and FX return is a function of SDFs).
But empirically, cons. is not sufficiently volatile (Mark ‘85 JME)
Earlier approaches found that: (on FX premium)
➢Tweaking the standard model (standard utility, iid consumption growth) was not
enough.
More recent work uses more currencies in carry strategies with rebalancing and Epstein
& Zin ’89 preferences(utility function).
pstein & Zin ’89 preferences are recursive,
• investors care about both expected utility and variance of utility (a trade-off).
• Popular in macro and finance now.
• EZ generate higher risk aversion and larger time-varying risk premium
➢Focusing on portfolios of currencies in carry-trade strategies and the cross-sectional
and time variation in predictable FX returns fit the data better.
Incorporating a low-frequency factor in the FX returns, “Peso problem”(Rare events, crash premia, and skewed returns)
▪ Risk-neutral investors anticipate switch from an appreciating to a depreciating FX regime.
➢Bias the Fama’s𝛽1 to -1, measured risk premium –upward (Evans & Lewis ’95 RFS).
▪ The FX options have the “volatility smile.” (Figure) Higher price of out-of-money FX options because
they help hedge the rare FX jumps (Bakshi et al. ‘08 JFE).
➢This hedging is predictive in calm times (Burnside et al. ’11 RFS) but is eliminated when Fin Crisis 2008 (a rare event) happened (Jurek ‘09).
Incorporating a low-frequency factor in the FX returns, the “crash risk” (Rare events, crash premia, and skewed returns )
Incorporating a low-frequency factor in the FX returns, the “crash risk”
▪ Risk-averse investors want hedge against a rare global event (Farhi & Gabaix ’16QJE).
➢Fahri et al. ’09: disaster risk accounts for more than a 1/3 of FX risk premia in advanced countries
over 1996-2011.
▪ Carry-trades face occasional liquidity spirals (Brunnermeier & Pedersen ’09RFS)
➢Brunnermeier et al. ‘09 showed that carry trades exhibit negative skewness (infrequent large
reversals).
➢The skewness in carry-trade returns is priced in options so that there are no long-
term gains, consistent with a crash-risk interpretation.
