Risk Characteristics of Investment-Grade Portfolio - Essay Example

Risk Characteristics of Investment-Grade Portfolio 5.1 Base Case Table 3 presents the risk characteristics of investment-grade portfolio and speculative-grade portfolio as described above in the base case, where the asset correlation is 0.2 (the same assumption as in Löffler’s paper), mean recovery rates are 39.68% (Investment) 17.63% (Speculative) respectively, and default rates are 0.10% (Investment) and 4.4945% (Speculative) respectively. Here we ignore the simulation error as the same purpose in Löffler’s paper, since the subject of interest is the additional variation brought about by noisy input parameters.

Let’s review the definition of VaR. “VaR is the worst loss over a target horizon such that there is a low pre-specified probability that the actual loss will be larger (Jorion & Philippe).” For example, a 1% VaR of 0.66% (from Table 3) for investment-grade bond is the cutoff probability of loss such that the probability of experiencing a greater loss is less than 1 percent. As we can see from Table 3, the value at risk number increases much from investment-grade portfolio to speculative-grade portfolio.

When the credit rating goes down from investment to speculative, the bonds are affected to a higher degree by the possibility of default. Thus, it causes the VaR figures to increase. Another thing to be noticed from Table 3 is that the value at risk numbers decrease as the percentile of the VaR figure gets bigger. It is because the greater possibility of portfolio loss is more likely to be in the extreme quintiles. The investment-grade portfolio’s base case VaR figures in our paper are less than BBB-rated portfolio’s base case VaR figures in Löffler’s paper, and the speculative-grade portfolio’s VaR figures are greater than B-rated portfolio’s.

This could be explained by the classification of the bond’s credit rating. We simply divide the bond’s credit rating into two grades in our paper: the investment and the speculative, instead of single rating bond such as BBB or B in Löffler’s paper. The investment-grade portfolio contains bonds rated BBB- and higher, and the rest goes into speculative-grade portfolio which are referred to as junk bonds (Wikipedia). 5.2 Simulated VaR Table 4 represents the simulated distribution of the percentage portfolio value at risk in the presence of estimation risk.

Estimation error in the following input parameters used in the table is modeled by default rates (estimates based on the S&P historical data), recovery rates (estimates based on prices of investment-grade and speculative-grade bonds) and default correlations (estimates based on joint distribution of asset values). In Table 4, we include the simulated confidence intervals for the 1% VaR, 5% VaR and 10% VaR of the two portfolios due to estimation error from different sources: uncertainty of recovery rates only, uncertainty of default correlations only, uncertainty of default rates only, and uncertainty of three input parameters together.

We also include the simulated standard errors of those VaR figures. Figure 1 and Figure 2 show the confidence interval for each portfolio VaR in graphic forms, so that the width of the intervals can be presented more clearly. For most of the cases of investment-grade bonds, uncertainty of default rates is the most important source of uncertainty, as measured by the width of the confidence intervals or the standard error. However, the role of correlation uncertainty in more extreme percentile levels is larger.

For example, uncertainty of default correlations is the most important source of estimation error for the precision of the 1% VaR of the investment-grade portfolio. It has the widest confidence interval (0.112%, 0.9917%) and the largest standard error (0.00197%) among all of the three input parameters. The reason is that when default rates rise, the elasticity of default correlations, with respect to changes in asset correlations, increases as well (cf. JP Morgan, 1997). Therefore, in the more extreme cases and riskier portfolios, an error in the asset correlation could lead to a larger error in the default correlation (Löffler, 2003).

On the other hand, for the cases of speculative-grade bonds, uncertainty of default correlations becomes the most important source of uncertainty in all three quintiles. The reasons for this could be the parameter estimation methodology used for default correlation or the original datasets (speculative-grade). Comparing Table 4 in our paper and Table 4 in Löffler’s paper, the results we get are very similar to what Löffler got in his paper except for the correlation uncertainty in speculative-grade portfolio.

In this portfolio, default correlation becomes the most significant source of estimation risk in all three different quintiles (i.e. 1%, 5%, 10% VaR). While in Löffler’s paper, correlation uncertainty only matters in some of the more extreme quintiles, as we mentioned in last paragraph, for example 1% VaR. The inconsistency may be due to the fact that we used different methodology to generate random numbers from the distribution of correlation, which was discussed previously in section 4.4.

3, other than the methodology used in Löffler’s paper. The small-sample estimation errors in the correlation parameters (190 observations, in our paper) could still possibly lead to large flaws in the quantifying of portfolio credit risk (Tarashev & Zhu). 5.3 Base case VaR and Simulated VaR comparison Due to different market scenarios, the estimated VaR will sometimes overstate risk and sometimes understate risk. We need to take estimation error into account to the above two sides and assess its overall effects on the distribution of portfolio value (Löffler, 2003).

In Table 5, we put the conventional VaR (from base case parameters) and the predictive VaR (from 20,000 times simulated distributions) together. The results show that for the investment-grade portfolio, the conventional VaR overestimates the predictive VaR by considering the existence of estimation error. The magnitude of the bias ranges from a 4.5 to a 8.8 basis. The documented biases thus appear to be very modest. From the numbers in Table 3 and the analysis here, we can conclude that the conventional VaR figures can be regarded as reasonable approximations to the true risk factors of a portfolio (Löffler, 2003).

However, the estimation error adjustments would still be important in an economical use, especially for more extreme events than 1% quintile (Löffler, 2003). On the other hand, the conventional VaR underestimates the predictive VaR in speculative-grade portfolio. The magnitude of the bias ranges dramatically from 2.2 to 360 basis points. The differences are significant between the conventional ones and the predictive ones. Estimation error really plays a role in this case. Again, it returns to the question of the large data range of speculative-grade portfolio.

In most of the cases, recovery rates are ranked as the third most important uncertainties among the three. Comparing Table 5 in our paper with Table 7 in Löffler’s paper, the conventional VaR estimates of the two different portfolios have different bias numbers in the presence of estimation risk. The bias for speculative-grade portfolio is much higher than the bias for investment-grade portfolio (i.e. a range of 0.045 to 0.088 for investment and a range of 0.022 to 3.60 for speculative). This is due to the large volatility of speculative bonds (from BB to C).

Therefore, the estimation error will matter much in the VaR calculation for speculative-grade portfolio.