Original | Diankuan Academy Author | Dian Xiaokuan
The total text is 2366 words, and the recommended reading time is 8 minutes.
01
Principles of Strategy
According to the CAPM theory, the price of an asset should only be related to systemic risks, and there is no excess return (α) in the constant term. Therefore, if there is an asset with a return on the market, the price of the asset deviates from its expected level at this time. Specifically, if α<0, it means that the stock’s yield is underestimated and should be bought; on the contrary, if α>0, it means that the stock’s yield is overvalued and should be sold.
02
Policy details setting
1. Market factor selection:
Shanghai Composite Index. The constituent stocks of the Shanghai Stock Exchange include all A-shares listed on the Shanghai Stock Exchange, including companies with large, medium and small market capitalization and various fineness and operating capabilities. They are highly universal and adaptable. Therefore, the Shanghai Stock Exchange is selected as the market portfolio .
2. Scope of stock selection:
All constituent stocks of CSI 300. The CSI 300 Index contains 300 highly representative and highly liquid stocks in Shanghai and Shenzhen stock markets, with excellent quality and suitable for stock selection pools.
3. Target pool capacity:
60 stocks.
4. Backtest time:
2018-01-01 to 2020-12-31.
03
Policy validity verification
For the CAPM market factor strategy, since the profit principle of the strategy is to constantly change positions to continuously buy undervalued stocks with small α values, the verification method should be to construct different portfolios of stocks with different α values, and compare whether there is a return rate of portfolios with different α values. The obvious difference is that the smaller the value of α, the higher the rate of return. The specific implementation ideas are as follows:
1. Calculate the daily rate of return of the market combination for the current month and form a sequence every month.
2. Calculate the monthly daily rate of return of the 300 Shanghai and Shenzhen stocks and construct a sequence for each stock every month.
3. Regress each stock with market combination factors every month to calculate the alpha value of individual stocks.
4. Sort the individual stocks according to the alpha value from small to large, and construct a portfolio of stocks with alpha values ranked in the top 60, ranked 120-180, and the bottom 60 stocks weighted according to the market value of the market.
5. For each investment portfolio, purchase all the targets in the investment portfolio.
6. For each investment portfolio, close all the stocks that are not in the current month's portfolio.
7. Compare the changes in the net value of the three investment portfolios.
Following the above verification steps, the net performance of the three sets of portfolios during the backtest period can be obtained:
Equity curve (1) 60 stocks with the smallest alpha value (group 1)
Equity curve (2) 60 stocks with alpha value from 121st to 180th (group 2)
For a more intuitive comparison, extract the net worth data of the three combinations, and plot the net worth curves of the three combinations and the CSI 300 in the same graph. The results are as follows:
From the above figure, we can clearly see that although the investment portfolios composed of different α values have similar net worth trends, the net worth between the portfolios is quite different. At the same time, the monthly exchange of positions continues to buy the 60 targets with the smallest α value, and the income brought by it does outperform the investment portfolio and index with a larger α value most of the time.
The relative situation between the second group and the third group reversed in May 2019. Since then, the net worth of the third group has risen by a higher rate, and the income of the first and second groups has begun to decline. This may be related to market sentiment. It is related to the change in style, that is, the market is showing an overall trend of chasing ups and downs, leading to the continued increase in the returns of overvalued stocks that already have higher excess returns, driving the growth of the net value of the investment portfolio with a larger α value.
From the perspective of the overall return in 3 years, it is more effective to purchase the target construction investment portfolio with a smaller α value despite the return fluctuations. Therefore, the CAPM market factor strategy still has great practical and exploratory value.
04
Reflection on potential problems of strategy
1. The validity of the CAPM model is based on many strict assumptions.
Investors have a preference for mean variance, asset returns obey a normal distribution, and the market reaches an equilibrium of supply and demand... In the real world, these assumptions are not so easy to meet. Perhaps during certain backtesting periods, certain assumptions will be better satisfied (for example, the return on assets in 2019 is more compliant with the normal distribution), which greatly enhances the explanatory nature of the model; but in certain periods these assumptions are not enough Persuasive (for example, the capital market will fluctuate greatly in 2020, and the distribution of returns on most assets has a long-tail characteristic compared to the normal distribution), resulting in a greater impact on the accuracy of the CAPM model.
2. The market portfolio may not fully explain the return on assets
In the CAPM formula, we believe that the exposure of assets in the market, that is, β, can fully explain the rate of return of assets. In reality, the rate of return on assets may depend on more factors besides the market. If we attribute all other factors to the company's diversified risks, the contribution of these factors to the return on assets will be ignored. Therefore, in certain time periods, if the neglected factors contribute a lot to the return on assets, the results obtained by using the CAPM model will have a larger error.
3. Market value weighting may have different effects under different market conditions
If under the current market conditions, if a large amount of capital flows into white horse stocks with high market capitalization to cause the index to rise, then it will be effective to set positions in a market-value-weighted way; conversely, if the main capital flows into small and medium-cap stocks with small market capitalization, the market will rise. Then the market value-weighted method may miss the rise in the market, and even cause losses due to the correction of the White Horse stocks. In this case, using average positions or even reverse weighting by market capitalization (small market capitalization stocks with large market capitalization) may have better results.
05
Validation of potential problems of the strategy
Based on the strategy reflection in the previous section, we hope to verify the problems of the CAPM strategy during the 2018-2020 period we backtested. The problem (2) mentioned in the reflection will be verified in the multi-factor model strategy. Here, we first verify the problem (1) and the problem (3).
Problem (1) The assumption is not satisfied: the rate of return on assets does not follow a normal distribution
For question (1), assumptions such as mean variance preference and market supply and demand balance are difficult to verify, so we choose to verify whether the return on assets obeys a normal distribution. We calculated the daily return rates of all the constituent stocks of the Shanghai and Shenzhen 300 Index from 2018 to 2020 and formed the return rate sequence for each target. Using the Jarque-Bera test, we calculated the JB value and the corresponding P value corresponding to each stock. This judges whether the stock price of the stock roughly obeys a normal distribution.
The output result is:
The number of constituent stocks with a P value greater than 0.05 in the JB test: 15
Through statistics, we found that only 15 of the 300 constituent stocks have passed the JB test, that is, we are 95% confident that their returns are roughly obeying a normal distribution. Since only 5% of stock returns are roughly normally distributed, the CAPM model assumptions are not very effective. This is an important reason that affects the net worth performance of the CAPM strategy in 2018-2020.
Problem (3) Market value weighting affects portfolio performance
In order to verify this problem, we changed the market value weighting in the strategy to equal weight to construct positions. We compare the performance of the 60-value stocks with the smallest α value obtained by the weighted market value and equal weighted positions:
Equity curve (1) The 60 stocks with the smallest market capitalization weighted alpha value (Group 1)
Equity curve (4) equal weight positions 60 stocks with the smallest α value (group 1)
Through the comparison of the equity curve (1) and (4), we see that the effect of equal-weighted positions is much worse than that of market-value-weighted positions. Especially from 2019 to the end of 2020, market-value-weighted gains are significantly higher than Equal weight. This is consistent with the trend in the A-share market in recent years that funds have gradually flowed from small-cap stocks into large-cap white horse stocks.
Through the analysis of questions (1) and (3), we found that the inability of CAPM theoretical assumptions to be fully satisfied is the main reason for the poor performance of the CAPM strategy. In this case, we should use other strategies (such as multi-factor model strategies) to obtain alpha excess returns, or use other strategies such as market neutrality and index enhancement.