Low-Risk Anomalies: Properties, Causes, and Low-Volatility Factor Construction

Chinese

In the long run, the expected return of low-volatility stocks is higher than that of high-volatility stocks. This is the low-volatility (low-risk) anomaly that has existed in global markets for a long time. This article introduces the main nature and causes of low-risk anomalies, and lists common factor construction methods, hoping to provide an outline and guidance for factor investment in the volatility category among volume and price factors.

Properties

Volatility, as the most common risk measure, describes the dispersion of returns. Its classification includes historical volatility, realized volatility and implied volatility. volatility), where historical volatility is the standard deviation of returns in the past period; realized volatility is the sum of squares of intraday high-frequency logarithmic returns. The theory guarantees that such a definition converges to the intraday integral volatility based on probability under the assumption that the price dynamic process does not contain jumps, and is a good estimator of it, which can better describe the fluctuation of intraday returns; Implied volatility is generally obtained by inverting the option price through the Black Scholes formula, and can be regarded as the expectation of the future volatility of the underlying asset. There is a significant negative correlation between stock volatility and future returns, which is called a low risk anomaly by academics.

Like most volume and price factors, the return rate of the volatility factor has obvious asymmetry, with short returns being much greater than long returns. What makes it unique is its countercyclical nature - it performs poorly in bull market phases but performs better in bear markets, thus providing some drawdown protection. The main reason for this phenomenon is that low-risk anomalies are mainly driven by irrational behavior. In a bull market with high investor sentiment, mispricing of highly valued stocks is difficult to repair, and volatility factors will experience sharp retracements. When the market is down, investors will pay more attention to the downside risks of stocks.

The volatility factor is inextricably linked to the value and market capitalization factors, and can also be partially explained by the quality factor. Low-volatility stocks tend to be large-cap stocks with low valuations. Small-capitalization stocks have higher impact costs and more speculation, so they have higher volatility. In fact, low volatility factors have better performance in stocks with higher impact costs, no analyst coverage, non-stock index futures index corresponding constituent stocks and non-securities lending stocks. If growth is used to define momentum and volatility is used to define risk, then the relationship between the momentum factor and the volatility factor is the relationship between the first-order moment and the second-order moment of the return rate. The two cannot explain each other, and there is such a relationship - the return of the high volatility loser portfolio is much lower than that of the high volatility winner portfolio, and the poor performance of high volatility is mainly contributed by the loser stocks. This nonlinear relationship should be considered in factor combinations.

Cause

Individual investors

Low-risk anomalies, especially in the A-share market, can mainly be attributed to mispricing caused by irrational investor behavior. Individual investors have irrational behaviors such as gambling preferences, representativeness bias, and overconfidence. They have excessive demand for high-volatility stocks and insufficient demand for low-volatility stocks, causing high-volatility stocks to overestimate the current price and low-volatility stocks to underestimate. Therefore, low-volatility stocks have higher expected returns than high-volatility stocks. Let’s focus on Gaming Preference. According to behavioral finance theory, people tend to overestimate the impact of small-probability events. Therefore, stocks with abnormal increases in the past (corresponding to positive skewness) will be purchased out of a speculative mentality, expecting to obtain high returns in a short period of time. Such stocks are also called lottery stocks.

Institutional Investors

Institutional investors are more professional than retail investors, but there are also behavioral deviations. The first is arbitrage restrictions. In an ideal market, investors would arbitrage stocks that are overvalued or undervalued, mispricings would be quickly repaired, and future prices are unpredictable. However, in reality, especially in the A-share market, there is a lack of effective, low-cost short-selling mechanisms. High-volatility stocks tend to be small-capitalization companies. The transaction costs, financing restrictions, and financing costs of shorting small-capitalization companies are very high, which limits short-selling transactions in high-volatility stocks.

The second is the principal-agent problem. Although overweighting low-volatility stocks will increase portfolio excess returns to a certain extent, it also brings more tracking errors compared to the performance comparison benchmark, which is not attractive to institutional investors whose investment goals are to maximize the information ratio (excess returns divided by tracking error) compared to the performance comparison benchmark. A darker idea is that the incentive mechanism for many fund managers is basic salary plus performance commission. The latter is like an option. Fund managers can maximize their expected income by picking stocks with higher volatility.

In short, due to the existence of arbitrage restrictions such as short selling costs, limited leverage, and fixed performance comparison benchmarks, institutional investors cannot arbitrage low-risk anomalies. In practice, this will even further exacerbate the low-volatility anomaly caused by individual investor behavioral deviations, causing the low-volatility anomaly to continue.

Factor construction

Daily frequency volatility

• Simple volatility std
• Daily return skew
• Real volatility
• Amplitude
  -Improvement: Founder Securities-Individual stock price jumps and improvements to the amplitude factor
  • Improvement: Open Source Securities - Hidden structure of amplitude factors
• Trait Class
  • Idiosyncratic volatility
  • trait skewness
  • Specificity
• MAX
• MIN

High frequency volatility

For details, see Measurement and Decomposition of High Frequency Volatility

• Higher order moments
  • Realized volatility
  • Realized skewness
  • Kurtosis achieved
  • Superskewness achieved
  • Excess kurtosis achieved
• Tail risk
  • VaR
  • cVaR
  • VaR_RT
  • cVaR_RT
• Risk uncertainty factors
  -VoV
  -VoK
  • VoHT
  • VoVaR/VocVaR
• Volatility decomposition
  • Upward Jump Volatility RJVP
  • Upside and Downside Jump Volatility Asymmetry SRJV
  • Long range upside jump volatility RLJVP
  • Long-range up and down jump volatility asymmetry SRLJV

In the calculation of all high-frequency factors, the rate of return can be replaced by the idiosyncratic rate of return. For details, see [Idiosyncratic Factor Analysis] (https://heth.ink/IdiosyncraticRisk/), which will not be described in detail here.

References

• Low-Risk Anomalies Ishikawa
• Minsheng Securities - Factor Research Topic 4 - Low Volatility Anomaly: Analysis, Improvement and Empirical Causes
• Caitong Securities-Gaming preference or risk compensation? Full analysis of high-frequency idiosyncratic skewness factors
• There are three ways to write the word “fennel”. What about the low-risk anomaly factor? llanglli