Stata project: Sovereign bond returns prediction based on the outliers with Value-at-Risk (VaR) models

Thesis: Testing VaR models on long-run Sovereign bond data

In the face of current chaos in finance, risk management is an urgent requirement in controlling losses. This thesis shed light on testing VaR model on monthly Sovereign bond data over 200 years. The main contents compare performance of one-day prediction of 25 selected portfolios via three methods – Historical Simulation (Engle and Manganelli (2001)), GARCH(1,1) (Robert Eagle (1982)) and Expected Shortfall (Artzner et al. (1997)). Remarkably, performance is evaluated by Kupiec test, Independence test and Conditional Coverage test, named shortly as Back-testing. After testing, Historical Simulation and Expected Shortfall of Historical Simulation are most effective. Besides, Normal GARCH(1,1) and ES Normal GARCH(1,1) are also potential. However, a persistent model applied throughout time should be carefully considered, especially in crisis. As regards GARCH(1,1), tested normal distribution works surprisingly better than Student-t. Last but not least, 1% percentile is more effective than 5% percentile in most approaches.

Keywords: Value-at-Risk; Sovereign bond; long-run; Historical Simulation; GARCH(1,1); Expected Shortfall; Back-testing

Support: risk management, portfolio optimization

Data source:

Meyer et. al (2018) with project "200 years of Sovereign Haircuts and Bond Returns", solve 25/91 single portfolios

Excel and Stata files contain the bondId (ID), Name, Country (c), issue date (issuey), maturity date (maturityy), monthly return (rdrealy), amount of issue (amtISS), currency, year y and month m

Information about the files

Descriptive statistics and Data Exploration

Thesis_Realization.do: Data Wrangling and EDA (Exploratory Data Analysis), visualize the statistics and distributions of dataset

Three methods to find the VaR values, check the outliers and do one-day prediction

Thesis_VaR_HistSim_final.do: The first method - Historical Simulation, no assumption about distribution, rolling the historical data in the window of 1 year, 5 years, 20 years, 50 years and 100 years

Thesis_VaR_GARCH_final.do: The second method - Generalized Autoregressive Conditional Heteroskedasticity GARCH, applying normality and t-distribution, considering the access kurtosis of loss distribution where losses are probably larger than expectation

Thesis_VaR_ES_final.do: The last method - Expected Shortfall or Conditional VaR (CVaR), Average VaR (AVaR) or Expected Tail Loss (ETL ES) implying the expected portfolio return when return exceeds the break of extreme threshold VaR

Back-testing

Thesis_Backtesting_final.do: examining the fitness of those models with the reality by the frequency of violations

It contains 3 tests:

a. Kupiec Test: checking the rate of failure which loss returns exceed the VaR

b. Independence Test: testing the independent violations over the years, no correlation with fluctuation between time t and (t-1)

c. Conditional Coverage Test: combination of those above tests, solving the shortcomings of Kupiec test (lack of time correlations) and Independence test (measurement in short-term, lack the rate of loss failures)

Visualization

All pictures uploaded support for the estimation and conclusions.

Results and conclusions

First of all, monthly realized returns of long-term Sovereign bond data are asymmetry, high peaks and fat tails. In other word, real returns do not distribute normally even in long run

Secondly, instead of applying same percentage for all portfolios, the proportions constructed in the paper have many benefits; for instance, accurately reflecting the monthly actual rates of each national portfolio in total of 25 selected categories.

In summary, traditional methods including Historical Simulation and Normal GARCH(1,1) are applicable in long run Sovereign bond data from perspective of Back-testing. Importantly, there is no persistent model that can be used throughout the periods, highly recommended to consider the estimation in the stable periods and crisis separately.

Future research:** GARCH model needs to be reviewed carefully before application because the biggest concern is the direction of realized returns. With the idea of regressing VaR model by squared deviation and past returns, GARCH model could be combined directly with the realized returns or with Historical Simulation