Uncovering the Hidden Quanto

Spreading Index Futures with different Currency Denominations

The advent of 24-hour trading in the global listed derivatives market creates opportunity to cross trade regional exposures against one another. While trading in the cash equity markets is largely confined to the local trading hours, benchmark stock index futures are virtually traded around the clock. CME E-mini S&P 500 futures, for example, have significant trading volume even during Asian trading hours.

With the ability to cross trade index futures, however, there are interesting characteristics that are not readily observable. One of these characteristics is the hidden currency risk associated with spread trading indexes with different currency multipliers. This risk is more transparent if the underlying index for the futures is the same, e.g. CME Japanese Yen- and US Dollar-denominated Nikkei 225 index futures. Indeed, this quanto risk phenomenon is well understood and documented.

The same risk due to currency/equity market interaction is present in general – particularly in the case of index futures with Asian-Pacific (APAC) currency multipliers. Due to the timing differences of the mark-to-market process, however, this risk is usually obscured from the trader.

E-mini S&P 500 Index Futures During Asian Trading Hours

Intuitively, global equity markets are highly integrated. Stocks across the world are widely owned by a diverse set of investors. Their valuation ought to be highly correlated. To prove the point is often difficult, however. The correlation between the daily returns of the Nikkei 225 and S&P 500 indexes, for example, is often reported to be in the range of 0.10 – 0.201. This is hardly congruent with the widely held belief of correlated global equity markets.

The oversight in this calculation appears to be the failure to account for the non-overlapping nature of the trading hours in the global equity market. In particular, APAC and U.S. equity market trades during the regions’ respective daytime hours. The daily index performance is measured at its closing index value from the previous day’s closing index value. Thus, the daily performances between U.S. indices and APAC indices is not synchronized at all. To prove the point, one can simply calculate the correlation of daily performance between the S&P 500 index and the E-mini S&P 500 Index futures with the latter measured at the close of Japanese trading hours. The correlation turns out to be 0.122.  Since E-mini S&P 500 futures track the S&P 500 index very closely, this shockingly low correlation feature can only be an artifact of the asynchronous returns measurement.

With this in mind, the correlation amongst the E-mini S&P 500 futures and local APAC stock market benchmarks can be more accurately calculated if the E-mini S&P 500 daily performance is calculated at the close of APAC hours.

1 The correlation of daily returns between Nikkei 225 and S&P 500 Index Futures was 0.14 for the sampling period of 3/1/2011 – 9/16/2016.

2 E-mini S&P 500 Index Futures prices are sample as the average mid-market price of the last minute of Japanese trading (1:00am EST/2:00am EDT depending on daylight savings time in the U.S.). The positions in the quarterly futures are rolled on the Monday prior to the expiration. The sampling period is 3/1/2011 – 9/16/2016.

Figure 1. Daily returns correlation between E-mini S&P 500 Index Futures and select APAC indexes

The correlation between the Hang Seng Index and the Hang Seng China Enterprise Index (HSCEI) tops the chart at over 0.90. This is not surprising, as the two indexes have a sizeable overlap of constituents and are based on stocks listed and traded in Hong Kong. The correlation amongst APAC indexes – Nikkei 225, KOSPI 200, TWSE, S&P/ASX 200, Hang Seng and HSCEI – are generally in the range of 0.51 – 0.64.

The correlation between E-mini S&P 500 index futures and the APAC indices3 are in the range of 0.62 – 0.71. This range of correlation estimate is actually in line or slightly higher than those between the APAC markets represented above. As such, E-mini S&P 500 futures can potentially be served as an overnight cross-hedge for APAC market exposures, noting that the liquidity of E-mini S&P will increase when European and U.S. trading hours start after the close of trading in Asia, when the liquidity of APAC Index futures dries up.

Secondly, the liquidity of E-mini S&P 500 index futures during APAC hours is comparable to the most liquid APAC index futures.

3 Correlation between E-mini S&P 500 index futures and Nikkei 225, KOSPI 200, TWSE and S&P/ASX 200 are measured using the average mid-market price of E-mini S&P 500 index futures in the last minute of trading leading up to the close of Japanese stock market (1:00 a.m. EST/2:00 a.m. EDT, depending on daylight savings time in the U.S.) Correlation between E-mini S&P 500 index futures and Hang Seng Index and HSCEI are measured using the average mid-market price of E-mini S&P 500 index futures in the last minute of trading leading up to the close of Hong Kong trading (3:00 a.m. EST/4:00 a.m. EDT, depending on daylight savings time in the U.S.)

Figure 2. Average Daily Turnover of APAC index futures and E-mini S&P 500 during APAC Trading Hours 4

4 E-mini S&P 500 futures volume is based on 8:00 a.m.-4:00 p.m. HKT.  All others are based on local trading hours.

Figure 3. Top-of-Book Bid/Ask Spread and Notional Quantity of E-mini S&P 500 index futures

Figure 3 illustrates the top-of-book liquidity of the E-mini S&P 500 during APAC trading hours. While the E-mini S&P 500 market during APAC trading is not as liquid as it is during European and U.S. trading hours, the top-of-book quantity still exceeds US$5 million while bid/ask spread is at 1.31 bps or below. The accessibility to E-mini S&P 500 futures opens the door for possible spread trading against those within the region is open.

Generally speaking, spread trading has to do with the belief that the valuation of two related assets are out of line, e.g. APAC stocks being temporarily over- or under-value relative to the U.S. stocks. As such, market participants buy one asset and sell the other. Index futures are convenient vehicles for such trades due to the fact that the principal amount of the transaction actually does not come into play. There is no need to convert the notional value of the trade from one currency to the other at trade settlement, or even arrange for financing under different currencies5. The financing component is already embedded in the futures contracts themselves. The performance of the trade is then only due to the changes in the value of the futures contracts themselves. An alternative interpretation is that the spread trade is already currency-hedged in the principal amount6.

5 Even allowing for the possibility of having to post initial margin on a foreign currency, given the magnitude of margin requirements for futures, the burden is greatly reduced.

6 If the underlying indexes have not moved, there would be no variation margin or P/L in the two index futures. As a result, no matter by how much the exchange rate has changed, the P/L of the spread trade is still zero. Thus, one can conclude that the principal amounts are currency-hedged.  It is equivalent to buying one stock portfolio and selling another stock portfolio while putting on a currency swap on the principal amount to remove the currency risk exposure.

Notwithstanding the convenience of the index futures as vehicles for spread trading, the differences in the currency denomination in the futures contract pose an interesting risk that is usually obscured. This is the subject of discussion in the ensuing part of this note.

Embedded Currency Risk in Cross-market Index Futures Spreads

The risk is best illustrated with an example. Imagine that a trader identifies a relative mispricing and wants to implement a trade of buying U.S. equities and selling Korean equities through index futures. Assuming that the trader has determined the correct ratio of contracts to use, the pair of futures position is put on: long E-mini S&P 500 and short KOSPI 200 index futures at KRX.

Recall that there is no currency transaction at the inception of the trade. As time elapses, the index futures drift.  As illustrated above, the global equity market is correlated, meaning that the S&P 500 and KOSPI 200 moves up and down together in general.  As such, the cash flow of the trade is as follows:

Global Equity Market Direction

Cashflow/P&L of long S&P 500

Cashflow/P&L of short KOSPI 200

Drifts Up

Receives Variation Gain in USD

Pays Variation Loss in KRW

Drifts Down

Pays Variation Loss in USD

Receives Variation Gain in KRW

While there is no currency risk in the principal amount, the net P/L result is nevertheless still exposed to currency risk. Namely, P/L in the two contracts are in different currencies. A foreign exchange trade is needed to convert them back to a single currency. When the global equity market is up, the trader is long USD short KRW. When the global market is down, the trader is short USD and long KRW. Assuming the “hedge ratio” was determined correctly, this residual FX position should be neutral…, namely, no particular FX gain/loss tendency. But is it true?

Examining the correlation between the FX market and the equity market, one would conclude that the strength of Korean Won (and, for that matter, most APAC currency excluding Japanese Yen) is positively correlated with the equity market. When the global equity market goes up, Korean Won tends to strengthen. When the equity market crashes, Korean Won tends to weaken as well. One can think of it as the “risk-on” or “risk-off” scenario, whereby all risky assets tend to float up and down together. Korean Won and other APAC currency are considered “risky assets”. Japanese Yen is the exception, of course, with its safe haven currency status.

Table 1. Correlation between strength of currency and S&P 500 and Realized Volatility under different VIX scenarios

 

Correlation Currency vs SPX

 

Realized Volatility

VIX

KRW

TWD

AUD

JPY

 

KRW

TWD

AUD

JPY

SPX

10-15

-0.24

-0.16

-0.19

0.34

 

7.7%

4.0%

9.8%

10.1%

9.0%

15-20

-0.47

-0.37

-0.45

0.34

 

7.4%

3.8%

10.5%

9.1%

13.6%

20-25

-0.58

-0.45

-0.54

0.34

 

9.0%

4.4%

12.2%

9.4%

18.4%

25-30

-0.79

-0.58

-0.72

0.25

 

11.2%

6.7%

14.7%

13.5%

26.1%

30-35

-0.60

-0.48

-0.74

-0.29

 

12.7%

4.9%

17.7%

8.9%

29.3%

Table 1 shows the correlation between the daily changes of currency exchange rate and the S&P 500 index. A negative correlation means that the currency tends to strengthen vs USD when the S&P 500 index goes up. Inspecting the correlation table, one can conclude that the APAC currencies tend to strengthen or weaken with the global equity market, as represented by the S&P 500. In fact, as the risk in the equity market increases, as indicated by the range of VIX, the magnitude of the correlation coefficients increases as well. This evident supports the view that APAC currencies are viewed as risk assets.

Japanese Yen is the lone exception in this table – its strength is negatively correlated with the equity market. When risk appetite wanes, money flows into Japanese Yen and its strength increases. In other words, it exhibits traits of safe haven currencies.

Back to the example of the spread trade in light of this correlation pattern – when the equity market drifts up, there is a tendency for KRW to strengthen and appreciate versus USD. This would magnify the losses in the short KOSPI side of the spread trade. Conversely, when the equity market drifts down or crashes, KRW tends to weaken and depreciate against USD. This would reduce the gain in the short KOSPI side of the spread trade. In other words, the currency/equity market correlation tends to work against the spread trade under both scenarios.

This phenomenon is particularly visible in the case of futures of the same index with multipliers of different currencies – CME Yen- and Dollar-denominated Nikkei 225 index futures being the prime example. Because the two futures are written on the same index, there is no relative value issue between the two futures as far as the underlying equity market is concerned. Thus, the entire price differential between the two contracts has to do with the different currencies in the multiplier. Since JPY tends to appreciate versus USD when the market declines, the USD-multiplier contract tends to outperform the JPY-multiplier contract after taking into consideration the currency effects. This outperformance is competed away by market participants by the USD-multiplier contract being bid up vs the JPY-multiplier contract. This phenomenon is well documented and CME Group has published an article on the topic.

In the case of two contracts trading at different venues and having different mark-to-market timings and banking cycles, the phenomenon is less obvious. However, the implication is clear: when the market volatility increases, the currency/equity market correlation increases and the size of the moves increases as well. This could introduce a sizeable tail risk that spread traders might not have anticipated given the leverage deployable with futures.

Strictly speaking, the index futures contracts are written on the local currencies and thus are not “quanto” contracts. Nevertheless, the embedded currency risk is somewhat akin to the quanto spread in Nikkei futures. This risk can be labelled as the “hidden” or “pseudo” quanto risk.

A Crude Mathematical Approximation of the Hidden Quanto risk

To further illustrate the nature of this hidden quanto risk, some mathematical notation is unavoidable. Since E-mini S&P futures (and options) are liquidity traded around the clock, it is chosen as the hedging vehicle in this derivation. Assuming the trade is going long on an APAC index and shorting the E-mini S&P 500 index futures, the P/L of the spread trade is depicted as follows:

P/L = ΔIND – H x ƒ x ΔES,

where

ΔIND

is the change in the APAC index futures;

H

is the hedge ratio, adjusted for the multipliers of the index futures;

ƒ

is the exchange rate8 at which the USD P/L in the E-mini S&P 500 index futures is converted back to the base currency of the APAC index futures; and

ΔES

is the change in the E-mini S&P 500 index futures.

8 To keep things tractable, f is assumed to have a quoting convention of number of local currency per 1 USD.

Note that all these variables except H are unknown at the time of the trade. They are, in fact, random variables that will resolve themselves in the future. The hedge ratio, of course, had to be determined prior to the trade and is dictated by the trader. One possibility is to run the usual regression analysis between the returns of the two index futures, after adjusting the return series corresponding to E-mini S&P with the currency translation.

By expanding the term ƒ around the most recent exchange rate of the currency and the movement in the exchange rate, ƒ0 + Δƒ , we can rewrite the P/L as:

P/L = ΔIND – H x (ƒ0 + Δƒ) x ΔES = (ΔIND – Hƒ0) – HΔƒΔES

Thus, the expected P/L can be written as:

E[P/L] = E[ΔINDHƒ0ΔES] – H x E[ΔƒΔES]

These expressions immediately provide two very interesting insights:

  • The expected P/L involves the term – H x E[ΔfΔES] , or covariance between the E-mini S&P returns and the change in the exchange rate. In other words, the P/L has a tendency to go one way, depending on the sign of the correlation. This is especially significant when the market is under distress, with the magnitude of the correlation as well as the volatilities increases simultaneously, as documented in table 1.

    As pointed out in footnote 6, the exchange rate here is quoted in terms of the APAC currency per 1 USD. As a result, a negative correlation coefficient between ƒ and E-mini S&P 500 index futures signifies a tendency of the APAC currency strengthening with the equity market. Thus, this term tends to be a positive number for KOSPI 200, TWSE, and S&P ASX/200, with its magnitude increasing with the volatility in the market. This is the “hidden quanto” effect.

    Of course, the spread trade in reverse, viz. short APAC index futures and long E-mini S&P 500, will then have an expected drift in its P/L that is negative. Market participants should pay attention to the direction of their spread trade that would lead to a negative drift.

  • Inspecting the first half of the first equation closely, it can be concluded that the E-mini S&P index futures hedge quantity, H x (ƒ0 + Δƒ), should actually vary with the returns of E-mini S&P since Δƒ is correlated with ΔES, vis. the hedge ratio should be adjusted along the way when the market moves. One can contemplate including some options on E-mini S&P index futures to automate the hedge adjustment.

While the spread position is maintained for a longer period of time, there could be a need to hedge the FX exposure generated along the way as well. Note that variation margins on both legs of the spreads are done in their respective currencies – therefore generating a concurrent FX position. Hedges can be established in the form of currency futures. In particular, Japanese Yen and Australian Dollar currency futures are liquidly traded at CME Group.

This note is concluded with a word of caution. Please be aware that the derivation above does not capture every possible detail that might be crucial in making a spread trade profitable. Rather, it is meant as a characterization of the hidden quanto risk and the factors driving the strength of such risk. Further analysis is advised.

Summary

Market participants frequently observe that APAC equity and currency tends to move in tandem. As illustrated in this note, a spread trade between APAC index futures and E-mini S&P 500 index futures is quite easy to execute given:

  • E-mini S&P 500 index futures is actively traded during APAC hours, with plenty of liquidity to execute both legs of the trade simultaneously;
  • Using index futures when spread trading equity across market obviates the need to hedge the principal currency risk – a very convenient feature of the trade;
  • However, not all currency-related risks are eliminated. The variation margin generates a temporary currency exposure. More importantly, the correlation between the currency and the equity market tends to create a P/L-drift for the spread trade, the direction of which depends on whether the currency is considered a risky asset or a safe haven;

With index futures spreading opportunities abound during the APAC hours, it pays to study the finer details of the trade and devise a complete hedging game plan.

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