Credit Spreads on Sovereign Debt An Explanatory Regression Model & Trading Strategy Submitted by...

Credit Spreads on Sovereign Debt

An Explanatory Regression Model & Trading Strategy

Submitted byVaswar Mitra, Vinaya Jain

May 5th, 2006

Independent Study Project under Prof. Campbell Harvey, Term 4 2006

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Agenda Summary Findings The Origins & Evolution of Sovereign Debt Factors that influence sovereign credit spreads Overview of Methodologies Overview of Regression Analysis Model 1: WB Annual

Regression Model & Trading Strategy Model 2: WB Monthly

Regression Model & Trading Strategies Model 3: ICRG Monthly

Regression Model & Trading Strategies Model 4: Lagged Spreads

Regression Model & Trading Strategy Momentum Trading Strategy Issues to be Explored Further Bibliography

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Summary Findings WB Data annual and monthly (Annual independent variables

replicated to give monthly data) data gave us high R-Squares in the 85% range

The ICRG monthly data gave us R-Squares in the 63% range, lower than what we got using WB data.

An explanatory model using lagged spreads gave us extremely high R-Squares over 96% even though the residuals were not distributed normally

Long-Only trading strategies using 1-year lags gave us good results, both with WB data and ICRG data. The Long-Short strategy did not work similarly well

Given the high R-Squares using lagged spreads, we felt that a momentum strategy should work well. Our strategy yielded a percent accuracy of only 49% and cannot be used in its current form

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The Origins of Sovereign Debt The first public bonds originated in 17th century European city-states –

lifetime/redeemable annuities that paid interest to bondholders. The UK “Consol” (1751) is the earliest example of a government bond used to

supplement revenues from taxation Liquid, perpetual (redeemable at par) and highly credible. Backed by sinking funds,

Consol’s formed 96% of Britain’s total debt from 1801-1914 The Bank of England (1694) was mandated to manage government debt, issue

currency and provide liquidity between bonds and cash Consols quickly became a “byword for financial security” and a benchmark for

other risky assets Alexander Hamilton (1789) created “Hamilton 6s” to refinance existing US debt –

the first US federal bonds based on the Consols Created the first US central bank, modeled on the Bank of England

The British system of public debt was widely adopted worldwide – Holland (1814), Italy (1893), Japan (1880’s)

Post World War 1 – the British Treasury developed more maturities of debt to supplement Consols The first “gilt edged government securities” were introduced

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The Evolution of Sovereign DebtThe magnitude of government budget deficits and consequently, the outstanding volume of sovereign debt has fluctuated significantly over the years

France, Russia and Italy averaged high deficits in the 18th and 19th century. The UK had the best record for balanced budget

Between the years of 1816 – 1899: UK – Only 4 years with a deficit >1% of GNP. Average budget surplus of 4.6% France – Only 7 years with a budget surplus during this period. Italy – Ran a deficit every year from 1862 – 1899 USA – Average deficit of 1% of GNP

Deficits were vastly larger during the World Wars particularly in combatant nations World War 1 Average Deficit : UK - 30% of GNP, Germany 40%, Italy 22% World War 2: Soviet Union – 19% of GNP, Germany 36%. Axis countries relied heavily on short term borrowings, while the US and UK had

more balanced maturity structures of sovereign debt “Wars of credit” - between 1776 and 1783, bonds financed 40% of the UK’s war

expenditure Short term debt (Bills) gained in popularity, as the attractiveness of long dated

war bonds declined

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The Evolution of Sovereign Debt Contd...

Early European kingdoms were notoriously prone to defaulting on sovereign debt. Defaults could be declared in many ways – the most common types were: Outright Default – Suspension of principal or interest payments Moratoria/ Rescheduling - Institutionalized processes to make creditors agree

to new terms on the debt Conversions – the exchange of one class of bond for another, usually with a

lower coupon or higher maturity. In the UK, conversions were always negotiated, while in other countries they could be imposed upon creditors.

Some well known examples of sovereign defaults: Spain & France defaulted on all or part of their debt, over 10 times in the 16th

and 17th centuries The UK declared a moratorium on interest payments in the 1680’s and

converted some debt Turkey defaulted in 1875, and after World War I Latin American countries like Brazil, Mexico and Colombia were “perennial

defaulters” in the late 19th and 20th centuries

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Factors Influencing Sovereign Debt Spreads

The credit spread or ”yield” is the main determinant of the borrowing cost for a country. According to traditional economic theory, spreads are determined by:

Expectations of real growth prospects, nominal interest rates and inflation for the country in question (Fisher Effect, Gibson’s Paradox)

They are thought to be linked to measures of “monetary growth” , “fiscal stability”, and the overall term structure of interest rates

The credit spread is viewed as a premium for default risk and other risks specific to the issuing country

Political and other types of idiosyncratic risks The “Feel good” factor – psychology and economics

Economic policy and its effect on the morale of the public “It’s the economy stupid” – Bill Clinton

The eternal Fiscal Policy question - do higher debts lead to higher interest rates? Regression analysis of UK data from 1727 shows a very low relationship between

yields and the debt/GNP and deficit/GNP Ratio However in the late 1970’s and 1980’s there is evidence of strong positive

correlation between debt/GNP ratios and rising real interest rates.

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Overview of Methodologies

To develop an explanatory model for sovereign debt spreads we created three methodologies:

1. Using World Bank (WB) annual data after correcting for missing data

2. Using World Bank (WB) annual data but transforming it to monthly by replicating the annual data (independent variables) 12 times but using actual monthly spreads (dependent variable)

3. Using ICRG monthly data

Next we tested for viable trading strategies:1. For each of the explanatory models developed above, we

developed a predictive model using in sample data and tested the model on out of sample data

2. Tested for a momentum trading strategy

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Overview of Regression Analysis

Stata used for regression analysis Assumed that there would be fixed time effects.

Eliminated these effects by using time dummies for each year

Used cluster standard errors Ensured that independent variable correlations and

multicollinearity were within reasonable levels Generated partial regression plots and checked for

any unusual or influential points Finally, tested that the regression residuals for

normality

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Model 1: WB Annual

World Bank Annual Data

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WB Annual: Regression Variables

Dependent Variable: Ln(Spread)

Independent Variable: GDP Per Capita, Reserves Per Capita, External Debt as a Percent of GDP

We expect spreads to be: Lower for higher GDP Per Capita Lower for higher Reserves per Capita numbers Higher for higher External Debt as a Percent of GDP

This was consistent with our regression results

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WB Annual: Modifications to Data

Lack of data for certain years for certain variables presented a problem

In general we excluded the years or countries for which data was missing

In one case we modified the data. Data for the independent variable “External Debt as a percent of GDP” was sometimes missing for certain years or for a specific country altogether. To handle this situation, we made the following modifications: Where the data was missing for a specific year but the country

had data for previous years, we simply used the country data from previous years

Where data was completely missing for the country, we used the average across all countries for the particular year

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WB Annual: Variables Graph

Scatter plot of spread against independent variables shows that points with Spreads = 1 ( Ln(Spread) =0 ) are outliers

Whether this is a problem will be confirmed if the Partial Regression Plots shows similar influential points

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WB Annual: Regression Results

Regression gives high (within) R-Square of 85.80% and overall R-Square of 84.45%

The t-stats are all significant

Fixed-effects (within) regression Number of obs = 267 Group variable (i): year Number of groups = 11 R-sq: within = 0.8580 Obs per group: min = 4 between = 0.9513 avg = 24.3 overall = 0.8485 max = 33 F(3,264) = 1494.43 corr(u_i, Xb) = 0.0807 Prob > F = 0.0000 (Std. Err. adjusted for 11 clusters in year) ------------------------------------------------------------------------------ | Robust lnspread | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- gdppercapita | -.0002804 9.58e-06 -29.28 0.000 -.0003017 -.0002591 reservespe~a | -.0007464 .00014 -5.33 0.000 -.0010583 -.0004344 externalde~p | 1.554783 .6288551 2.47 0.033 .1536062 2.955959 _cons | 7.382482 .4902899 15.06 0.000 6.290048 8.474916 -------------+---------------------------------------------------------------- sigma_u | .53247918 sigma_e | 1.0329095 rho | .20995742 (fraction of variance due to u_i) ------------------------------------------------------------------------------

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WB Annual: Correlation & Multicollinearity

| lnspread gdpper~a reserv~a extern~p -------------+------------------------------------ lnspread | 1.0000 gdppercapita | -0.9009 1.0000 reservespe~a | -0.5422 0.4458 1.0000 externalde~p | 0.3701 -0.3038 -0.0834 1.0000

Variable | VIF 1/VIF -------------+---------------------- gdppercapita | 1.37 0.729692 reservespe~a | 1.25 0.798312 externalde~p | 1.11 0.904308 -------------+---------------------- Mean VIF | 1.24

Variable Correlation:

Low correlation between variables

Multicollinearity:

A VIF (variance inflation factor) lower than 10 denotes low collinearity

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WB Annual: Partial Regression Plots

Partial Regression Plot does not reveal any unusual or influential observations.

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WB Annual: Residual Plots

Test for Normality: There is a slight skew but overall residuals are normally distributed

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WB Annual: Trading Strategy Methodology

In Sample Period: 1994 – 2001 Out of Sample Period: 2002 – 2003 Predictive Equation:

Ln(Spread) (1-year forward) = 8.64547 – 0.00031 * GDP Per Capita – 0.00108 * Reserves Per Capita

Sorted on the % Change expected during the next year % Change = (Next year forecasted spread - Current Spread) / Current Spread

If % Expected Change is negative, the decision is to buy the country’s debt Conversely if % Expected Change is positive, the decision is to sell the country’s debt Eliminated developed countries which had spreads = 1

Long Short Strategy: After sorting, selected the top quintile (five most negative % Expected Change) to go long and bottom five quintile (most positive % Expected Change) to go short

Long Only Strategy: After sorting, selected the top two quintiles (ten most negative % Expected Change) to go long only

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WB Annual: Trading Strategy Results

Overall Accuracy: The overall accuracy was 73% and 56% in the two years.

Long Short Result: The % Accuracy during the two years of OOS data is over 50% in both the OOS years.

Long Only Result: The % Accuracy is 100% and 90% in the two years. These results are very promising.

Year Long Short Long Only Overall2002 50% 100% 73%2003 60% 90% 56%

Directional Accuracy

Trading Strategies Comparison

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WB Annual: Conclusions

Strong explanatory power of World Bank annual data. Gives us R-Sq in the 85% range

Long only Trading Strategy shows a lot of promise Need to explore reasons why the short side of the

strategy does not yield as good results

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Model 2: WB Monthly

World Bank Annual Data

converted to Monthly

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WB Monthly: Regression Variables


Independent Variable: GDP Per Capita, Reserves Per Capita, External Debt as a Percent of GDP

We expect spreads to be: Lower for higher GDP Per Capita Lower for higher Reserves per Capita numbers Higher for higher External Debt as a Percent of GDP


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WB Monthly: Modifications to Data

Starting with the WB annual data used in Model 1, we made the following modifications:

1. We replicated the annual data (independent variables) 12 times, once for each month of the year

2. used the actual monthly spreads (dependent variable)

3. Ran our regressions and our trading strategy as if we had monthly data

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WB Monthly: Variables Graph



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WB Monthly: Regression Results

Regression gives high (within) R-Square of 85.22% and overall R-Square of 84.48%

The t-stats are all very significant

Fixed-effects (within) regression Number of obs = 2957 Group variable (i): year Number of groups = 11 R-sq: within = 0.8522 Obs per group: min = 33 between = 0.9577 avg = 268.8 overall = 0.8448 max = 369 F(3,2954) = 2931.56 corr(u_i, Xb) = 0.0714 Prob > F = 0.0000 (Std. Err. adjusted for 11 clusters in year) ------------------------------------------------------------------------------ | Robust lnspread | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- gdppercapita | -.0002817 9.45e-06 -29.80 0.000 -.0003028 -.0002607 reservespe~a | -.0006339 .0001369 -4.63 0.001 -.0009388 -.0003289 externalde~p | 1.482868 .6366234 2.33 0.042 .0643827 2.901353 _cons | 7.333897 .4741553 15.47 0.000 6.277413 8.390381 -------------+---------------------------------------------------------------- sigma_u | .56187781 sigma_e | 1.0392333 rho | .22619749 (fraction of variance due to u_i) ------------------------------------------------------------------------------

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WB Monthly: Correlation & Multicollinearity


Low correlation between variables, the highest being 50.27%

Multicollinearity:


| lnspread gdpper~a reserv~a extern~p -------------+------------------------------------ lnspread | 1.0000 gdppercapita | -0.9044 1.0000 reservespe~a | -0.5648 0.5027 1.0000 externalde~p | 0.4019 -0.3509 -0.0904 1.0000

Variable | VIF 1/VIF -------------+---------------------- gdppercapita | 1.53 0.653220 reservespe~a | 1.35 0.738856 externalde~p | 1.15 0.866977 -------------+---------------------- Mean VIF | 1.35

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WB Monthly: Partial Regression Plots

Partial Regression Plot does not reveal any unusual or influential observations. The horizontal bars are because we have replicated the annual independent variable data 12 times.

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WB Monthly: Residual Plots

Test for Normality: There is a slight skew but overall residuals are normally distributed

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WB Monthly: Trading Strategy Methodology- 1Methodology – 1 uses 1-month predictive model

In Sample Period: 1994 Jan – 2002 Dec Out of Sample Period: 2003 Jan – 2004 Nov Predictive Equation:

Ln(Spread) (1-month forward) = 8.090379 – 0.00029 * GDP Per Capita – 0.001111 * Reserves Per Capita

+ 0.580377 * External Debt as a % of GDP

Sorted on the % Change expected during the next month % Change = (Next month forecasted spread - Current Spread) / Current Spread

If % Expected Change is negative, the decision is to buy the country’s debt Conversely if % Expected Change is positive, the decision is to sell the country’s debt Long Short Strategy: After sorting, selected the top quintile (five most negative %

Expected Change) to go long and bottom five quintile (most positive % Expected Change) to go short


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WB Monthly: Trading Strategy Results - 1


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Month Long short Long Only OverallJan-03 30% 40% 43%Feb-03 70% 70% 65%Mar-03 50% 80% 57%Apr-03 60% 70% 64%

May-03 50% 40% 45%Jun-03 60% 80% 65%Jul-03 20% 60% 39%

Aug-03 60% 70% 65%Sep-03 60% 60% 52%Oct-03 50% 60% 57%Nov-03 40% 60% 52%Dec-03 60% 30% 43%Jan-04 60% 40% 61%Feb-04 40% 70% 52%Mar-04 50% 40% 48%Apr-04 50% 10% 35%

May-04 40% 50% 52%Jun-04 60% 90% 65%Jul-04 50% 70% 61%

Aug-04 50% 70% 39%Sep-04 70% 70% 52%Oct-04 50% 90% 61%Nov-04 70% 70% 57%

Average 52% 60% 54%

Overall Accuracy: The overall accuracy ranged from 39% to 66%, and the average was 54%

Long Short Result: The % Accuracy ranged from 20% to 70%, and the average was 52%. In its current form, this strategy doesn’t show much promise

Long Only Result: The % Accuracy ranged from 30% to 90% and the average was 60%. In 17 of the 23 projected months, the % Accuracy was 50% or higher. This is a potentially viable trading strategy

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WB Monthly: Trading Strategy Methodology- 2Methodology – 2 uses 1-year predictive model

In Sample Period: 1994 Jan – 2001 Dec Out of Sample Period: 2002 Jan – 2003 Dec Predictive Equation:

Ln(Spread) (1-year forward) = 8.491300 – 0.000295 * GDP Per Capita – 0.001160 * Reserves Per Capita





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WB Monthly: Trading Strategy Results - 2

Overall Accuracy: The overall accuracy ranged from 50% to 82%, and the average was 65%. It was over 50% for all the months

Long Short Result: The % Accuracy ranged from 40% to 80%, and the average was 60%. In 23 of the 24 projected months, the % Accuracy was 50% or higher. This strategy can be explored further

Long Only Result: The % Accuracy ranged from 30% to 100% and the average was 86%. In 23 of the 24 projected months, the % Accuracy was 50% or higher. In 17 of the 24 months, the % Accuracy was 90% - 100%. This strategy represents a viable trading strategy and needs to be explored further


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Month Long short Long Only Overall

Jan-02 70% 50% 55%Feb-02 60% 50% 55%Mar-02 70% 30% 59%Apr-02 50% 60% 64%

May-02 80% 90% 71%Jun-02 70% 100% 77%Jul-02 70% 100% 82%


May-03 70% 80% 67%Jun-03 40% 70% 55%Jul-03 60% 90% 55%

Aug-03 60% 90% 64%Sep-03 60% 90% 59%Oct-03 70% 100% 77%Nov-03 70% 90% 59%Dec-03 60% 90% 50%

Average 60% 86% 65%

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WB Monthly: Conclusions

Strong explanatory power of World Bank monthly data. Gives us R-Sq in the 85% range

Trading strategy using 1-Year lag holds the most promise Long Short Trading Strategy shows some promise Long only Trading Strategy represents a viable trading

strategy and needs to be explored further Need to explore reasons why the short side of the strategy

does not yield good results

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Model 3: ICRG Monthly

ICRG Monthly Data

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ICRG Country Ratings Overview The International Country Risk Guide (ICRG) methodology

Developed in 1980, by the editors of the newsletter International Reports Considers 22 total variables under 3 categories of risks – Economic,

Financial and Political with separate indices for each category Economic (50 Points)

GDP/ Head, Real GDP growth, Inflation, Fiscal & Current Account Deficit

Financial (50 Points) % of Foreign Debt, Exchange Rate stability, Debt Service, Current

Account % of Exports Political (100 Points – Scale from 1-12)

Government Stability, Socioeconomic Conditions, Corruption, Law & Order

These 3 indices are used to produce a composite score out of 100 80 – 100: Very Low Risk Countries 0 – 49.5: Very High Risk Countries

The ICRG team generates current, 1 year and 5 year forecasts for each risk category as well as for the 3 separate indices

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ICRG Monthly: Regression Variables


Independent Variable: GDP Per Head Annual Inflation Rate Foreign Debt as a Percent of GDP

We expect spreads to be: Lower for higher GDP Per Head Higher for higher Annual Inflation rates Higher for higher Foreign Debt as a Percent of GDP


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ICRG Monthly: Variables Graph



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ICRG Monthly: Regression Results

Regression gives a (within) R-Square of 64.67% and overall R-Square of 63.26%

The t-stats are all very significant

Fixed-effects (within) regression Number of obs = 3910 Group variable (i): year Number of groups = 13 R-sq: within = 0.6467 Obs per group: min = 4 between = 0.1186 avg = 300.8 overall = 0.6326 max = 436 F(3,3907) = 748.37 corr(u_i, Xb) = -0.0196 Prob > F = 0.0000 (Std. Err. adjusted for 13 clusters in year) ------------------------------------------------------------------------------ | Robust lnspread | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- gdpheade | -.9568297 .0356213 -26.86 0.000 -1.034442 -.8792177 inflatione | -.3191931 .0336124 -9.50 0.000 -.3924281 -.245958 fordebtf | -.3175541 .0171611 -18.50 0.000 -.3549449 -.2801632 _cons | 11.32238 .2604515 43.47 0.000 10.75491 11.88986 -------------+---------------------------------------------------------------- sigma_u | .61515417 sigma_e | 1.4789064 rho | .14749679 (fraction of variance due to u_i) ------------------------------------------------------------------------------

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ICRG Monthly: Partial Regression Plots

Partial Regression Plot does not reveal any unusual or influential observations.

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ICRG Monthly: Residual Plots

Test for Normality: The curve is doesn’t follow the normal curve too closely especially in the first half. But broadly the residuals are normally distributed.

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ICRG Monthly: Trading Strategy Methodology- 1Methodology – 1 uses 1-month predictive model

In Sample Period: 1993 Dec – 2003 Dec Out of Sample Period: 2004 Jan – 2005 Nov Predictive Equation:

Ln(Spread) (1-month forward) = 11.05438 – 0.94991 * GDP Per Head Rating – 0.33263 * Annual Inflation Rate Rating

- 0.30559 * Foreign Debt as a % of GDP Rating





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ICRG Monthly: Trading Strategy Results - 1


Long Short Result: The % Accuracy ranged from 20% to 70%, and the average was 50%. In 14 of the 23 projected months, the % Accuracy was above 50%. We cannot use this strategy in its current form

Long Only Result: The % Accuracy ranged from 0% to 100% and the average was 60%. In 16 of the 23 projected months, the % Accuracy was 50% or higher. This is a potentially viable trading strategy but would have to be refined further


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Month Long Short Long Only OverallJan-04 70% 40% 61%Feb-04 70% 100% 64%Mar-04 40% 30% 32%Apr-04 40% 10% 36%

May-04 30% 60% 50%Jun-04 60% 90% 64%Jul-04 50% 80% 75%


May-05 40% 80% 59%Jun-05 50% 80% 59%Jul-05 50% 50% 61%

Aug-05 60% 100% 57%Sep-05 40% 20% 36%Oct-05 40% 50% 50%Nov-05 70% 30% 50%

Average 50% 60% 55%

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ICRG Monthly: Trading Strategy Methodology- 2Methodology – 2 uses 1-year predictive model

In Sample Period: 1993 Dec – 2002 Dec Out of Sample Period: 2003 Jan – 2004 Dec Predictive Equation:

Ln(Spread) (1-year forward) = 11.10612 – 0.97069 * GDP Per Head Rating – 0.28848 * Annual Inflation Rate Rating

- 0.31489 * Foreign Debt as a % of GDP Rating





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ICRG Monthly: Trading Strategy Results - 2

Overall Accuracy: The overall accuracy ranged from 43% to 67%, and the average was 56%.

Long Short Result: The % Accuracy ranged from 40% to 80%, and the average was 55%. In 19 of the 24 projected months, the % Accuracy was 50% or higher. This strategy can be explored further

Long Only Result: The % Accuracy ranged from 70% to 100% and the average was 89%. This result represents a viable trading strategy and needs to be explored further


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Month Long Short Long Only Overall

Jan-03 50% 90% 57%Feb-03 50% 90% 54%Mar-03 60% 90% 61%Apr-03 40% 90% 61%

May-03 50% 80% 52%Jun-03 40% 70% 50%Jul-03 50% 90% 64%


May-04 40% 90% 52%Jun-04 50% 100% 59%Jul-04 60% 100% 64%

Aug-04 50% 90% 57%Sep-04 60% 100% 54%Oct-04 40% 90% 43%Nov-04 50% 80% 43%

Average 55% 89% 56%

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ICRG Monthly: Conclusions

Explanatory power of ICRG data was surprising below that of the World Bank monthly data. This gave us R-Sq in the 63% range compared to 85% range for WB data

Trading strategy using 1-Year lag holds the most promise Long Short Trading Strategy shows some promise with 19

of the 24 months having over 50% accuracy Long only Trading Strategy represents a viable trading

strategy but needs to be explored further Need to explore reasons why the short side of the strategy

does not yield good results

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Model 4: Lagged Spreads

Monthly Spreads Regressed on 1-Month Lagged Spreads

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Lagged Spreads: Regression Variables


Independent Variable: Ln(Spread) 1-Month Lag Foreign Debt Service as a Percent of Exports of Goods and

Services We expect spreads to be:

Higher if the previous month spread was high due to a momentum effect.

Higher for higher Foreign Debt Service ratio. A high ratio shows that a country may default in the near future.


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Lagged Spreads: Variables Graph

The Graph above shows extremely high correlation of the lagged spreads with the current spreads

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Lagged Spreads: Regression Results

Regression gives extremely high (within) R-Square of 96.93% and overall R-Square of 96.96%

The t-stats are all significant

Fixed-effects (within) regression Number of obs = 3869 Group variable (i): year Number of groups = 12 R-sq: within = 0.9693 Obs per group: min = 67 between = 0.9903 avg = 322.4 overall = 0.9696 max = 435 F(2,3867) = 38349.32 corr(u_i, Xb) = -0.0290 Prob > F = 0.0000 (Std. Err. adjusted for 12 clusters in year) ------------------------------------------------------------------------------ | Robust lnspread | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- lnspread1m~g | .9672258 .0134447 71.94 0.000 .9376343 .9968173 debtservf | -.0429803 .0203903 -2.11 0.059 -.087859 .0018984 _cons | .5121753 .2146835 2.39 0.036 .03966 .9846905 -------------+---------------------------------------------------------------- sigma_u | .07105769 sigma_e | .43487784 rho | .02600427 (fraction of variance due to u_i) ------------------------------------------------------------------------------

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Lagged Spreads: Correlation & Multicollinearity



Multicollinearity:


| lnspread lnspre~g debtse~f -------------+--------------------------- lnspread | 1.0000 lnspread1m~g | 0.9841 1.0000 debtservf | -0.0967 -0.0646 1.0000

Variable | VIF 1/VIF -------------+---------------------- debtservf | 1.00 0.995828 lnspread1m~g | 1.00 0.995828 -------------+---------------------- Mean VIF | 1.00

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Lagged Spreads: Partial Regression Plots

Partial Regression Plot shows the extremely high correlation between lagged and current spreads.

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Lagged Spreads: Residual Plots

Test for Normality: The curve is doesn’t follow the normal curve throughout the curve and this shows a potential problem with this model

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Lagged Spreads: Trading Strategy Methodology

In Sample Period: 1993 Dec – 2003 Dec Out of Sample Period: 2004 Jan – 2005 Nov Predictive Equation:

Ln(Spread) (1-month forward) = -0.40302 + 1.00144 * Ln(Spread) + 0.04623 * Debt Service Ratio Rating

(The positive sign for the Debt Service Ratio coefficient on the in sample regression came as a surprise especially because the sign was negative in the explanatory model. This despite the low variable correlation and high t-stats. We reasoned that if a country has a high Debt Service ratio today, it might be making efforts to reduce its debt which would lead to fall in future spreads)





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Lagged Spreads: Trading Strategy Results


Long Short Result: The % Accuracy ranged from 0% to 80%, and the average was 50%. In 14 of the 23 projected months, the % Accuracy was 50% or higher. We cannot use this strategy in its current form

Long Only Result: The % Accuracy ranged from 0% to 100% and the average was 57%. In 14 of the 23 projected months, the % Accuracy was 50% or higher. Again we cannot use this strategy in its current form


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Month Long Short Long Only OverallJan-04 70% 40% 39%Feb-04 60% 90% 54%Mar-04 40% 10% 32%Apr-04 40% 10% 43%

May-04 60% 70% 61%Jun-04 60% 100% 75%Jul-04 40% 60% 54%


May-05 40% 80% 48%Jun-05 60% 100% 59%Jul-05 50% 40% 43%

Aug-05 50% 90% 50%Sep-05 10% 0% 32%Oct-05 80% 60% 50%Nov-05 80% 40% 64%

Average 50% 57% 50%

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Lagged Spreads: Conclusions

Explanatory power of ICRG data was surprisingly high with R-Sq over 96% much higher than all other models

However the residuals did not show a normal distribution – there might be potential problems with the model

Trading strategy using 1-month lag did not show much promise. The results lacked any consistency

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Momentum Strategy Given the high correlation of lagged monthly spread with current

spread, we felt that a momentum strategy should work well We calculated the monthly change in spread (CAGR) for last 6

months, 3 months and 1 month If the current month CAGRs are higher than previous month

CAGRs in at least two of the above three calculations, then the decision is to sell, else buy

Result: The percent accuracy of this strategy (after ignoring all the records with spreads = 1) was 49%. This was well below what we would have liked in a good trading strategy

Conclusion: There is promise in this strategy but it needs to be explored further

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Issues to be Explored Further

Despite attempting several trading strategies it was difficult to come up with a convincing one

The short side of the Long-short strategy was especially poor and would need to be explore

Our OOS was typically for periods in 2003 and 2004 when the economy was coming out of a recession. The results may be skewed because of this effect. We should test the strategy in more “normal” periods

Finally, the momentum strategy seems to hold promise and needs be explored

59

Bibliography

Ferguson, Niall. “The Cash Nexus – Money and Power in the Modern World 1700-2000. Penguin Books. Chapters 4 – 8

Ferguson, Niall. “Paper & Iron – Hamburg business and German politics in the era of inflation, 1897 – 1927”

The International Country Risk Guide, http://www.icrgonline.com/page.aspx?page=icrgmethods#Background_of_the_ICRG_Rating_System

The University of California, Los Angeles. “Resources to help you learn and use Stata”

http://www.ats.ucla.edu/stat/stata/ The World Bank, International Monetary Fund and World Markets Research

Center websites.

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