Predictability and mispricing/good deals in currency markets Richard Levich (New York University)Valerio Potì (Dublin City University) Presented by Valerio Poti’ Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore, Pisa 12 November 2010
FX determination puzzle • Meese and Rogoff (JIE, 1983): exchange rate disconnect puzzle (‘Houston, we have a problem’) • Engel and West (2004, 2005): disconnect not as bad as you think, fundamentals do not need to forecast exchange rates (‘Hang on Houston, problem solved!’) • Lyons and Moore (JIMF, 2006), Brennan and Xia (RFS, 2006): disconnect is bad if you compare volatilities of fundamentals and exchange rates (‘Sorry Houston, we still have a problem’)
Flexible-Price Monetary ModelExcess Exchange Rate Volatility • Volatility of the US$/GB£ exchange rate vs. the volatility of the US-GB money growth rate differential:
What we are asking • We want to make inferences on mispricing in FX markets (and once we’ve fine tuned the techniques, also in other ones) • The benchmark for no mispricing is pricing in accordance with RE and ‘plausible’ assumptions about decision making under uncertainty, • That is, we look at the strong-form EMH and the in-sample exchange rate properties it implies • Why? We want to tell you guys to what extent (if any) RE gets and E(U) get it wrong so you can devise a better theory
A peek preview of the main results • Some mispricing but…nope, prices (exchange rates) are not really badly out of whack with RE, at least when you make realistic assumptions about the environment in which trading takes place • They wander a bit though around a RE benchmark, and you’d wonder what this wandering is about…learning?, search for the right heuristic?, cycles in ‘supply’ of skilled investors?
The pricing problem…a potentially ill posed one • From no arbitrage, mt+1 > 0 exists s.t. Pt= Et(mt+1xt+1) = Et*(xt+1) m(s) = q(s)/p(s) This can be solved for the expected excess-return that rational investors should equate to their own required rate of return, and in so doing they fix the state prices q(s) and thus, given p(s), Pt and mt+1 The problem is that a pile of combinations of Q(s) and P(s) are observationally equivalent, i.e. give you the same traded price Pt given payoff xt+1!!!
Variance of conditional mean excess-returns Coefficient of determination of ‘true’ (consistently estimated) reduced form representation of DGP Variance of excess-returns on asset with payoff xt+1 The tight link between predictability and discount factor volatility: an upper bound • Straight from Pt= Et(mt+1xt+1), We don’t know everything about mt+1 but we do know a thing or two, so we can look at predictability to make inferences on EMH/mispricing
Deriving the bound I • From Pt= Et(mt+1xt+1),
Deriving the bound(s) II • Dividing through by the variance of the asset excess-return, • And, by the Cauchy–Schwarz inequality:
What about the kernel? • Two possibilities: • We know the strategies/factors that span the MV frontier, in which case m is any kernel that prices them • We know the IMRS of the marginal trader and use the fact that, as shown by Ross (2005), σ(m) ≤ σ(IMRS) for the least volatile m • In either case we rule out “good deals”, e.g. Cochrane and SaàRequeio (JPE, 2000), Cerný and Hodges (2001).
The currencies we consider • Exchange rates against the US Dollar of : • Australian and Canadian Dollar (AUD and CAD, respectively) • the Euro (denoted as ECU/EUR because we combine data on the ECU before the introduction of the Euro and on the latter after its launch) • Japanese Jen (JPY) • British Pound (GPB) • Swiss Franc (CHF) • Our benchmark dataset uses currency futures prices on these currencies, but we also consider spot rates
We assume (hope) DGP can be represented as simple ARMA(p,q) reduced-form model • DGP: • Reduced form model:
From estimated mean returns to Max SRs strategies • We can attain the max SR by using the estimated t as a filter, constructing an inter-temporal portfolio with ‘time weights’ wt
Max SR2 is an upper bound to R2 • R2 is approx. the squared max SR • We also prove that the excess-return on an asset satisfies the predictability bound for a given pricing kernel iff that kernel prices the Max SR strategy
Excess-returns on predictability-based max SR strategies for each currency, strategies that mimic the trading action of a trader endowed with RE whose aim is to generate the largest attainable SR by trading a currency at a time Max SR strategies vs. F-F factors(1988-2006, t.c. = 2 bps)
Overall max SR strategy tracks well the AFX index of Lequeux and Acar (EJF , 1998)
Overall max SR strategy vs. ‘carry trade index’ of Lustig et al. (2007)
Excess-predictability relative to • Meese and Rogoff (JIE, 1983): exchange rate disconnect puzzle (‘Houston, we have a problem’) • Engel and West (2004, 2005): disconnect not as bad as you think, fundamentals do not need to forecast exchange rates (‘Hang on Houston, problem solved!’) • Lyons and Moore (JIMF, 2006), Brennan and Xia (RFS, 2006): disconnect is bad if you compare volatilities of fundamentals and exchange rates (‘Sorry Houston, we still have a problem’)
Lots of time-variation in excess-predictability (net of sampling error) Note: Not as bad as it looks for EMH! Consecutive excess-predictability episodes are rare, i.e. the market corrects within a few months at most.
Stylized facts summary • Evidence of statistically significant excess-predictability in terms of ‘alphas’ but not so much SRs • This is economically significant net of realistic transaction costs, i.e. a RE investor would find it attractive • The marginal currency trader seeks SRs but leaves ‘alphas’ on the table • Why?
A ‘Limits to Speculation’ story? • We conjecture ‘limits to speculation’ à la Lyon • Gathering and exploiting available public AND private information about exchange rate fundamentals requires specialization to exploit economies of scale and scope • It means that traders cannot take ‘marginal’ positions in currencies, they must invest in ‘size’ and thus take on diversifiable risk as well as undiversifiable risk (hence, the emphasis on the SR) • These currency traders are likely capital-constrained due to incomplete contracting and agency costs (hence, max SR should vary inversely with the availability of risk capital)
Does risk-capital matter? • Swamy’s (1970) ‘Random Coefficient’ panel regressions of the BVIs against their own lags and three alternative sets of regressors (Panel A, B and C):
Conclusions • Lots more ‘alpha’ for longer periods, evidence that FX traders seek reward for total not systematic risk. • Excess-predictability is declining but still present, despite profitability of popular trading rules has disappeared (?) for main currencies, e.g. Taylor (2005). • Markets more weak-form efficient but not more strong form efficient? This needs further investigation. • Most obvious patterns are cyclicality, in agreement with Lo’s (JPM, 2004) AMH, and role of risk-capital.
Extensions I (boring ) • Can we explain excess-predictability further? • Economic cycle, microstructure issues and/or order-flow (e.g. COT reports)? • Central Banks? LeBaron (JIE, 1998) found that excess-profitability of MA trading rules disappears when Fed is not active, what about more general forms of mispricing? Opportunity to compare impact of Fed and ECB
Extensions II (exciting ) • Lo’s (2004) AMH vs. Fama’s (1970) EMH: • Need to formally test whether excess-predictability is trending downwards, e.g. Neely, Weller and Ulrich (JFQA, forthcoming) • Can we match bursts of excess-predictability with regime changes, e.g. along the lines of Killeen, Lyons and Moore (2000)? • Learning or reflexivity?
Concluding thoughts: learning vs. reflexivity • What if traders do not recurringly re-learn to process information after a regime change but instead every so often they ‘imagine’ new regimes? • Financial media and think tanks as possible intermediaries of reflexive influences between traders, economists and the economy • It basically means that it is much harder to define such thinks as “fundamentals”, “fair value”, “long tern economic value”, etc. • Implications for ‘synchronization risk’ studied by HF literature • Soros’ (2009) General Theory of Reflexivity (!) radical take • In this setup, neither financial markets nor the economic profession and the media are side shows • Lots of scope for interdisciplinary discourse/research here • A case of extreme ‘coordination failure’ and ‘non anchored expectations’ or is it ‘reality’ reminding us dismal scientists about what being humans is all about?
Joint hypothesis problem • The null is typically EMH + asset pricing/FX determination model, • i.e. H0 : ‘μt+1 E(rt+1|It) = kt+1’ • What about H0 : EMH + ‘|kt+1| ≤ boundk’? • i.e., H0 : ‘|μt+1| ≤ boundk’? • First, will recast ‘|μt+1| ≤ boundk’ as
What we are not asking • Not concerned with out-of-sample forecastability, we don’t need it • Cochrane (2005, p. 396), “‘excess volatility’ is exactly the same thing as (abnormal) return predictability” • The point is that RE investors know the DGP • Why not look at out-of-sample forecastability too, since we are at it? • Because of our (of us econometricians) coarse information set, that would be at best a test of weak-form EMH and plenty has already been done on it, e.g. Neely et al. (2007)
A curious finding! • The international finance/asset pricing disconnect puzzle • The connection between excess-predictability and possible currency mispricing was well known to earlier researchers, e.g. Obstfeld and Rogoff (2000). • Recent work in the broad international finance domain, with the emphasis placed on out-of-sample forecast when making inferences about the EMH, seems less aware of this connection.
Some perspective • Economy Max SR: • CAPM world (RRArepr. inv = 2.5): • Higher-moment CAPM or ICAPM (RRArepr. inv = 5):
Transaction costs • Not all predictability is exploitable, not even by an investor endowed with RE, due to transaction costs. • Turns out that the maximal SR attainable by exploiting predictability is approximately the maximal R2 of predictive regressions • We can assess implications of transaction costs by looking at impact on SRs of max SR strategies. • We find that, unlike daily predictability, monthly predictability is ‘robust’ to transaction costs
‘Time-weights’ of CAD max SR strategies (95-06) Daily: (Strategy drowns in transaction costs) Monthly: (Transaction costs not much of a problem)
Sampling error estimate • We compute a lower bound on the 5th percentile of the distribution of estimated excess-predictability. • This is done by subtracting, from the point estimate of the latter, (an upper bound of) the 95th percentile of the R2 distribution under OLS assumptions and the null of no explanatory power:
Open Issue • Little question: how do you capture very high order lag auto-correlation? (plot refers to serial correlation of CAD at lags 1-200) • Fractionally integrated ARMA (ARFIMA), else?