Portfolio Allocation with Realized Volatility Components

ponents

High frequency data also allows us to extract different components of total realized volatility. In this section, we investigate whether decomposing real- ized volatility into different components can improve portfolio allocation. The

purpose is twofold: Firstly, we investigate whether strategies using realized volatility components can outperform low frequency strategies. Secondly, we also want to assess whether the decomposition leads to significant incremental improvement over the high frequency benchmark strategy, i.e. the RV strategy we used in the previous section.

Table 3.7 documents the out-of-sample portfolio allocation results using real- ized volatility components. Initially, we show that both the upside and downside volatility strategy (RS) and the jump and diffusive volatility strategy (RJ) can

lead to higherSRs relative to the low frequency benchmark and high frequency

benchmark strategies. The result holds true for both zero and DCC correlations and for different rebalancing frequencies. The upside and downside volatility strategy performs better than the jump and diffusive volatility strategy, which is consistent with its statistical performance. At the daily rebalancing frequency,

the upside and downside volatility strategy can generate SRs of 0.59 and 0.60

for zero and DCC correlations respectively. We observe improvements of SRs

to 0.75 and 1.01 at the weekly frequency. At the monthly frequency, SRs are

0.63 and 0.56. Different from strategies using realized volatility alone, strategies using realized volatility components with DCC perform better than with zero correlations when we rebalance portfolios at daily and weekly frequencies.

We also find that strategies using upside and downside volatility componnets have lower turnover rates than the total realized volatility strategy. Although, the strategy using total realized volatility has higher turnover than the low frequency benchmark as we documented in the previous section, we find that the strategy using upside and downside volatility components has even lower

turnover than the low frequency benchmark under zero correlation for different rebalancing frequencies. For instance, at a daily level, the turnover statistics of the upside and downside volatility strategy under zero correlation is 0.93% per day, which is lower than 0.96% for the high frequency benchmark and 0.94% for the low frequency benchmark. With DCC correlation, the strategy has lower turnover than the high frequency benchmark but not the low frequency bench- mark. Although upside and downside volatility component strategies need to incorporate recent downside risks information quickly, they can still have lower turnover, supporting that further decomposing realized volatility into different component can be beneficial for portfolio allocation.

Moreover, we show that strategies using realized volatility components can out- perform the low frequency benchmark strategies and deliver larger economic improvements compared to high frequency benchmark strategies. At the daily frequency, the upside and downside volatility strategy can generate performance

fees from 60 (γ = 10) to 208 (γ = 2) basis points using zero correlations, rep-

resenting 81% and 67% increases respectively compared with ones we obtained from realized volatility strategy discussed above. Using DCC correlations again

increases the economic values. However, since the SRs are also higher with

DCC, these larger economic values do not entirely reflect the poor performance of the low frequency benchmark strategy, but also reflect the benefit of mod- elling the correlation dynamics. Upside and downside volatility strategies and jump and diffusive volatility strategies have positive and statistically significant performance fees with t-statistics above 3.00 and 2.00 respectively. The perfor- mance fees remain positive and statistically significant when we rebalance the portfolio at the weekly frequency. In the last section, we show that RV strate-

gies become insignificant at the monthly frequency. In this section, however, we show that both the realized volatility component strategies are significant for zero correlation and the jump and diffusive strategy is still significant for DCC correlations. The larger economic magnitudes and the success even in longer horizons imply that decomposing total realized volatility into different components improves portfolio allocation.

Strategies using realized volatility components can also generate incremental economic benefits over the high frequency benchmark strategies using realized volatility alone. We compute the performance fees of realized volatility com- ponent strategies relative to high frequency benchmarks. The economic mag- nitudes of incremental benefits are smaller due to the use of high frequency benchmarks. However, all performance fees relative to high frequency bench- marks are positive. Moreover, at the daily frequency, the strategy using upside and downside volatility components can generate positive and statistically sig- nificant performance fees relative to the high frequency benchmarks with zero correlations. The incremental benefits range from 27 to 83 basis points. At the weekly frequency, upside and downside volatility strategies under both zero and DCC correlations can generate positive and statistically significant incremental economic values relative to high frequency benchmarks, ranging from 37 to 109 (zero) and 109 to 386 (DCC). The large incremental benefit for DCC implies its benefits for modelling correlations, while its statistical insignificance at the daily frequency suggests that it is still unstable. To summarize, our findings sug- gest that the previous documented statistical success of decomposing realized volatility into different components is also economically significant. We show that separating total realized volatility into different components can lead to

higher SRs, lower T Os, large economic improvements to low frequency bench- marks, and positive and statistically significant incremental improvements over high frequency benchmarks.

3.4.4

Portfolio Allocation with Realized Higher Moments

High frequency data further contributes to the construction of realized higher moments. In this section, we investigate whether including realized higher mo- ments as additional volatility predictors can improve portfolio allocation.

Table 3.8 reports out-of-sample portfolio allocation results using realized higher moments. Although models using realized higher moments have mixed volatil- ity forecasting performance as we documented before, we find that strategies

using realized skewness and kurtosis can generally generate higher SRs com-

pared to both low frequency and high frequency benchmarks. At the daily

frequency, SRs are 0.59 (zero) and 0.72 (DCC) for skewness strategies (RSK)

and 0.72 (zero) and 0.78 (DCC) for kurtosis strategies (RKU).SRs for skewness

strategies strengthen at the weekly frequency to 0.89 and 1.14, while SRs for

kurtosis strategies become 0.63 and 0.79. The skewness strategy also performs better at the monthly frequency. However both higher moment strategies have higher turnover compared to the low frequency benchmarks, the high frequency benchmarks, and the realized volatility component strategies. For example, at

the daily frequency, the T Os are 0.99% (zero) and 1.43% (DCC) for skewness

strategies, and 1.02% (zero) and 1.54% (DCC) for kurtosis strategies. The

higher SRs and T Os of higher moment strategies suggest that these strategies

maybe more volatile compared to the realized volatility and volatility compo- nent strategies.

Similar to volatility component strategies, higher moment strategies also gen- erate larger economic benefits relative to low frequency benchmarks. At the daily frequency, performance fees are 56 to 200 basis points for the skewness strategy and 102 to 324 basis points for the kurtosis strategy with zero corre- lations. Both higher moments strategies can generate positive and statistically significant economic values, although the kurtosis strategy with zero correla- tions has slightly weaker statistical significance. At the weekly frequency, while the skewness strategy remains positive and significant, the kurtosis strategy be- comes insignificant. At the monthly frequency, both higher moment strategies are generally insignificant for zero correlations but the kurtosis strategy is sig- nificant for DCC correlations. Different from all high frequency strategies we considered before, the kurtosis strategy fails to generate significant benefit rel- ative to the low frequency benchmark with zero correlations in short horizons, implying that including kurtosis as an additional volatility predictor actually introduces more noise.

We further investigate the incremental benefit of using realized higher moment information. At the daily frequency, the skewness strategies with DCC are marginally significant with incremental values of 87 to 338 basis points. At the weekly frequency, the skewness strategies generate positive and statistically significant performance fees of 61 to 233 basis points (zero) and 134 to 538 basis points (DCC). Kurtosis strategies, however, generate insignificant perfor- mance fees at daily and weekly frequencies, and even underperform the high frequency benchmark at the monthly frequency with zero correlation. To sum- marize, realized higher moments, measuring asymmetry and tail events, contain

important information to improve portfolio performance. Compared with re- alized volatility and volatility component strategies, higher moment strategies generate larger economic benefits, however their improvements are generally more unstable.

3.5

Robustness Checks

In this section, we conduct comprehensive robustness checks. We compare high frequency strategies with different low frequency benchmarks and consider dif- ferent correlation structures. We also assess the impact of market microstruc- ture noise and transaction costs on portfolio performance.