# Troubled markets and volatility

### Challenging financial models through an exploration on the crash of Argentina’s ADRs

American Depositary Receipts (ADRs) are financial instruments that allow US investors to purchase stocks in foreign companies. Argentina has a number of companies listed in US exchanges through ADRs.

In this notebook, we will explore the performance of these ADRs with a focus on the period from January to August 2019, where political uncertainty sent markets into turmoil: the country’s Merval stock index fell 48% in dollar terms in a single day, the second-largest one-day drop in any of the 94 markets tracked by Bloomberg since 19501, causing a 20% devaluation of the Argentine peso and a sharp drop in bond prices.

We will be looking at the end-of-day data of the Argentine ADRs, and their corresponding put and call options, to examine whether the daily log returns of stocks are distributed normally, a conclusion that follows from the standard model due to Bachelier.

## Exploration

We begin our exploration of the end-of-day (EOD) data for Argentina’s ADRs.

Date
Symbol Close
High
Low
Open
Volume
2006-03-27 BMA $$23.05$$ $$23.05$$
$$22.23$$ $$22.89$$
$$1065200$$
$$15.52$$ $$15.52$$ $$14.08$$ $$15.42$$ $$1065200$$ $$0$$ $$1$$
2006-03-28 BMA $$22.38$$ $$22.47$$ $$21.90$$ $$22.47$$ $$1556100$$ $$15.07$$ $$15.13$$ $$14.75$$ $$15.13$$ $$1556100$$ $$0$$ $$1$$
2006-03-29 BMA $$22.84$$ $$23.14$$ $$22.05$$ $$22.10$$ $$641300$$ $$15.38$$ $$15.59$$ $$14.85$$ $$14.88$$ $$641300$$ $$0$$ $$1$$
2006-03-30 BMA $$22.75$$ $$23.10$$ $$22.70$$ $$23.00$$ $$293600$$ $$15.32$$ $$15.56$$ $$15.29$$ $$15.49$$ $$293600$$ $$0$$ $$1$$
2006-03-31 BMA $$22.93$$ $$22.93$$ $$22.35$$ $$22.83$$ $$113600$$ $$15.44$$ $$15.44$$ $$15.05$$ $$15.38$$ $$113600$$ $$0$$ $$1$$

The data is indexed by date, with the symbol column holding the ticker name, and columns for the open and close prices (the price of the symbol at the start/end of the market day) and the high and low prices seen for the symbol at that date.
We’ll begin plotting the adjusted close prices for each symbol (price adjusted for dividends payed and stock splits). The reset of the columns can be safely ingored for our purposes.

Daily ajusted close prices for Argentina’s ADRs (USD).

Let’s zoom in on the 2019 adjusted close prices.

Daily ajusted close prices for Argentina’s ADRs (USD) in 2019.

We can see most stocks experienced a sharp decline in August 2019, after a surprise result of the presidential primaries caused a market crash. We also see that MELI (MercadoLibre) is less vulnerable to the volatility in the Argentine market because it operates in over a dozen countries in Latin America. Symbol Count Mean Std Min 25% 50% 75% Max BFR $$4936$$ $$8.28$$ $$5.71$$ $$0.75$$ $$3.95$$ $$5.72$$ $$12.03$$ $$25.45$$ BMA $$3371$$ $$31.18$$ $$25.47$$ $$5.00$$ $$15.79$$ $$24.6$$ $$48.91$$ $$125.43$$ CEPU $$386$$ $$10.99$$ $$2.89$$ $$3.46$$ $$9.06$$ $$9.97$$ $$12.28$$ $$17.92$$ CRESY $$4936$$ $$9.94$$ $$3.95$$ $$2.92$$ $$6.75$$ $$9.47$$ $$12.01$$ $$21.64$$ EDN $$3099$$ $$15.31$$ $$12.47$$ $$1.71$$ $$6.33$$ $$12.11$$ $$20.25$$ $$62.55$$ GGAL $$4795$$ $$13.55$$ $$13.20$$ $$0.21$$ $$5.40$$ $$7.97$$ $$16.44$$ $$71.46$$ IRCP $$3971$$ $$15.63$$ $$14.42$$ $$1.29$$ $$4.38$$ $$10.02$$ $$21.43$$ $$62.22$$ IRS $$4936$$ $$10.07$$ $$5.63$$ $$1.90$$ $$6.13$$ $$8.54$$ $$13.28$$ $$32.17$$ LOMA $$449$$ $$14.07$$ $$5.36$$ $$5.40$$ $$10.34$$ $$11.74$$ $$21.12$$ $$25.02$$ MELI $$3025$$ $$138.09$$ $$126.90$$ $$8.02$$ $$59.11$$ $$93.59$$ $$153.61$$ $$69.01$$ NTL $$4519$$ $$13.15$$ $$8.40$$ $$0.39$$ $$6.55$$ $$12.76$$ $$18.68$$ $$51.70$$ PAM $$2479$$ $$21.47$$ $$18.06$$ $$2.85$$ $$9.89$$ $$14.59$$ $$30.80$$ $$71.65$$ PZE $$4608$$ $$5.87$$ $$2.46$$ $$1.52$$ $$4.36$$ $$5.37$$ $$6.72$$ $$14.55$$ SUPV $$816$$ $$15.18$$ $$7.34$$ $$3.16$$ $$8.92$$ $$13.91$$ $$17.84$$ $$32.37$$ TEO $$4936$$ $$12.20$$ $$6.37$$ $$0.38$$ $$7.64$$ $$12.43$$ $$16.01$$ $$35.96$$ TGS $$4936$$ $$4.00$$ $$4.34$$ $$0.29$$ $$1.62$$ $$2.46$$ $$3.51$$ $$20.52$$ TS $$4195$$ $$25.94$$ $$10.95$$ $$2.26$$ $$21.35$$ $$28.22$$ $$34.12$$ $$55.72$$ TX $$3408$$ $$20.25$$ $$6.30$$ $$3.27$$ $$16.04$$ $$19.85$$ $$24.57$$ $$39.30$$ YPF $$4936$$ $$21.58$$ $$9.67$$ $$3.16$$ $$14.03$$ $$21.59$$ $$29.67$$ $$47.31$$ ### Simple returns Next we’ll calculate the daily simple returns. $R_t \equiv \frac{S_t - S_{t-1}}{S_{t-1}} \%$ Date Symbol Close High Low Open Volume adjClose adjHigh adjLow adjOpen adjVolume divCash splitFactor Return 2006-03-27 BMA $$23.05$$ $$23.05$$ $$22.23$$ $$22.89$$ $$1065200$$ $$15.52$$ $$15.52$$ $$14.08$$ $$15.42$$ $$1065200$$ $$0$$ $$1$$ NaN 2006-03-28 BMA $$22.38$$ $$22.47$$ $$21.90$$ $$22.47$$ $$1556100$$ $$15.07$$ $$15.13$$ $$14.75$$ $$15.13$$ $$1556100$$ $$0$$ $$1$$ $$-2.91$$ 2006-03-29 BMA $$22.84$$ $$23.14$$ $$22.05$$ $$22.10$$ $$641300$$ $$15.38$$ $$15.59$$ $$14.85$$ $$14.88$$ $$641300$$ $$0$$ $$1$$ $$2.06$$ 2006-03-30 BMA $$22.75$$ $$23.10$$ $$22.70$$ $$23.00$$ $$293600$$ $$15.32$$ $$15.56$$ $$15.29$$ $$15.49$$ $$293600$$ $$0$$ $$1$$ $$-0.39$$ 2006-03-31 BMA $$22.93$$ $$22.93$$ $$22.35$$ $$22.83$$ $$113600$$ $$15.44$$ $$15.44$$ $$15.05$$ $$15.38$$ $$113600$$ $$0$$ $$1$$ $$0.79$$ Symbol Count Mean Std Min 25% 50% 75% Max BFR $$4936$$ $$0.053$$ $$3.67$$ $$-55.85$$ $$-1.73$$ $$0$$ $$1.69$$ $$46.76$$ BMA $$3371$$ $$0.08$$ $$3.28$$ $$-52.67$$ $$-1.49$$ $$0$$ $$1.65$$ $$27.01$$ CEPU $$386$$ $$-0.26$$ $$4.31$$ $$-55.92$$ $$-1.91$$ $$-0.32$$ $$1.58$$ $$16.88$$ CRESY $$4936$$ $$0.038$$ $$2.77$$ $$-38.09$$ $$-1.25$$ $$0$$ $$1.184$$ $$27.19$$ EDN $$3099$$ $$0.051$$ $$3.88$$ $$-58.98$$ $$-1.69$$ $$-0.031$$ $$1.63$$ $$27.55$$ GGAL $$4795$$ $$0.095$$ $$4.63$$ $$-56.12$$ $$-1.63$$ $$0$$ $$1.69$$ $$153.6$$ IRCP $$3971$$ $$0.14$$ $$4.23$$ $$-32.42$$ $$-0.68$$ $$0$$ $$0.85$$ $$36.99$$ IRS $$4936$$ $$0.016$$ $$2.68$$ $$-38.29$$ $$-1.25$$ $$0$$ $$1.21$$ $$18.08$$ LOMA $$449$$ $$-0.166$$ $$4.53$$ $$-57.30$$ $$-1.88$$ $$-0.087$$ $$1.51$$ $$22.65$$ MELI $$3025$$ $$0.16$$ $$3.57$$ $$-21.20$$ $$-1.40$$ $$0.084$$ $$1.59$$ $$36.00$$ NTL $$4519$$ $$0.082$$ $$3.34$$ $$-46.19$$ $$-1.32$$ $$0$$ $$1.37$$ $$30.00$$ PAM $$2479$$ $$0.06$$ $$2.96$$ $$-53.82$$ $$-1.42$$ $$0$$ $$1.41$$ $$16.94$$ PZE $$4608$$ $$0.066$$ $$3.91$$ $$-19.22$$ $$-1.46$$ $$0$$ $$1.42$$ $$179.84$$ SUPV $$816$$ $$-0.025$$ $$4.18$$ $$-58.75$$ $$-1.41$$ $$0$$ $$1.49$$ $$28.33$$ TEO $$4936$$ $$0.035$$ $$3.08$$ $$-33.38$$ $$-1.42$$ $$0$$ $$1.45$$ $$23.07$$ TGS $$4936$$ $$0.078$$ $$3.39$$ $$-48.03$$ $$-1.49$$ $$0$$ $$1.62$$ $$25.20$$ TS $$4195$$ $$0.085$$ $$2.53$$ $$-21.31$$ $$-1.18$$ $$0.11$$ $$1.35$$ $$21.57$$ TX $$3408$$ $$0.047$$ $$3.02$$ $$-19.68$$ $$-1.35$$ $$0.037$$ $$1.41$$ $$49.09$$ YPF $$4936$$ $$0.033$$ $$2.56$$ $$-34.05$$ $$-1.12$$ $$0$$ $$1.12$$ $$37.25$$ Let’s plot a histogram of the daily returns for each symbol. Histogram of daily returns. We see most returns cluster around 0, with a few outliers. Since we are interested particularly in the outliers, to see their quantity and magnitude, we can visualize them using a boxenplot. Daily returns per symbol. We can filter the days with 30% or larger movement in prices (either up or down). Large daily returns(+/-30%). Now if we remove outliers, say discard days where return was higher than 10% or lower than -10%: Histogram of daily returns (between -10% / +10%). ### Log returns In finance, it is common to look at the log returns of an asset. They are defined as follows: $r_t \equiv \ln{\frac{S_t}{S_{t-1}}} = \ln{S_t} - \ln{S_{t-1}}$ There is an equivalence between simple and log returns: \begin{align} r_t &= \ln{(R_t + 1)} \ R_t &= \exp{r_t} - 1 \end{align} You can find further information on the two return types in this post. Stock prices are assumed to follow a log-normal distribution, hence we should expect log returns to be distributed normally. $ln(S_T)\sim N\big[ln(S_0)+(\mu-\frac{\sigma^2}{2})T,\;\sigma^2T\big] \ ln(\frac{S_T}{S_0})\sim N\big[(\mu-\frac{\sigma^2}{2})T, \;\sigma^2T\big]$ Where $$S_T$$ is the price of the underlying at time $$T$$. For a more detailed discussion on the assumptions of the Black-Scholes-Merton model, see chapter 15 of Options, Futures and Other Derivatives (9th Ed) by John Hull. You can read more on the distribution of prices and returns here. Now we can calculate the volatility $$\sigma$$ for each symbol, defined as the standard deviation of log returns. As a comparison, we’ll add the daily volatility (from 2000 to 2019) for four of the so called blue chip stocks, Coca-Cola (KO), Goldman Sachs ($GS), IBM ($IBM) and Walmart ($WMT). Daily volatility for each symbol (std of log returns). We can see that Argentine stocks show much higher volatility than the blue chip stocks. Let’s plot the mean yearly returns for each symbol. Again, we’ll add the mean daily return of the US blue chips. Mean yearly returns of Argentina’s ADRs. As expected, besides increased volatility, Argentine stocks, for the most part, exhibit higher yearly returns than the chosen US stocks. ### A closer look at outliers Let’s plot the returns that are at least $$3\sigma$$ away from the mean. If log returns were truly distributed normally, then we should expect this group to represent only $$0.3\%$$ of the data, while the remaining $$99.7\%$$ should lie in the interval $$(\mu_r - 3\sigma_r, \mu_r + 3\sigma_r)$$. 3$$\sigma$$ outlier daily returns. We see a large number of outlier return days. To put that in perspective, let’s calculate the proportion of outlier returns for each symbol in the data, that is the number of days where $$3\sigma$$ returns where observed over the total number of observations. Outlier proportion (outlier daily return count / total daily returns). We see many more outliers than the expected $$0.3\%$$. For example,$MELI has almost 7 times more outlier return days than expected if we assumed normal log returns.

Finally, we’ll look at the cumulative log returns over time.

Cumulative log returns.

If you had invested in $MELI’s IPO in 2007, you’ve had have over 25 times your initial investment by August 2019. You would also have to stomach losing close to 60% at the end of 2008. ### ADR options and the volatility smile We’ve observed ADRs experienced a very high volatility, and this leads us to question wether the prices of financial derivatives such as options were affected. We will explore how volatility in the prices of the underlying assests impacted option prices during the crash. To this end, we will examine the options end-of-day data for the ADRs. Options are derivative contracts based on an underlying asset such as stocks. They offer the buyer the opportunity to buy or sell the underlying asset at a given price (or strike price). You can find more information on options in this article. quotedate underlying underlying_last exchange optionroot type expiration strike last net bid ask volume openinterest impliedvol delta gamma 2019-07-03 TEO 17.79 CBOE TEO190719C00002500 call 2019-07-19 2.5 0 0 13.0 17.8 0 0 0.02 1.28 0.0000 2019-07-03 TEO 17.79 CBOE TEO190719C00005000 call 2019-07-19 5.0 0 0 10.5 15.2 0 0 6.32 0.94 0.0045 2019-07-03 TEO 17.79 CBOE TEO190719C00007500 call 2019-07-19 7.5 0 0 8.0 12.8 0 0 3.57 0.93 0.0093 2019-07-03 TEO 17.79 CBOE TEO190719C00010000 call 2019-07-19 10 0 0 5.5 10.2 0 1 2.04 0.94 0.0156 2019-07-03 TEO 17.79 CBOE TEO190719C00012500 call 2019-07-19 12.5 0 0 3.0 7.8 0 199 1.28 0.92 0.0297 The options data is also indexed by date. These are the most important columns: • underlying: The ticker of the underlying asset. • underlying_last: The last quoted price of the underlying asset. • optionroot: The name of the contract. • type: Contract type (put or call) • strike: The price at which owner can execute (buy/sell underlying). • expiration: Date of expiration of the option. • bid: The price at which investor can sell this contract. • ask: The price at which investor can buy this contract. • openinterest: The total number of contract outstanding. • impliedvol: Volatility of the underlying as implied by the option price (according to BSM model) Let’s plot the volatility smile for each symbol at 2019-08-09, the Friday before the primaries. The volatility smile plots the implied volatility (IV, a measure of the volatility of an underlying security as implied by the option prices) at the different strike levels. We’ll plot the IV for puts and calls for each symbol. The dashed line represents the spot price. Volatility smiles - August 9th 2019. We see that as options move more at the money (ATM) their implied volatility drops. In contrast, options that are further out of the money (OTM) or in the money (ITM) have higher IVs. Now let’s try the same plot for the following Monday (2019-08-12). That day, the MERVAL (an index that tracks the biggest companies listed in the Buenos Aires Stock Exchange) crashed and lost close to 50% of its USD value. Volatility smiles - August 12th 2019. As stock prices droped sharply, we find less put contracts were being offered. Again, we see IV getting higher as the strike priced moves away from the spot price. ### Option price evolution Next, we’ll analyze how option prices changed during the month of August, 2019. Let’s find the 10 most actively traded options (those with the highest open interest) for each symbol at the start of the month. Ask price for most actively traded calls in August 2019. Note that the$BFR plot shows all calls with an ask price of 0.0. In June 2019, Banco Francés SA announced it would change its ticker symbol from $BFR to$BBAR. We will update the plots when we get the correct data for the missing months.

This plots reveal a huge drop in prices for the calls, and, conversely, a large increase in the price of puts, between Friday 9th and Monday 12th.

June 2019

As a comparison, let’s try plotting the option prices for June 2019, a more uneventful month for the Argentine market.

Next we’ll have a look the the actively traded puts for June 2019.

October 2015

Let’s have a look at the options data from October, November and December 2015.
During those months, the Argentine elections took place, which marked the beginning of a bull market. In the following four years, the MERVAL index increased four-fold its value in Pesos.

Now let’s plot the actively traded puts for October 2015

November 2015

December 2015

January 2008

We’ll examine the Argentine ADR options data for January 2008, the beginning of the US mortgage crisis, which had global effects. We only have data for 3 companies: $MELI,$TS and \$TX.