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Risk-Return Relationship in High Frequency Data: Multiscale Analysis and Long Memory Effect

57 Pages Posted: 30 May 2008  

Jihyun Lee

KEB Hana Bank

Tong Suk Kim

KAIST College of Business

Hoe Kyung Lee

KAIST Business School

Date Written: May 2008


This study investigates the relationship between the return on a stock index and its volatility using high frequency data. Two well-known hypotheses are reexamined: the leverage effect and the volatility feedback effect hypotheses. In an analysis of the five-minute data from the S&P500 index, two distinct characteristics of high frequency data were found. First, it was noted that the sign of the relationship between the smallest wavelet scale components for return and volatility differs from those between other scale components. Second, it was found that long memory exists in the daily realized volatility. The study further demonstrates how these findings affect the risk and return relationship.

In the regression of changes in volatility on returns, it was found that the leverage effect does not appear in intraday data, in contrast to the results for daily data. It is believed that the difference can be attributed to the different relationships between scale components. By applying wavelet multiresolution analysis, it becomes clear that the leverage effect holds true between return and volatility components with scales equal to or larger than twenty minutes. However, these relationships are obscured in a five-minute data analysis because the smallest scale component accounts for a dominant portion of the variation of return.

In testing the volatility feedback hypothesis, a modified model was used to incorporate apparent long memory in the daily realized volatility. This makes both sides of the test model balanced in integration order. No evidence of a volatility feedback effect was found under these stipulations.

The results of this study reinforce the horizon dependency of the relationships. Hence, investors should assume different risk-return relationships for each horizon of interest. Additionally, the results show that the introduction of the long memory property to the proposed model is critical in the testing of risk-return relationships.

Keywords: risk-return relationship, high-frequency data, leverage effect, volatility feedback effect, multiresolution, wavelet, long memory

JEL Classification: C22, G1

Suggested Citation

Lee, Jihyun and Kim, Tong Suk and Lee, Hoe Kyung, Risk-Return Relationship in High Frequency Data: Multiscale Analysis and Long Memory Effect (May 2008). KAIST Business School Working Paper Series No. 2008-007. Available at SSRN: or

Jihyun Lee

KEB Hana Bank ( email )

66, Euljiro, Jung-Gu
Seoul, 100-719
Korea, Republic of (South Korea)

Tong Suk Kim

KAIST College of Business ( email )

85 Hoegiro, Dongdaemoon-gu
Seoul, 130-722
Korea, Republic of (South Korea)

Hoe Kyung Lee (Contact Author)

KAIST Business School ( email )

85 Hoegiro Dongdaemun-Gu
Seoul 130-722, 130-722
Korea, Republic of (South Korea)

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