Assessing the accuracy of delta-normal VaR evaluation for Serbian government bond portfolio

Figures & data

Table 1. Dates of maturity for bonds.

Symbol Date of maturity
A2013	31.05.2013
A2014	31.05.2014
A2015	31.05.2015
A2016	31.05.2016

Source: www.belex.rs

Table 2. Calculated VaR values by applying delta-normal method on the different dates, for different confident levels.

VaR	31.12.2012	31.12.2011	31.12.2010	31.12.2009	31.12.2008
	0.76%	1.36%	0.74%	0.90%	1.21%
	0.69%	1.23%	0.67%	0.81%	1.09%
	0.49%	0.87%	0.47%	0.57%	0.77%
	0.38%	0.68%	0.37%	0.45%	0.60%

Source: Authors’ calculation.

Figure 1. Graphical representation of the portfolio returns and VaR values obtained by applying delta-normal method for portfolios of bonds traded on the market of the Republic of Serbia, for confidence level of 99.5%, for the period 2008–2012. Source: Created by the authors.

Figure 2. Graphical representation of the portfolio returns and VaR values obtained by applying delta-normal method for portfolios of bonds traded on the market of the Republic of Serbia, for confidence level of 99%, for the period 2008–2012. Source: Created by the authors.

Figure 3. Graphical representation of the portfolio returns and VaR values obtained by applying delta-normal method for portfolios of bonds traded on the market of the Republic of Serbia, for confidence level of 95%, for the period 2008–2012. Source: Created by the authors.

Figure 4. Graphical representation of the portfolio returns and VaR values obtained by applying delta-normal method for portfolios of bonds traded on the market of the Republic of Serbia, for confidence level of 90%, for the period 2008–2012. Source: Created by the authors.

Table 3. Review of the calculated values – how many times the actual loss exceeded the previous day VaR value for a portfolio consisting of bonds traded on the market of the Republic of Serbia, using the delta-normal method, for each year and for the entire period 2008–2012.

Delta normal method	2012	2011	2010	2009	2008	2008–2012.
	T = 250	T = 253	T = 251	T = 254	T = 254	T = 1262
p = 0.005	N = 3	N = 9	N = 10	N = 1	N = 8	N = 31
p = 0.01	N = 5	N = 10	N = 12	N = 2	N = 9	N = 38
p = 0.05	N = 7	N = 19	N = 17	N = 6	N = 14	N = 63
p = 0.1	N = 13	N = 26	N = 21	N = 9	N = 22	N = 91

Source: Authors’ calculation.

Table 4. Model verification: regions in which the model is not rejected at the significance level of 0.05.

Delta normal method	2012	2011	2010	2009	2008	2008–2012.
	T = 250	T = 253	T = 251	T = 254	T = 254	T = 1262
p = 0.005	0<N<4	0<N<4	0<N<4	0<N<4	0<N<4	0<N<12
p = 0.01	0<N<7	0<N<7	0<N<7	0<N<7	0<N<7	5<N<21
p = 0.05	5<N<20	5<N<20	5<N<20	5<N<21	5<N<21	47<N<79
p = 0.1	15<N<35	15<N<36	15<N<35	15<N<36	15<N<36	104<N<148

Source: Authors’ calculation.

Table 5. Model verification for a portfolio consisting of bonds traded on the market of the Republic of Serbia, using the delta-normal method, for different confidence levels, for each year and for the entire period 2008–2012.

Delta normal method	2012	2011	2010	2009	2008	2008–2012.
	T = 250	T = 253	T = 251	T = 254	T = 254	T = 1262
p = 0.005	accepted	rejected	rejected	accepted	rejected	rejected
p = 0.01	accepted	rejected	rejected	accepted	rejected	rejected
p = 0.05	accepted	accepted	accepted	accepted	accepted	accepted
p = 0.1	rejected	accepted	accepted	rejected	accepted	rejected

Source: Authors’ calculation.