# Dynamic volatility management: from conditional volatility to realized volatility

## Rongju Zhang, Nicolas Langrené, Yu Tian and Zili Zhu

#### Need to know

• The volatility of concern in conventional volatility-managed strategies such as volatility targeting and mean–variance optimization is the expected conditional volatility.
• However, for investors, it is the realized volatility that is important, because there is only one realization in the market.
• This paper provides a multiperiod strategy that directly manages the realized volatility over a long horizon.

#### Abstract

The volatility of concern in conventional volatility-managed  strategies such as volatility targeting and mean–variance optimization is the expected conditional volatility. However, for investors, it is the realized volatility that is important, because there is only one realization in the market. Simply managing the conditional volatility may not help regulate the realized volatility of the actual portfolio performance. This paper provides a multiperiod strategy that directly manages the realized volatility over a long horizon. More specifically, the strategy maximizes the expected portfolio value subject to an upper cap on the realized volatility. Our out-of-sample backtesting results show that this novel strategy delivers higher risk-adjusted returns than volatility targeting, and it successfully caps the realized volatility below the targeted level. The results are consistent across twelve equity markets and five targeted volatility levels.