Latam Goverment Bonds: a Value at Risk revision

Recent political and economic turmoils in Argentina, Bolivia and Ecuador have resulted in a stark change in the short term trends of Latin America bond prices. In the year ended on 19th November 2019, such a regional portfolio's value decreased 5.2%. However, going-forward the yearly potential losses amount to 18.4%.

Using bonds from Ecuador, Colombia, Bolivia, Chile, Peru, Argentina, Brazil, and Mexico which represent 88% of the regional GDP (excluding Cuba and Venezuela on data-grounds), we build three value-at-risk (VaR) measures to represent the potential losses due to exposure to the region. We present the results for the total portfolio and the individual bonds.

Although the portfolio benefits the from diversification (the aggregate individual bonds perform 2x poorer), the risk/return relationship has categorically deteriorated on all but the Brazil, Colombia and Mexico bonds. While all bonds have seen a reduction on the average return, the later ones managed a volatility reduction. Arguably, Brazil performance stands out as the best one - strong volatility reduction and minimal return reduction. Ecuador and Argentina were excluded from the figure as they literally have off-the-charts volatilities. 

Ecuador and Argentina excluded on grounds 

The risk/return plot confirms the finding on the VaR measures. The three VaR measures are the standard version (VaR) which indicates the potential loss given normal market conditions; the conditional (CVaR) that expresses the expected loss once on unusual market conditions, and the entropic (EVaR) expresses the limit for standard VaR losses and improves the theoretical properties of the standard version. All three measures are based on a 95% confidence level and use the historical price changes to allow for the fat tails and skewed distributions.

The portfolio results show 1-day potential losses range from 0.45% to 0.96%. The yearly equivalent figure, mentioned at the beginning, stands between 8.7% and 18.4%. At the individual level, Peru and Mexico champion the minimum CVaR, our preferred risk metric, with potential 1-day losses of 0.43% and potential yearly losses of  8.2%. Mexico and Brazil have the least CVaR to VaR ratio which implies less amount of surprise between normal and unusual market conditions. Overall Mexico holds the best risk-averse profile with the lowest CVaR and EVaR and second-highest return.

Rank	Bond	VaR	CVaR	EVaR
1	PER	-0.30	-0.43	-0.57
2	MEX	-0.34	-0.43	-0.86
3	COL	-0.34	-0.47	-0.91
4	BRA	-0.35	-0.48	-0.81
5	CHL	-0.28	-0.53	-0.81
6	BOL	-0.46	-0.98	-1.18
7	ECU	-1.45	-3.29	-2.75
8	ARG	-2.54	-7.26	-5.23
	TOT	-0.45	-0.96	-0.83

1-day losses (summary)

By assumption, the portfolio was comprised of an equal amount of each individual bond, but this assumption could be relaxed to optimize returns and minimize risks. Argentina and Ecuador only serve to reduce returns and increase potential losses, and would be excluded on most portfolios. While political uncertainty stirs many advanced economies and the Sino-US trade-war pulls interest rates down, complacency for emerging economies will be short-lived. In the fight to attract global capital, these VaR measures should be a call-to-action for the Governments.

Annexe: setup, and time series

Among all the bonds issued by each country, I selected the ones that were 1) long term, 2) issued in US Dollars and in 2017 or early 2018, and 3) comparatively high issued amount. Albeit the purpose of these conditions is to ease comparability there are a couple of details worth mentioning: Argentina bond prices have 73 missing values and Bolivia hasn't issued a bond above the USD 1 billion mark. Ecuador bond didn't trade on the 19th November and on the 20th decreased almost 1,300 bp. The following table summarizes the selected bonds and their main characteristics.

Issuer and bond	ISIN Code	Issued (USD billion)	Listing date	Final maturity
Ecuador 7,875% 23/01/2028 Reg S	XS1755429732	2,130	24-ene-18	23-ene-28
Colombia 3,875% 25/04/2027	US195325DL65	2,400	26-ene-17	25-abr-27
Bolivia 4,5% 20/03/2028 Reg S	USP37878AC26	774	22-mar-17	20-mar-28
Chile 3,24% 06/02/2028	US168863CF36	2,000	07-feb-18	06-feb-28
Peru 4,125% 25/08/2027	US715638BU55	1,250	14-oct-15	25-ago-27
Argentina 6,875% 26/01/2027 Reg S	US040114HL72	3,749	28-abr-17	26-ene-27
Brazil 4,625% 13/01/2028	US105756BZ27	3,000	13-oct-17	13-ene-28
Mexico 3,75% 11/01/2028	US91087BAE02	2,555	23-jan-18	11-jan-28

On a technical note, the underlying distribution of price-variations is not normal. The historical distribution or daily price variations is skewed in most bonds and has fatter tails in all bonds. A couple of normality test (Shapiro-Wilk and SK test) failed to reject the normality hypothesis and the following plots highlight this fact:

Argentina has 2 observation points outside of the graph region; Ecuador only one. 

Normal function is the theoretical density distribution assuming the sample mean and standard deviation for each of the selected countries.