What is a quant ETF? A CSI 800 ETF Enhancement Strategy
Based on Disposition Effect
This research report is to design a hedge fund strategy based on the Disposition effect. Ourstart point is that: can we design a hedge fund strategy that can beat the passively managed ETF? So we finally came to our solution to design an index enhancement strategy, and we take the CSI800 index as our benchmark.
Disposition effect may result in delayed reaction on asset price to new information. What disposition effect exhibits is that investors are prone to sell winning stocks to lock in gains and hold losing stocks in the hope of breaking even. There are two explanations to the disposition effect: prospect theory and mental accounting, which we will explain in detail.
We examine the existence of a disposition effect using the CGO factor. Aiming to estimate the profit-and loss balance price of average investors, the reference price is developed. In order to express the position of the current stock price movement relative to the reference price, we also design the capital gains overhang (CGO). With the help of CGO, we will see the effect of disposition effects clearly.
We construct index enhancement trading strategies based on disposition effects. We can take advantage of this phenomenon to further select investment targets in the index constituents. To make it one step further, we combine the disposition effect with unexpected earnings shock. And finally we design an index enhancement hedge fund strategy, which has significant excess return over the index.
Table of contents
2. Disposition effect and its explanation
2.1 Disposition effect
We recognize that the market can fail at any time, but individual irrationality always exists. From the perspective of behavioral finance, alpha can be mined to avoid market style fluctuations and obtain stable absolute returns. Since the 1980s, behavioral finance has developed gradually, and more and more conclusions have been proved quantitatively in the market. These academic achievements can be converted into effective alpha sources.
One of the well-known effects is called the disposition effect. Disposition effect refers to the behavioral tendency of investors to cash in book gains as soon as possible when they are buoyant and resist selling to recognize losses when floating down. Prospect theory combined with mental accounting can explain the reasons behind this behavior. Disposition effect may result in delayed reaction on asset price to new information. We can take advantage of this phenomenon to further select investment targets and enhance the return of event investment. At the same time, we believe that the early book return is an important precondition for influencing the subsequent performance of the factor, which we can utilize to enhance the factor portfolio return.
2.2 Disposition effect explanation
Prospect theory and mental accounting can explain the disposal effect to some extent: 2.2.1 Prospect Theory
The prospect theory proposed by Kahneman and Tversky mainly describes and predicts people’s behavior in the process of decision making while having risk exposures with the differences of behavior from the traditional expected theory and expected utility theory. It embedded psychology research results into traditional finance, and tries to understand financial phenomena from deviation
of human psychological bias, that is, irrationality to explain financial phenomena, and revises the traditional utility function. The prospect theory has the following elements:
1. Reference Point: Under clear investment returns, having completely different feelings compared with others. In expected utility theory, satisfaction doesn’t make any difference.
2. Loss Aversion: Losing $100 hurts more than gaining $100.
3. Asymmetry Risk Preference: Traditional expected utility theory holds that investors are risk-averse no matter in the face of losses or gains, but the assumption does not comply with the real situation in investment. To improve understanding, consider the following two scenarios:
A: 80% chances of winning $4000 vs. 100% chances of winning $3000
B: 80% chances of losing $4000 vs. 100% losing of $3000
In option A, people tend to choose the latter, and choose the former in option B. In fact, the former of option A has a higher expected gain, and the latter for option B has a lower expected loss. It is obvious from the comparison of the two options that investors prefer certain income, and guaranteed gain is more relevant. And when you have certainty in losing money, it’s better to gamble and take the chances of losses. Therefore, according to the prospect theory, investors are risk-averse in facing gains and risk-prone in facing losses.
2.2.2 Mental Accounting
Mental accounting is the process of encoding, classifying and valuing outcomes, especially economic outcomes, which reveals the mental cognitive processes involved in making financial decisions. Mental accounting theory contains a set of rules, the most important of which is relevant to this article:
1. When a person is faced with two events that will affect his/her wealth, he/she will evaluate each event individually rather than as a whole. That is to say, even for portfolios, people usually analyze single security, and do not take into consideration the impact of the portfolio or other securities in the portfolio. This principle allows us to discuss a single stock investment without considering other stocks’ profitability.
2. Stocks already been sold with loss and stocks that bear loss but haven’t been sold are put in different mental accounts. Before selling, it is the loss on the book, and after selling it is actual loss. Objectively, there is no difference between the two cases, but in psychology people differentiate the two strictly. From book losses to actual losses, the latter felt more “real” and more painful, so it seems that the two accounts give people different feelings, and people don’t equate them psychologically. This rule provides a psychological basis for the asymmetry of risk preference in prospect theory.
To further explain the disposition effect, we take this for example: an investor holds stock A, the relative purchase price of the stock has risen by $10, and future stock price may rise by $10 or fall by $10, with a 50/50 chance. Since the utility function yields convex, the utility of lock-in return of selling the stock is greater than the expected utility of holding it to the next period, and investors naturally trade on strategies that make them more effective.
Similarly, if an investor holds stock with a current book loss of $10, with the same fluctuation in stock price, immediate sell-off would result in lower expected utility of the two cases. Therefore, investors will choose to hold the stock for the next period.
3. Reference Price and Capital Gain Overhang
Since investment behavior and risk preference are closely related to their profit and loss (P/L), it is relatively easy to calculate the P/L for a single investor. However, for a class of assets, the average P/L of investors can be estimated by historical asset price information.
3.1 Reference Price (RP)
It is difficult to accurately characterize the cost of every investor on every stock. We can assume that each investor has a psychological price, and pricing below or above the price would have an impact on the investment behavior afterwards. When a stock exhibits group behaviors, it would certainly affect the future trend of this stock, so it is necessary to define a unified reference price for each stock, and the defined psychological price or reference price (RP) must reflect enough information of market changes. Many individual investors like to set upper and lower bounds in line with the moving average, while their trading strategies align with the changes of the moving average. In a sense, the moving average is a reference price. However, the moving average only contains price changes, without including volume, turnover rate, or other information; Moreover, the moving average is manipulable as it is calculated by closing price, which is easy to be manipulated at the end of the day.
For the American stock market, Grinblatt (2005) took 260 weeks as a cycle and proposed to take the weekly average transaction price weighted by the weekly turnover rate as the reference price of individual stocks. Considering the large number of short-term traders in the A-share market, we redefine the cycle as 100-days, with average daily transaction price weighted by daily turnover, our RP is:
!”! = 1%& ((!”#) (1 − (!”#$%))”!”#
k as normalization coefficient of weight; Pt-n as the average transaction price of the past t-n day; Vt n as the turnover rate. Calculated by forward adjusted price (前复权价格).
The calculation of the reference price is the average price weighted by the average transaction price of the past 100 days in accordance with the attenuation of turnover rate. If turnover rate on day t is Vt, then the number of shares traded on day t will account for Vt *100% of outstanding shares. The cost is approximately the average price Pt of day t. According to such weight of outstanding shares to calculate, these stocks represent Vt * (1 – Vt+1) * 100%.
The multiplication part of the formula allows the weight to decay with time. If the turnover rate of the day is large, then it would be smaller after, then more effectively the information carried to the future, then the larger the weight of the average transaction price of the day, and vice versa.
3.2 Capital Gain Overhang (CGO)
In order to express the position of the current stock price movement relative to the reference price, we redefine the capital gains overhang (CGO) based on Grinblatt (2005).
!”#! = %“#$%&,!() − ‘%!
In the formula, %“#$%&,!()represents the closing price of a stock yesterday, and !”#! represents the average rise and fall of stock investors relative to the reference price. From the fluctuation relationship between CGO and stock price, the performance of CGO factor can well express the sentiment of investors. For example, when the stock price sequence is rising, if the turnover rate is very low in the early rise, then the CGO sequence will rise rapidly.
If people have different expectations on the future rise of the stock price, the stock price rises but the turnover rate also increases rapidly, then THE CGO will decline. Due to the profit-taking effect, if the CGO sequence suddenly drops after a rapid rise, such a performance may herald the arrival of a stock price top.
Accordingly, in the falling channel of stock price, due to the existence of a selling effect, the turnover rate of investors also sharply decreased. The sharp bottoming of CGO reflects the loss of high holders, but after the shock, the turnover rate is increased and the market sentiment is repaired, and the stock price is easy to rebound.
3.3 Factor Analysis
Distribution of CGO: We select the performance of CSI 800 components from 2019-01-04 to 2022-03-18 for CGO factor analysis, and the time window is 100 days. We find that the median
Cross section distribution is not obvious to the left, indicating that the bull is short and the bear is long in the Chinese stock market. However, the distribution of full-space sample CGO is almost unbiased, indicating that investors of individual stocks have equal profit and loss, presenting a balance.
The performance of different CGO groups: To check the performance of our CGOs, we divide stocks into five groups from the lowest to the highest CGOs every day and hold them from 2019- 01-01 to 2022-05-31. Group 1 has the lowest CGOs, and group 5 has the highest CGOs. The performances (mean excess return) of these five groups are shown as follows. We see that there is a significant monotonicity across groups, which is corresponding to the disposition effect.
Layer back test. After paving the way of the previous theory and model, we empirically tested the CGO factor. According to the size of CGO, we designed the weekly swap strategy. We divided the CONSTITUENT stocks of CSI 800 into five segments to construct a five-digit portfolio, and traded positions on the last trading day of each week. From the perspective of grouping average excess return, the returns of different quantile portfolios have good monotonicity, and the lowest CGO quantile portfolio performs the best in the five stalls.
4. Quantitative trading strategy
Firstly we construct a brief trading strategy based on CGO trying to take the advantage of the proposition effect.
4.1 Long-short Strategy Based on CGO
We use stocks in the top 1/5 quantile with lowest CGO and stocks in the bottom 1/5 quantile with highest CGO to build a long-short quantitative trading strategy. Long the stocks that belong to the top 1/5 quantile, and short the stocks that belong to the bottom 1/5 quantile. Comparing the long short strategy, long-only strategy and short-only strategy, the long position of the long-only strategy can get the best return, and the long and short position of the best and worst quantile portfolio can also get a good return, which is far better than benchmark CSI800.
The detail KPI is as follows:
L/S Long Short CSI800
Annualized return 23.6% 55.0% -34.7% 2.6%
Annualized volatility 32.5% 53.2% 47.1% 19.3%
Accumulated return 97.0% 306.9% -74.5% 14.2%
Accumulated excess return 82.8% 292.7% -88.7%
Sharpe ratio 63.3% 97.6% -80.2% -2.3%
Maximal drawdown -39.4% -73.5% -94.1% -26.6%
● Annualized return: Long > Long-short> CSI800>Short, and the sharpe ratio of Long strategy is closed to 1, which indicates that long strategy shows a better risk-return balance among these four, but there is still room for improvement for the long strategy
● Maximal drawdown: all the strategies underperform the market index
We see although the proposition effect delivers excess returns, the risks are also high. So we are considering a way to reduce the risk.
To make it one step further, we combine the disposition effect with unexpected earnings shock. And finally we design an index enhancement hedge fund strategy.
4.2 Disposition effects and the delay in pricing new information
We firstly derive a Standardized Unexpected Earnings (SUE) factor:
E*,+ = E*,+(, + C*,+ + ε+
-./-,! = /-,. − /-,.(, − 0-,!
In which: /-,!: /345678 9: 0;44<5= >;34=<4 , !-,!:?46:= 6=<@,=ℎ< 3C<437< 9: /-,. − /-,)(,, σ-,!: /-,. − /-,.(,′8 8=35E34E E<C63=695.
SUE is used as a measure of excess expectations. A seasonal stochastic wandering model with a drift term is used to model quarterly net earnings to derive expected net earnings, which are then normalized to exceed expectations.
We derive the following two hypotheses.
1. Positive information has a more prolonged upward price drift in the higher unrealised profitability (CGO) group.
2. Negative information has a more prolonged downward price drift in the lower unrealised earnings (CGO) group.
The basic logic is that:
According to the efficient market hypothesis, new information (e.g. earnings beat) will be priced in instantaneously. However, as a result of the disposition effect, share prices do not adjust to the new reasonable price level as quickly as would be envisaged in an ideal state. Under certain conditions, investors may under-react to new information, resulting in a slower price adjustment, making returns more predictable.
We discuss the impact of new information in different ways:
1) High CGO & High SUE: This means the new information is positive, and most buyers have already made profits. In this case, investors tend to sell their stocks to lock in profit, creating selling pressure. However, due to the unexpected earnings, the price will finally go up until the new information is price-in. This is a strong trend because the new information is not immediately price in.
2) High CGO & Low SUE: This means the new information is negative, and most buyers have already made profits. In this case, investors tend to sell their stocks quickly to lock in the profit, the new information will be quickly priced-in and go down quickly. The opportunity here is smaller because the price response is fast.
3) Low CGO & High SUE: This means the new information is positive, but most buyers are losing. In this case, investors tend to continue to hold their stock, hoping to make profit, reducing the supply of the stock. However the demand for the stock is high due to high unexpected earnings, so the price will quickly go up until the new information is price-in.
4) Low CGO & Low SUE: This means the new information is negative, but most buyers are losing. In this case, investors tend to continue to hold their stock, hoping to make profit, reducing the supply of the stock, so the price will slowly go down until the new information is price-in.
In summary: Taking these two points together, we can hypothesize that the post-event price drift will be more prolonged when the direction of price adjustment is consistent with the current book-to-bill situation due to the disposition effect.
In line with what is stated ahead , we have two portfolios:
1. long: top 20% of SUE + top 20% of CGO
2. Short: 20% after SUE + 20% after CGO
1. Long: 20% before SUE + 20% after CGO
2. Short: 20% after SUE + 20% before CGO
|High CGO||Low CGO|
|High SUE||A long: Strong up trend||B short: Wake up trend|
|Low SUE||B long: Weak down trend||A short: Strong downtrend|
According to the analysis above, we should expect A L/S
4.3 Back-testing result and analysis
We adjust our portfolio on weekly basis, the result is shown as follows:
1) Group A and Group B’s NAVs:
We see a stronger performance from A L/S strategy, which is in line with our intuition. 2) NAV of L/S strategy:
The detail KPI analysis is shown as follows:
A L/S B L/S CSI800
Annualized return 31.7% -4.9% 2.5%
Annualized volatility 20.9% 17.1% 16.5%
Accumulated return 325.3% -23.1% 13.6%
Accumulated excess return 311.6% -36.7%
Sharpe ratio 137.5% -46.1% -3.2%
Maximal drawdown -22.9% -35.0% -30.3%
Beta 0.5 0.95 1
Alpha 2.40% -0.01% –
● Annualized return: A L/S > B L/S > CSI800, and the sharpe ratio of A L/S strategy is higher than 1, which indicates a great return-risk balance capability. ● Maximal drawdown: B L/S > CSI800 > A L/S, A L/S strategy indicates a greater risk control ● Alpha/Beta: A L/S’s Beta<1, indicating that our strategies are less exposed to market risks, alpha>0 means our strategies effectively find alphas out.