Effects of risk aversion on securities portfolio performance in underdeveloped capital markets: the case of the capital market of Bosnia and Herzegovina

Figures & data

Figure 1. Illustration of the theoretical concept.

Source: Created by the authors.

Table 1. Mathematical models used in portfolio optimisation.

Optimality criterion:
Portfolio weights structure (for each model)

Source: Created by the authors in accordance with Modern Investment Technologies (2006–2008).

Table 2. General model performance analysis.

MODEL PERFORMANCE CHARACTERISTICS
		2	4	6	8	10
M1
Average Return Measures	Excess Mu	154.16%	78.98%	53.92%	40.58%	32.42%
	Expected Excess Growth Rate	116.25%	69.26%	49.42%	38.02%	30.78%
Risk Measures	Volatility	87.07%	44.08%	29.98%	22.59%	18.08%
	Value-at-Risk	27.15%	14.07%	9.63%	7.28%	5.84%
	Conditional Value-at-Risk	34.42%	18.52%	12.84%	9.78%	7.88%
Performance Measures	Sharpe Ratio	1.34	1.57	1.65	1.68	1.70
M2
Average Return Measures	Excess Mu	426.92%	212.87%	141.52%	105.84%	84.44%
	Expected Excess Growth Rate	319.90%	186.11%	129.62%	99.15%	80.15%
Risk Measures	Volatility	146.31%	73.16%	48.77%	36.58%	29.27%
	Value-at-Risk	34.83%	17.49%	11.62%	8.71%	6.96%
	Conditional Value-at-Risk	45.38%	24.47%	16.68%	12.65%	10.19%
Performance Measures	Sharpe Ratio	2.19	2.54	2.66	2.71	2.74
M3
Average Return Measures	Excess Mu	161.72%	80.86%	53.91%	40.43%	32.34%
	Expected Excess Growth Rate	121.29%	70.75%	49.42%	37.90%	30.73%
Risk Measures	Volatility	89.92%	44.96%	29.97%	22.48%	17.98%
	Value-at-Risk	27.82%	14.32%	9.62%	7.24%	5.81%
	Conditional Value-at-Risk	35.25%	18.85%	12.84%	9.73%	7.83%
Performance Measures	Sharpe Ratio	1.35	1.57	1.65	1.69	1.71
M4
Average Return Measures	Excess Mu	604.67%	302.33%	201.56%	151.17%	120.93%
	Expected Excess Growth Rate	453.50%	264.54%	184.76%	141.72%	114.89%
Risk Measures	Volatility	173.88%	86.94%	57.96%	43.47%	34.78%
	Value-at-Risk	36.09%	17.50%	11.42%	8.45%	6.70%
	Conditional Value-at-Risk	48.19%	25.72%	17.40%	13.13%	10.54%
Performance Measures	Sharpe Ratio	2.61	3.04	3.19	3.26	3.30

Source: Created by the authors.

Table

Criteria	Evaluation
Openness to foreign ownership
Investor qualification requirement	++
Foreign ownership limit (FOL) level	++
Foreign room level	++
Equal rights to foreign investors	++
Ease of capital inflows / outflows
Capital flow restriction level	++
Foreign exchange market liberalisation level^a	+
Efficiency of the operational framework
Market entry
Investor registration & account set up	++
Market organisation
Market regulations^b	+
Competitive landscape
Information flow	-/?
Market infrastructure
Clearing and Settlement	-/?
Custody^c	++
Registry / Depository^d	++
Trading	-/?
Transferability	-/?
Stock lending	-/?
Short selling	-/?
Stability of institutional framework	+

Table

Variables:	BATX	BHTSR	BIGFRK3	BSNFRK2	BSNLR	ELGJR	FDSSR	IBZRK2	JHKP	JPESR	MIGFRK2	NOVB	TCMKR	TLKM	ZPTP
Paremeters:
Mean	−0.0006	−0.0007	−0.00071	−0.0056	0.0080	−0.0076	−0.0652	−0.0005	0.0001	0.1525	−0.00328	−0.0011	0.0036	1.59E−05	0.0002
Median	−0.00053	−0.00124	−0.000488	0.000000	−3.20E-05	0.000000	−0.00197	−7.00E-05	−0.00023	−1.43E-17	−0.000118	−0.00037	1.93E-18	1.76E-18	−0.00052
Max	0.00486	0.008479	0.017360	0.081488	0.099162	0.019053	0.006402	0.017098	0.01093	1.66051	0.051293	0.00808	0.076961	0.00544	0.00856
Min	−0.00433	−0.00434	−0.022398	−0.110395	−0.01113	−0.13068	−0.73620	−0.01482	−0.01174	−0.01992	−0.053069	−0.01201	−0.04721	−0.00552	−0.00851
Std. Dev.	0.00178	0.002844	0.007164	0.031369	0.024359	0.027735	0.173159	0.006972	0.00507	0.41507	0.017961	0.00453	0.024036	0.00240	0.00411
Skewness	0.272735	1.041191	−0.856298	−0.406899	2.627860	−3.27656	−2.83694	0.466639	−0.01510	2.664181	−0.490007	−0.23236	1.364079	−0.29985	0.12488
Kurtosis	4.47014	4.191558	5.286723	6.285706	9.001441	13.58116	9.983538	3.631116	2.950997	8.78173	6.100412	3.28348	6.115168	2.94786	2.78733
Jarque-Bera	3.68828	8.634188	12.24314	17.18719	95.45983	232.3565	121.4439	1.903971	0.004969	92.72970	15.85947	0.444494	25.72067	0.543539	0.161417
Probability	0.15816	0.013339	0.002195	0.000185	0.000000	0.000000	0.000000	0.385974	0.99752	0.00000	0.000360	0.80072	0.000003	0.76203	0.92246
Sum	−0.02158	−0.02359	−0.025376	−0.20007	0.28580	−0.27401	−2.34705	−0.01929	0.003779	5.488825	−0.118226	−0.03859	0.129085	0.000573	0.00704
Sum Sq. Dev.	0.00011	0.000283	0.001796	0.034439	0.020768	0.026923	1.049436	0.001701	0.00090	6.03003	0.011291	0.00072	0.020221	0.00020	0.00059

Figure C1. Skewness and kurtosis excess.

Source: Created by the authors.

Table

		BATX	BHTSR	BIGFRK3	BSNFRK2	BSNLR	ELGJR	FDSSR	IBZRK2	JPESR	JHKP-R-A	MIGFRK2	NOVB-R-E	TCMKR	TLKM-R-A	ZPTP-R-A
BATX	Pearson Correlation	1	0.683^**	0.568^**	−0.115	0.119	−0.008	0.022	0.407^*	0.002	0.048	0.133	0.161	−0.100	0.295	0.200
	Sig, (2-tailed)		0.000	0.000	0.496	0.484	0.961	0.899	0.012	0.990	0.778	0.433	0.342	0.558	0.076	0.236
BHTSR	Pearson Correlation		1	0.324	−0.392^*	−0.043	0.056	0.117	0.311	−0.108	0.039	−0.079	−0.136	−0.282	−0.034	−0.065
	Sig, (2-tailed)			0.051	0.017	0.799	0.748	0.491	0.061	0.526	0.817	0.641	0.423	0.091	0.843	0.702
BIGFRK3	Pearson Correlation			1	0.071	0.115	−0.077	−0.046	0.337^*	0.053	0.294	0.298	0.176	−0.060	0.223	0.488^**
	Sig, (2-tailed)				0.675	0.498	0.655	0.788	0.041	0.755	0.077	0.073	0.299	0.725	0.184	0.002
BSNFRK2	Pearson Correlation				1	0.200	−0.088	−0.201	−0.184	0.246	0.149	0.254	0.074	−0.145	0.196	0.145
	Sig, (2-tailed)					0.236	0.611	0.232	0.274	0.143	0.377	0.129	0.663	0.390	0.245	0.392
BSNLR	Pearson Correlation					1	0.018	−0.981^**	0.105	0.985^**	0.257	0.158	0.060	0.077	−0.055	0.230
	Sig, (2-tailed)						0.915	0.000	0.535	0.000	0.125	0.350	0.722	0.650	0.746	0.172
ELGJR	Pearson Correlation						1	−0.036	−0.026	0.018	0.312	−0.020	0.184	0.152	0.222	−0.029
	Sig, (2-tailed)							0.836	0.882	0.917	0.064	0.906	0.282	0.376	0.192	0.867
FDSSR	Pearson Correlation							1	−0.078	−0.996^**	−0.285	−0.133	−0.018	−0.132	0.056	−0.200
	Sig, (2-tailed)								0.647	0.000	0.087	0.433	0.914	0.437	0.742	0.234
IBZRK2	Pearson Correlation								1	0.081	0.114	0.173	−0.005	0.208	0.236	0.178
	Sig, (2-tailed)									0.632	0.502	0.307	0.976	0.217	0.160	0.291
JPESR	Pearson Correlation									1	0.276	0.133	0.018	0.101	−0.038	0.207
	Sig, (2-tailed)										0.098	0.431	0.916	0.551	0.824	0.218
JHKP-R-A	Pearson Correlation										1	0.201	0.034	0.081	0.084	0.660^**
	Sig, (2-tailed)											0.232	0.843	0.634	0.621	0.000
MIGFRK2	Pearson Correlation											1	0.329^*	0.008	−0.038	0.066
	Sig, (2-tailed)												0.047	0.963	0.824	0.698
NOVB-R-E	Pearson Correlation												1	−0.144	0.179	0.159
	Sig, (2-tailed)													0.396	0.290	0.349
TCMKR	Pearson Correlation													1	0.289	0.042
	Sig, (2-tailed)														0.082	0.807
TLKM-R-A	Pearson Correlation														1	0.262
	Sig, (2-tailed)															0.117
ZPTP-R-A	Pearson Correlation															1
	Sig, (2-tailed)

Table

Model:	M1					M2					M3					M4
λA(x) →	2	4	6	8	10	2	4	6	8	10	2	4	6	8	10	2	4	6	8	10
Portfolio structure ↓	Portfolio weights ↓
Cash	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	−1.99	−0.50	0.00	0.25	0.40	149.96	75.48	50.65	38.24	30.79
BSNLR	0.00	0.00	0.00	0.00	0.00	−62.68	−31.23	−20.75	−15.51	−12.37	0.00	0.00	0.00	0.00	0.00	−94.29	−47.15	−31.43	−23.57	−18.86
JHKP-R-A	0.00	0.00	0.00	0.00	0.00	−19.54	−9.70	−6.41	−4.77	−3.79	0.00	0.00	0.00	0.00	0.00	−41.79	−20.90	−13.93	−10.45	−8.36
JPESR	0.98	0.49	0.33	0.25	0.20	6.42	3.20	2.13	1.59	1.27	0.98	0.49	0.33	0.25	0.20	9.22	4.61	3.07	2.31	1.84
TCMKR	0.02	0.51	0.67	0.55	0.43	1.15	0.57	0.37	0.28	0.22	2.01	1.00	0.67	0.50	0.40	3.26	1.63	1.09	0.82	0.65
TLKM-R-A	0.00	0.00	0.00	0.21	0.37	34.69	17.71	12.05	9.22	7.52	0.00	0.00	0.00	0.00	0.00	−74.94	−37.47	−24.98	−18.74	−14.99
ZPTP-R-A	0.00	0.00	0.00	0.00	0.00	40.96	20.45	13.61	10.20	8.15	0.00	0.00	0.00	0.00	0.00	49.58	24.79	16.53	12.39	9.92
∑	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00

Modern Investment Technologies. (2006-2008). Multi-period asset allocation: SmartFolio theoretical background. Moscow: Modern Investment Technologies Ltd.

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