LuoShu Investment: A Priori Factors and Volatility-Equal Weighting

Starting today, we officially launch a new series: Decoding Private Fund Founder Interviews. The core objective of this series is to distill practical quantitative investing knowledge and key industry insights from founders’ public shares. In our inaugural episode, we dive into LuoShu Investment to analyze founder Xie Dong’s interview.

The Origin: An Alumni Connection

Why did we choose LuoShu Investment for this first episode? Previously, we reviewed the academic backgrounds of numerous private fund founders. Amidst a sea of pedigrees from Tsinghua, Peking University, Fudan, Shanghai Jiao Tong University, MIT, and Stanford, I unexpectedly discovered that Mr. Li Nanfeng of LuoShu Investment is an alumnus of my own university (note: the author of this article is Flora). This alumni connection sparked a sense of familiarity and pride, motivating me to explore this institution in depth.

Today, we are analyzing an interview with Xie Dong published by the China Securities Journal in March 2025, titled "The Quantitative Long-Distance Runner: Ten Years of Pioneering". In this concise interview, my primary interest lies in Mr. Xie’s introduction to LuoShu’s research system. Let’s explore what valuable insights we can extract from his sharing.

Regarding the company’s current investment and research system, Mr. Xie uses quantitative CTA strategies as an example, noting that the process generally involves two core stages.

“First is factor mining, which forms the basic units of various strategies. We identify quantifiable factors and build a factor library for combination. For instance, after selecting factors related to trends, term structures, and fundamentals, we use quantitative methods to test and present them. In this process, Mr. Xie emphasized that unlike most peers who believe quantitative methods rely on statistical arbitrage—i.e., ‘believing history will repeat itself’—LuoShu’s a priori factors place greater faith in ‘the economic laws behind factors remaining valid in the future’ rather than simple ‘phenomenon repetition’.”

“Second, in strategy combination, the company adopts a volatility-equal-weighted allocation method. We do not subjectively time the market or adjust strategy weights based on market conditions. Instead, we rely entirely on refined risk management models for scientific and objective management, truly practicing quantitative investing methods and philosophy.”

LuoShu’s Core Distinction: A Priori Logic vs. Statistical Arbitrage

I extracted two key points from this statement.

The first piece of information is that LuoShu Investment’s a priori factors differ from peers’ reliance on “history repeating itself” via statistical arbitrage; they believe more in the economic laws underlying factors.

This brief sentence precisely highlights the essential difference between LuoShu’s quantitative logic and that of most peers. How should we understand this?

Let’s first examine the quantitative logic of most peers mentioned by Mr. Xie. Please note the terms history repetition and statistical arbitrage. Relying on “history repeating itself” through statistical arbitrage means many quants construct strategies by挖掘 (mining) statistical correlations that appear related in historical data but lack clear logical support. They treat quantitative analysis as purely data-based statistical induction.

Next, please note the terms a priori factors and economic laws. The key to LuoShu’s “a priori factors” lies in the word a priori. This means their factor construction first anchors explicit economic laws and then uses data to verify the sustainability of those laws. In other words, it is not simply piecing together correlations from data but is a deductive reasoning process based on economic logic.

In a previous podcast episode on quantitative basics, I mentioned that in the book Inside the Black Box, author Rishi Narang classifies alpha models into theory-driven alpha models and data-driven alpha models.

Theory-driven alpha models can be further divided into six categories. Using two strategies as examples, let’s establish a basic understanding of the “theory-driven” definition for such strategies. For instance, the basic theory of mean reversion strategies posits that prices fluctuate around their value center. Identifying this center and the direction of fluctuation is sufficient to capture trading opportunities. Similarly, trend-following strategies are based on the assumption that “markets tend to move in the same direction over a certain period.” Judging market trends based on this assumption can serve as the basis for formulating trading strategies. The fundamental economic principle underlying trend methods is market equilibrium theory.

In contrast, the input variables for data-driven alpha models are primarily trading-related, such as price data. They attempt to find patterns within this data that have explanatory power for the future. The advantage of these experience-based models, as noted in the text, is their ability to identify market behaviors regardless of whether current theory can explain them, thereby allowing discovery even without understanding the causes of certain market behaviors. However, theory-driven models can only capture behaviors that people have some understanding of, so their scope is limited to the six categories mentioned, such as mean reversion and trend following. The disadvantages of data-driven alpha models are also obvious. For example, if the data used by researchers for modeling has no connection or very low correlation with what they want to predict, it leads to backtests that “buy the earth” but live trading results that “lose like a dog.”

With this knowledge background, we can naturally discover that the quantitative strategies of most peers mentioned by Mr. Xie belong to data-driven alpha models, while LuoShu’s strategies belong to theory-driven alpha models.

Thought Experiment: The Bayesian Detective’s Logic

Additionally, when you hear the term “a priori,” what comes to mind? When I see “a priori,” I subconsciously associate it with the Bayesian school in statistics. The core philosophy of Bayesianism is that our understanding of the world is not a blank slate but comes with “prejudices” (priors); new evidence is merely used to correct these prejudices. The other important branch of statistics, contrasting with this, is the Frequentist probability school.

To help everyone understand the difference between Bayesian and Frequentist approaches, let’s use a detective case example.

Imagine you are an experienced Bayesian detective investigating a密室 (locked-room) burglary. You would reason through the case in three steps:

Step 1: Establish the “Prior” (Prior). Before visiting the scene to look for evidence, based on experience and case files, you discover that Suspect A owes huge gambling debts and has a prior theft record, while Suspect B is a famous philanthropist with immense wealth. At this point, your logical judgment (prior probability) tells you: the likelihood of A committing the crime is high, while B’s is extremely low. This is starting with “prejudice,” which is what LuoShu emphasizes as “economic logic.”

Step 2: Examine the “Likelihood” (Likelihood). This involves looking at the evidence. You arrive at the scene and find a fingerprint on the safe. After comparison, this fingerprint surprisingly belongs to B. This new evidence (data) is very strong and greatly supports the hypothesis that “B is the murderer.”

Step 3: Derive the “Posterior” (Posterior). You need to update your judgment by combining the prior that “A has motive” with the evidence that “B has the fingerprint.”

At this point, the leader assigns another detective, a Frequentist, to work with you. Here, the divergence between the two schools appears.

The Frequentist believes that data can only tell us probabilities and confidence intervals around those probabilities. Therefore, regarding the interpretation of the case, they would say: “The data shows a 99.9% fingerprint match (significant P-value), and facts indicate this fingerprint was left by suspect B. Based on the data, we infer B is the criminal.” They only describe the facts presented by the data, caring not whether B is a philanthropist, nor do they presuppose a stance like “B has no motive.”

The Bayesian, however, would be more cautious. They would argue: Although the fingerprint belongs to B (data support), B has absolutely no motive (strong prior logic). Could it be that someone forged his fingerprint to frame him?

Therefore, although the Bayesian would increase suspicion of B due to the fingerprint evidence (correcting the prior), they would not blindly trust a single piece of data evidence because of the strong prior logic (economic laws) underlying their analysis.

Similarly, if a strategy’s backtest data is exceptionally good but cannot be explained logically, LuoShu might consider it a “forged fingerprint”—i.e., overfitting—and thus abandon it.

By now, I believe astute readers have vaguely sensed the philosophical connections between the economic theories of theory-driven alpha models and Bayesian priors, as well as between data-driven alpha models and Frequentist statistics.

The Art of Position Management: Volatility-Equal Weighting

Next, let’s look at the second point of focus. Mr. Xie mentioned: “In strategy combination, LuoShu adopts a volatility-equal-weighted allocation method and does not subjectively time the market or adjust strategy weights based on market conditions.” Please pay attention to the terms volatility and equal-weight.

The book Inside the Black Box classifies risk measurement into two dimensions: longitudinal and cross-sectional. The core logic and application scenarios of these two methods differ significantly.

The first is longitudinal risk measurement, which focuses on the uncertainty of returns for a single product over time. The specific calculation method is to collect the return data of a product across different periods—note the keyword “different periods”—and then measure the risk level by calculating the standard deviation of that product’s returns. In the financial field, this standard deviation metric is collectively referred to as volatility. The higher the volatility value, the more剧烈 (severe) the return fluctuations of that product, and the greater the risk of the single asset.

The second is cross-sectional risk measurement, which focuses on the performance differences among various financial products at the same point in time and within a given scope. Please note the keywords “same point in time” and “given scope.” The calculation method for cross-sectional risk measurement is to collect the return situations of all related financial products at the same moment and calculate their cross-sectional standard deviation. The larger the value of the cross-sectional standard deviation, the more pronounced the performance differentiation and the higher the diversification degree of these financial products. This often indicates that the overall market risk is at a lower level, as investors can select enough differentiated assets to construct a portfolio, thereby achieving risk diversification.

The term volatility-equal-weight essentially relates to position allocation. The core of portfolio weight allocation is to find a dynamic balance among expected returns, risk levels, and transaction costs. Excessive tilt toward any one of these three will lead to portfolio imbalance. If one focuses solely on capturing trading opportunities, blindly chasing potential returns while ignoring risk control, it often leads to unnecessary losses for the portfolio when asset volatility exceeds the tolerance range. If one focuses too much on risk avoidance, constantly shrinking positions and restricting trading, it misses high-quality investment opportunities, causing portfolio returns to fall below expectations long-term. If one is overly sensitive to transaction costs, even refusing to adjust the portfolio due to fear of costs, the system falls into long-term fixed holdings, unable to adapt to market changes or realize return potential.

Regarding how to divide the “cake” effectively, Rishi Narang divides it into two major categories: rule-based models and optimization-based models. There are four common types of rule-based portfolio construction models: equal position weighting, equal risk weighting, alpha-driven weighting, and decision tree weighting. Let’s briefly explain these four weighting methods:

The first, equal position weighting, also known as the equal-weight allocation model, is the most basic rule-based weighting method. It means that the position size of all assets in the portfolio is exactly the same. That is, regardless of whether the asset’s risk is high or low, or its returns are good or bad, funds are uniformly and equally distributed among all assets in the portfolio. For example, if I have 1 million RMB and buy 10 stocks, I buy 100,000 RMB worth of each.

The second, equal risk weighting, has the core objective of making the risk contribution of each asset in the portfolio to the overall portfolio equal, thereby reducing the problem of excessive concentration of risk in a single asset. This model requires first calculating the risk indicators of each asset, such as volatility or VaR values, and then adjusting position sizes so that the marginal risk contribution of each asset tends to be consistent. In simple terms: “Whoever has higher risk, I buy less of; whoever has lower risk, I buy more of,” ultimately making the risk of each asset equal. Therefore, the volatility-equal weighting used by LuoShu belongs to this equal risk weighting category.

The third, alpha-driven weighting, uses the asset’s alpha value, i.e., excess return, as the core weighting basis. Assets with higher alpha values receive larger position weights. The rule logic is to prioritize allocating assets that can create returns exceeding the benchmark for the portfolio. This requires using quantitative models to predict and rank the future alpha values of assets. In other words: “Whoever has the stronger signal, I overweight.” For example, if the model predicts a 90% probability of Stock A hitting the daily limit and only a 51% probability for Stock B, I would allocate 80% of the position to Stock A.

The fourth, decision tree weighting: This constructs a weight allocation system based on the rule logic of decision tree algorithms, setting up multi-layer quantitative rules, such as asset price-to-earnings ratio intervals, liquidity thresholds, and industry classifications, to perform hierarchical screening and weight assignment for assets. For example, first determine weight proportions by industry, and then determine specific position sizes within the industry based on individual stock financial indicators.

The above is an introduction to the first category, rule-based models. Next, let’s briefly understand optimization-based models.

These models use specific algorithms to find the optimal solution that achieves the preset goals of the quant. The algorithms mentioned here are essentially a set of pre-set, interlocking rules that guide users step-by-step from an initial state to a target state. The preset goal to be achieved in the model is usually called the objective function. In the field of quantitative investing, the typical application scenario of the objective function is to construct a portfolio that maximizes potential returns per unit of risk, commonly known as “maximizing risk-adjusted returns.” The characteristics of these optimization models determine that mastering their underlying algorithmic details is not easy, but their core logic is actually quite clear and easy to understand.

Summary

Mr. Xie stated, “LuoShu Investment’s nine-square grid is not just mathematical symbols, but also a reverence for financial markets and their laws, along with relentless pursuit.” By deconstructing the interview content, we have gained a deep understanding of LuoShu’s investment and research management approach. More importantly, it reveals the core thinking of top private fund managers in constructing robust investment logic.