On the usefulness of dynamically spilled risk: An optimal portfolio allocation based on cross-sector information contagion

Figures & data

Table 1. Sharpe ratio of each portfolio and each transaction cost

Mean	Maximum	Minimum	Std.	Skewness	Kurtosis	JB	ADF
0.9425	31.9418	0.1102	1.5245	9.6510	140.9759	1.5794*	−19.3398*

Notes: The statistics of the JB test is $\times {10}^6$, and * shows that the null hypothesis is rejected at the 1% level.

Figure 1. Total volatility spillover. The red and green dotted lines denote the increase and decrease of the total volatility spillover.

Figure 2. The time-varying portfolio weight of the food and steel sectors. The blue line is reallocated every day, and the red line is reallocated depending on the increase or decrease of the volatility spillover.

Figure 3. Cumulative returns net of three types of transaction costs with an initial value of ¥ 10,000. The spillover weight portfolio is based on the increase and decrease in the volatility spillover.

Table 2. Sharpe ratio of each portfolio and each transaction cost

	0 bp	1 bp	5 bp	10 bp	20 bp	50 bp	Times
Daily	0.0239	0.0226	0.0173	0.0107	−0.0025	−0.0418	1704
Weekly	0.0189	0.0183	0.0158	0.0126	0.0062	−0.0129	341
Monthly	0.0201	0.0198	0.0184	0.0167	0.0132	0.0029	78
Yearly	0.0244	0.0243	0.0238	0.0232	0.0219	0.0182	7
Spillover	0.0273	0.0271	0.0266	0.0260	0.0247	0.0208	9
Equal	0.0096	0.0096	0.0096	0.0096	0.0096	0.0096	0

Notes: The bp means 0.01%, and Times is the number of reallocations.

Figure 4. Cumulative returns net of three types of transaction costs with an initial value of ¥ 10,000. The spillover weight portfolio is based on the increase in the volatility spillover.

Figure 5. Cumulative returns net of three types of transaction costs with an initial value of ¥ 10,000. The spillover weight portfolio is based on the decrease in the volatility spillover.

Table 3. Sharpe ratio of two spillover weight portfolios depending on the increase and the decrease in the volatility spillover

	0 bp	1 bp	5 bp	10 bp	20 bp	50 bp	Times
Spillover (increase)	0.0281	0.0280	0.0277	0.0272	0.0263	0.0236	4
Spillover (decrease)	0.0172	0.0171	0.0168	0.0163	0.0154	0.0128	5

Notes: The bp means 0.01% and Times is the number of reallocations.

Figure 6. Robustness checks of time-varying spillover. The red line shows the baseline spillover whose order, window size, and forecast error horizon are $p=2$, $\omega =250$, and $H=5$, respectively. The light blue area shows from the minimum value to maximum value, and the dark blue area denotes the 25% and 75% quantiles.

Table 4. Sharpe ratio of each portfolio and each transaction cost

	0 bp	1 bp	5 bp	10 bp	20 bp	50 bp	Times
order ($p$)	$\omega =200$
Yearly	0.0261	0.0260	0.0254	0.0247	0.0232	0.0188	7
1	0.0275	0.0273	0.0267	0.0259	0.0244	0.0196	10
2	0.0267	0.0265	0.0259	0.0250	0.0234	0.0183	10
3	0.0263	0.0261	0.0255	0.0246	0.0230	0.0178	10
order ($p$)	$\omega =250$
Yearly	0.0261	0.0260	0.0255	0.0248	0.0235	0.0195	7
1	0.0306	0.0305	0.0300	0.0293	0.0280	0.0241	9
2	0.0302	0.0300	0.0295	0.0288	0.0275	0.0233	9
3	0.0295	0.0294	0.0288	0.0281	0.0268	0.0226	9
order ($p$)	$\omega =300$
Yearly	0.0101	0.0099	0.0095	0.0089	0.0078	0.0043	7
1	0.0173	0.0171	0.0167	0.0161	0.0150	0.0117	8
2	0.0176	0.0175	0.0170	0.0164	0.0153	0.0118	8
3	0.0176	0.0175	0.0171	0.0165	0.0153	0.0118	8

Notes: The order ($p$) denotes the order of each VAR model, and $\omega$ is the rolling-sample window and the sample size of sample covariance matrixes. The underline denotes the benchmark we used in Section 4.3.2, and the bold values are the best values among same rolling-sample window $\omega$.

Table 5. Sharpe ratio of minimum variance and mean-variance portfolios without short position

	0 bp	1 bp	5 bp	10 bp	20 bp	50 bp
Minimum variance without short
Daily	0.0121	0.0117	0.0102	0.0084	0.0048	−0.0062
Weekly	0.0098	0.0096	0.0089	0.0079	0.0061	0.0004
Monthly	0.0094	0.0093	0.0088	0.0083	0.0073	0.0042
Yearly	0.0138	0.0137	0.0136	0.0134	0.0130	0.0119
Spillover	0.0152	0.0152	0.0150	0.0148	0.0143	0.0130
Mean-variance without short
Daily	0.0344	0.0343	0.0339	0.0334	0.0323	0.0293
Weekly	0.0343	0.0342	0.0340	0.0337	0.0331	0.0313
Monthly	0.0346	0.0345	0.0344	0.0342	0.0338	0.0327
Yearly	0.0340	0.0340	0.0339	0.0339	0.0337	0.0334
Spillover	0.0365	0.0365	0.0364	0.0363	0.0361	0.0356

Notes: The bp means 0.01%, and Times is the number of reallocations.