Introduction
Country Ratings
Model
Results
Forecasting Returns
Model 1:
Model 2:
Model 3:
Model 4:
Variance Models
Model 1:
Model 2:
Portfolio Tracking
Discussion
Introduction
Our topic for this assignment is “Predicting Returns and Volatility in Developed Countries”.
The idea of this exercise is to develop a model, which uses country risk indices for portfolio management. We want to find out if using country indices in a prediction model is better than using other factors (variables) affecting a particular country’s returns.
As in our previous assignment, we find that using economic and financial variables in forecasting returns can lead to some great results. However, we wanted to know if using credit ratings would improve that model. Even though economic and financial variables alone have predicting power to a certain extent, they are still using past data only.
Country credit ratings are forward looking nature. Organizations predict ratings of a country on the basis of what is going to happen to the economic or financial situation in a country. Even though it is not a precise predictor of the future and may not be able to predict financial crises, it is more futuristic than other variables.
Country Ratings
For our model to work effectively, we needed credit ratings which were released monthly since there is high variation in emerging markets from month to month and using a time period larger than that would have too much noise. Also, we needed to use a rating which was available easily so that the model can be user friendly and updated easily.
The International Country Risk Guide (ICRG) was the most suitable rating for our purposes. ICRG compiles monthly data on a variety of political, financial and economic risk factors to calculate risk indexes in each of these categories, as well as a composite risk index. Five financial, thirteen political and six economic factors are used.
The ICRG ratings have the following advantages:
- It is issued monthly and thus the noise in the predictions is reduced.
- The ICRG rating divides the country into three different risks and that gives us a better picture on how each type of risk is changing within a country. Thus, high variations in a certain type of risk can be identified and discarded or smoothed from the data.
Critical Factors in the ICRG rating system are shown in Exhibit 1.
Model
In our model, we use the Morgan Stanley Capital International (MSCI) equity markets’ index as a proxy for the returns on the equity markets in 18 countries. We forecast the annual return and volatility on this index. Our sample begins in January, 1984 and ends in September, 1998. A list of the countries included in analysis is provided in Exhibit 2.
Out of the four monthly risk ratings published by ICRG (political, economical, financial and composite index) we use the first three, since the fourth is a linear combination of the first three. We fit the model using both the ratings and the monthly changes in the ratings. We reserve the last three years of data to do out-of-sample validation of the model.
The ICRG indices are based on a 100-point scale, with 100 being the best rating (the least risk). Since we expect the markets to prize risk, we expect to find negative coefficients in our regressions.
After this, we track the performance of a portfolio based in the markets that have positive, negative or no change in last month’s ratings. All the countries, which have a positive change in their credit rating, are grouped into one portfolio and the same is done for all the countries, which have a negative change, or no change in their ratings. This portfolio is used as a reference to understand how a change in the ratings of different countries affects the value of a portfolio made up of the same directional ratings. However, In certain months there were situations where none of the countries in the MSCI Index either a positive change, or a negative change or no change. Thus one would not be able to form a portfolio since there were no countries with a certain type of change. Thus for those months and for the particular portfolios we used a 0.5% return for that month assuming that the money could be invested in a risk free instrument.
Results
We decided to run two different models to forecast returns and variance. For the first model used the difference between the monthly changes in all the components of the ICRG rating i.e. political, economic and financial. However, we found that the economic variable has a very high p-value, which made it insignificant. Thus, we decided to run two more models using only the political and financial components of the ratings as out independent variables.
Thus totally, we ran four models with different combinations of the variables to forecast returns and two models to forecast variance. These models are described below:
Forecasting Returns
Model 1:
In model 1 our variables were the monthly change in the financial and political ratings as published by ICRG. The monthly change between the ratings was used because we felt that a change in the ratings would be a factor of whether the financial and political situation in the country was becoming better or worse and that would help us better predict future returns.
Table 1: Statistics for Model 1
Co-Efficients, Adjusted R-Squared, Out of Sample Mean Average Error and ANOVA F-Ratio for each country
As can be seen from the table above, this model is giving us inconsistent results. It does not seem to be a good predictor of future returns since a lot of countries have an adjusted R-Squared of zero and the F-Ratio at 1.21 is not very significant. Also, some of the co-efficients are positive which implies that higher risk yields lower returns, which defies rationality. However, the out of sample mean absolute error is 0.20 which is lower than the other models seen later, but still extremely high to give meaningful results.
Model 2:
In model 2 we used all the components of the ICRG ratings i.e. the political, financial and economic ratings and we used the monthly change in them as the variables.
Table 2: Statistics for Model 2
Co-Efficients, Adjusted R-Squared, Out of Sample Mean Average Error and ANOVA F-Ratio for each country
The results from Model 2 are not encouraging either. As can be seen again, there are several countries with a zero R-squared, the average F-Ratio is extremely insignificant at 0.97 and again several countries have a positive co-efficient. The out of sample mean absolute error at 0.21 is even higher than model 1.
From the above two models we conclude that our original hypothesis that the monthly change in the variables will be better predictors of future returns of a particular country is false. The models are not showing significant results to support that theory. In the next two models we do not use the monthly change in the ratings but the absolute value of the ratings.
Model 3:
In model 3 we used the absolute values of all the components of the ICRG ratings i.e. political, financial and economic. Note that we do not use the monthly change in the ratings as our variables but the absolute value of the ratings.
Table 3: Statistics for Model 3
Co-Efficients, Adjusted R-Squared, Out of Sample Mean Average Error and ANOVA F-Ratio for each country
The results for model 3 are much more encouraging. Even though the out of sample mean absolute error is very high at 0.25, the R-squared for the individual countries and the average R-squared (22.53%) is very good. The F-Ratio at 16.90 is very significant and even though there are a few positive co-efficients, they are much fewer than in model 1 and 2.
Model 4:
In model 4, we used the absolute values of only the political and financial ratings as our variables.
Table 4: Statistics for Model 4
Co-Efficients, Adjusted R-Squared, Out of Sample Mean Average Error and ANOVA F-Ratio for each country
The results for model 4 match those of model 3. The R-squared for the individual countries and the average R-squared is good at 20.42%. The out of sample mean absolute error is the same as model 3 at 0.25. The F-Ratio at 22.83 is even more significant than model 3.
Variance Models
Model 1:
In model 1 to forecast variance, we used the values of all the components of the ICRG ratings.
Table 5: Statistics for Variance Model 1
Co-Efficients, Adjusted R-Squared, Out of sample Mean Absolute Error and ANOVA F-Ratio for Variance Model 1
As can be seen from the above table, the in sample results look very promising, with an average R-Squared of more than 24% and a very high F-ratio for most of the countries (only Austria and Sweden were lower than 4). However, out of sample the model didn’t behave very well. The MAE is too high for the magnitude of the average Variance (about 0.5%).
Model 2:
In variance model 2, we used the monthly change in the three variables.
Table 6: Statistics for Variance Model 2
Co-Efficients, Adjusted R-Squared, Out of sample Mean Absolute Error and ANOVA F-Ratio for Variance Model 1
In variance model 1, there are too many countries with a 0% adjusted R-Squared and the highest F-Ratio is only 3.46 (average F-Ratio of 0.81). This implies that the model is insignificant. However, this model behaved better than Model 1 out of sample.
Portfolio Tracking
We developed another model for tracking portfolios based on the change in the composite rating. We had three portfolios, one with the countries that had negative changes (decreases) in the composite rating in the last month (portfolio –1), one with the countries that had no change in the compositerating (portfolio 0) and one with the countries that had an increase in the ratings in the last month (portfolio 1).
We tracked the performance of these three portfolios an of the MSCI World index returns by calculating the value in December 1998 of an initial investment of $100 in January 1984. For those months when a portfolio didn’t have any countries (because there was no country with the required change in the composite rating) we applied a ficed rate of 0.5%
The following plot shows the values and volatilities of each of these portfolios.
Discussion
Overall, the results for the models in general were very discouraging. It does not seem that country credit ratings have too much predictive power. Also, the models are very inconsistent for the following reasons:
- Positive Signs
There were too many positive signs on the co-efficients of individual countries which completely defies rationality. It implies that the market returns are lower for higher risk which is not logical.
- Inconsistency in results between in sample and out of sample data
The models with the monthly change in the ratings behave better in the out of sample data but are very poor in sample. On the other hand, the models using the values of the ratings, have good in sample statistics but underperform out of sample.
One plausible explanation of the behaviour of the models that used the monthly changes in the ratings is that the monthly changes are too discrete. Most of the changes were either –0.5, 0 or +0.5. The discrete distribution of the predictions is seen from the example graph of Variance Model 2 for Sweden: