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Our main findings provide clear evidence that high frequency data improves portfolio allocation. However, we do observe that the magnitudes of economic improvements are affected by the choice of the benchmark strategies and the selection of correlation structures. In this section, we analyse whether high fre- quency data can still improve portfolio allocation when alternative benchmarks and correlation structures are employed.

Rather than attempting to develop the optimal portfolio strategy, our paper aims for a better understanding of the use of high frequency data in portfolio allocation. Hence, the benchmark strategies in the main analysis are selected to facilitate answering our main research questions, but they do not neces- sarily reflect the real world investment problems, e.g. the poor performance of GARCH-DCC as a low frequency benchmark tends to overestimate the true

benefit of high frequency data in real world portfolio allocation exercises. Hence, we are interested in how high frequency strategies perform in comparison to low frequency strategies commonly used in the literature. We use two alternative low frequency benchmark strategies: the 1/N strategy and the RiskMetrics (RM) strategy. The naive 1/N strategy assigns static and equal weights to all assets, which is proportional to the number of assets (hence 1/N). Previous studies (DeMiguel, DeMiguel, and Uppal 2009, DeMiguel, Plyakha, Uppal, and Vilkov 2013, Jacobs, Muller, and Weber 2014) document that the 1/N strategy performs very well compared to a few more sophisticated and dynamic strate- gies, despite its simplicity. The RiskMetrics 1994 (RM) is a standard approach following a simple exponentially weighted moving average rule used in the in- dustry to forecast covariance matrix. We follow J.P.Morgan/Reuters (1996) and Hautsch, Kyj, and Malec (2013), and specify the model as follows:

ˆ Σt+1 = 1₋λ 1₋λL−1 L X l=1 λl−1ut−l+1u′t−l+1 (3.24)

We follow J.P.Morgan/Reuters (1996) to select the smoothing parameter λ =

0.94, and the rolling window lengthL= 250. In this section, we are interested

in how high frequency based strategies perform relative to these alternative low frequency benchmark strategies.

In the main analysis, we observe a large difference in magnitudes of economic values due to the use of different correlations structures. In this section, we consider two additional correlation structures. Firstly, we extract the correla- tion matrix from the RM model we employed above and combine it with high frequency based volatilities. Secondly, we use the sample correlation (SC) com-

puted using in-sample data.4 _{We investigate the performance of high frequency}

strategies with four different correlation structures (zero, DCC, RM, SC) rela- tive to two low frequency benchmark strategies (1/N and RM). Table 3.9 reports out-of-sample portfolio performance results for these different strategies. We fo- cus on the annualized Sharp Ratios for different rebalancing frequencies.

We first examine how our existing strategies perform relative to these two bench- mark strategies. For the zero correlations, the RV strategy cannot outperform either benchmark strategy at any frequency, suggesting that these two low fre-

quency benchmarks (e.g. SRs are 0.61 and 0.57 for 1/N and RM respectively

with daily rebalancing) are higher than ones used in the main analysis. How- ever, decomposing volatility into components and using higher moments can outperform these benchmarks at daily and weekly frequencies. Strategies us-

ing upside and downside volatility components (RS) can generate higher SRs

than the RM strategy at the daily frequency and than the 1/N at the weekly frequency. Strategies using skewness (RSK) can beat the RM at the daily fre- quency and both benchmarks at the weekly frequency. Jump strategies (RJ) fail to outperform either benchmark while Kurtosis strategies (RKU) outperform both benchmark at the daily frequency but underperform both at the weekly frequency. Our findings confirm that high frequency data is important for port- folio allocation even if we do not model the correlation dynamics.

For the DCC correlations, we show that the RV strategy still fails to outper- form either benchmark. However, strategies using volatility components and 4_{In an unreported analysis, we also consider two additional correlation structures based on}

smoothing the DCC correlations: the in-sample mean of DCC based correlation and 250 days rolling window mean of DCC based correlation, we found results are similar to the raw DCC based strategies.

higher moments generally perform better at daily and weekly frequencies. The RS strategy beats the RM at the daily and both benchmarks at the weekly

frequency. The RJ strategy can now generate higher SRs relative to both

benchmarks at the weekly frequency. Higher moment strategies can outper- form both benchmarks at weekly and monthly frequencies. Therefore, the large economic values with DCC correlations, especially incremental improvements relative to high frequency benchmarks documented in the main analysis are not entirely due to the selection of benchmarks. Instead, modelling time varying correlations does lead to further portfolio performance improvements.

We then discuss portfolio performance with alternative correlation structures. Despite the success of zero and DCC based strategies, the relative unstable performance for the DCC correlations motivates us to consider more stable cor- relation structures. The smoothed (RM) and static (SC) correlations are less volatile than DCC. Hence their associated portfolios are also expected to per- form better. We find that all high frequency strategies with RM correlations can outperform both low frequency benchmarks. Different from results before, RV strategies can outperform both 1/N and RM benchmarks at all frequen-

cies, when RM correlations are used. For instance, it has a SR of 0.86 at the

daily frequency, which is also higher than RV strategies with zero (0.50) and DCC (0.41) correlations. Moreover, high frequency strategies with RM can even outperform benchmarks at the monthly frequency, which is not observed when other correlation structures are used. However, we find that incremen- tal benefits for volatility components and higher moments relative to RV are reduced or even negative, which is different from strategies using other correla-

(0.80 and 1.28) underperform RV (0.86 and 1.13) at the daily frequency and outperform slightly at the weekly frequency. Due to the smoothed correlations from RM, the drop of incremental benefit of using more rapidly changing alter- native realized measures are as expected. Our findings imply that combining high frequency based volatilities with a slow moving correlation structure seems to be promising for portfolio allocation.

For SC correlations, RV strategies again fail to outperform the benchmarks. However, portfolio performance improves when we decompose volatility into different components. The RS strategy outperforms benchmarks for all fre-

quencies (SRs are 0.75, 1.09, and 0.88 respectively). The RJ strategies outper-

form benchmarks at weekly and monthly frequencies. Higher moment strate- gies, which performed well with other correlation structures, generally perform poorly. Results with sample correlations (SC) are more consistent with sta- tistical performance, which may be largely due to the use of static correlation structures.

Although the zero correlation based strategies look oversimplified while the DCC based strategies seem unstable, we find that these high frequency strate- gies can outperform well known low frequency strategies used in the litera- ture under some circumstances. Using alternative correlation structures even strengthens our main results. We also show that the additional benefits from volatility components and higher moments depend on the choice of the correla- tion structures. To summarize, our main arguments remain hold when different low frequency benchmarks and different correlation structures are used.