Quantos are derivatives that settle in currencies different from the denomination of the underlying contract. Therefore, quanto index contracts for the S&P 500 provide information on the premia that investors are willing to pay for a currency’s risk and hedge value with respect to U.S. stocks. Currencies that command high risk premia and provide little hedge value should have superior future returns. These premia can be directly inferred from quanto forward prices, without estimation. Empirical evidence supports the case for quanto contracts as a valid signal generator of FX strategies.

Kremens, Lukas and Ian Martin (2017), “The Quanto Theory of Exchange Rates”, May 2017.

*The post ties in with this sites’ lecture on implicit subsidies.
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*The below are excerpts from the paper. Emphasis and cursive text have been added.*

### What is a quanto?

*A quanto is a derivative that settles in a currency that is different from the currency of the principal underlying instrument. For example, a quanto of the S&P 500 index can be a derivative that settles in euro. This means that the dollar value of the S&P 500 is translated into a corresponding amount in euros by using a fixed exchange rate. Hence, quantos depend both on primary asset prices and exchange rates. There are quanto futures contracts, swaps and options. The valuation of quanto derivatives depends on the expected joint distribution of the future exchange rate and future underlying contract price.*

“An investor who is bullish about the S&P 500 index might choose to go long a forward contract at time t, for settlement at time t + 1. If so, he commits to pay a fixed price at time t + 1 in exchange for the level of the index…A quanto forward contract is closely related. The key difference is that __the quanto forward commits the investor to pay a fixed price in units of currency i at time t+1, in exchange for the level of the index in units of currency i__ [*at that time*]… The quanto forward and conventional forward prices are equal if and only if currency i is uncorrelated with the stock index under the risk-neutral measure. Moreover, the quanto risk premium term…is directly revealed by the gap between quanto and conventional index forward prices.”

### Why are quantos valid predictors for FX returns?

“Investors’ expectations about currency returns can be inferred directly from the prices of…quanto contracts.”

“Consider, for example, a quanto contract whose payoff equals the level of the S&P 500 index at time T, denominated in euros. The value of such a contract is sensitive to the correlation between the S&P 500 index and the dollar/euro exchange rate. If the euro is strong relative to the dollar at times when the index is high, and weak when the index is low, then this quanto contract is more valuable than a conventional, dollar-denominated, claim on the index. We show that __the relationship between (currency i) quanto and conventional forward prices on the S&P 500 index reveals the risk-neutral covariance between currency i and the index__. Quantos therefore __allow us to determine which currencies are risky,in that they tend to depreciate in bad times, i.e., when the stock market declines, and which are hedges__. It is possible, of course, that a currency is risky at one point in time and a hedge at another.”

“The quanto theory decomposes currency forecasts into a component based on interest-rate differentials and a risk-based component inferred from quanto prices…Intuitively, one expects that __a currency that is (currently) risky should, as compensation, have higher expected appreciation__ than predicted by the uncovered interest rate parity, and that hedge currencies should have lower expected appreciation. Our framework formalizes this intuition. It also allows us to distinguish between variation in risk premia across currencies and variation over time: according to the theory, the relative importance of the two should be revealed by the behavior of quanto prices.”

“Investor concerns about peso events [*extreme values of stochastic discount factors or fear of massive depreciation*] should be reflected in the forward-looking asset prices that we exploit, and thus our __quanto predictor variable should forecast high appreciation for currencies vulnerable to peso events__, even if no such events turn out to happen in sample.”

“Our quanto predictor …does not require that one takes the perspective of a risk-neutral investor [*and*] possesses the three appealing properties…

- forecasts are determined by asset prices alone rather than on infrequently updated and imperfectly measured macroeconomic data…
- the forecast has no free parameters; with no coefficients to be estimated…perfectly suited to out-of-sample forecasting…
- the forecast has a straightforward interpretation.”

### What is the empirical evidence?

“We obtained forward prices and quanto forward prices on the S&P 500, together with domestic and foreign interest rates, from Markit; the maturity in each case is 24 months. The data is monthly and runs from December 2009 to November 2014 for the Australian dollar (AUD), Canadian dollar (CAD), Swiss franc (CHF), Danish krone (DKK), Euro (EUR), British pound (GBP), Japanese yen (JPY), Korean won (KRW), Norwegian krone (NOK), Polish zloty (PLN), and Swedish krona (SEK).”

“We test our approach by running panel currency-forecasting regressions, and__ find that the quanto predictor variable is strongly significant in both statistical and economic terms__. We also show that the quanto predictor variable – equivalently, risk-neutral covariance – substantially outperforms lagged realized covariance as a forecaster of exchange rates; and that it is a strongly significant predictor of future realized covariance.”

“We [*test*]…the out-of-sample predictive performance of the quanto variable…Since our data span a relatively short period (from 2009 to 2014) over which the dollar strengthened against almost all the other currencies in our dataset, __we focus on forecasting differential returns on currencies. This allows us to isolate the cross-sectional forecasting power of the quanto variable__ in a dollar-neutral way.”

“When the coefficient on the quanto predictor is fixed at the level implied by the theory, we end up with a forecast of currency appreciation that has no free parameters, and which is therefore…perfectly suited for out-of- sample forecasting…__We compute mean squared error and mean absolute error for the forecasts made by the quanto theory and by three competitor models__: uncovered interest parity, which predicts currency appreciation through the interest-rate differential; purchasing power parity… and a random-walk forecast. __The quanto theory outperforms all three competitors on both metrics__.”