How to Portray Odds? Post-Rebound Market Odds Attractiveness

On September 24th, the press conference held by the State Council Information Office marked the beginning of the rebound in A-shares. By the end of the six trading days on October 8th, the Wind All A Index had accumulated a 35% increase, with the Shanghai Composite Index reaching 3,674 points, setting a new high for 2022. The total trading volume on both markets reached nearly 11 trillion yuan (with an average daily volume of nearly 2 trillion yuan, four times the previous low). Such a rapid rise caught old investors off guard, while new investors were in high spirits, accelerating the process of opening accounts and depositing funds. After ample turnover, A-shares experienced some adjustments in the first week after the holiday. What are the current odds for A-shares?

Let's first state our conclusion: The odds for A-shares are still not considered low. Here, we use the risk premium as a measure of the odds for equity assets, and we will discuss the calculation method in the following text. The current risk premium for Wind All A is still above neutral, and for the large-cap indices such as the Shanghai 50, CSI 300, and Zhongzheng 500, the risk premiums are in the range of 40%-50%, slightly below neutral. In terms of style, the risk premium for finance has lost its attractiveness, but consumption is still in an extremely cheap range (above the 90th percentile historically), while the risk premiums for cyclical and growth styles are slightly below and slightly above neutral, respectively.

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The terms "win rate" and "odds" should not be unfamiliar to professional investors. They originate from a famous game theory formula—the Kelly criterion. In this context, odds refer to the multiple of profit (excluding the principal) a bettor would receive if they bet correctly, while the win rate is the probability of betting correctly.

However, it should be noted that the Kelly criterion is based on known win rates and odds to solve for the proportion of bets. But the capital market is quite different from the scenario in the Kelly criterion, as both the win rate and odds during the holding period of assets are uncertain. How to quantify and describe these two aspects has been a hot research topic for asset allocation researchers for many years. In this article, we will first go through our approach to characterizing odds from scratch for your reference.

In actual trading, the most classic odds indicator is valuation—PE, PB, and PS, among others. For example, assume that a company's valuation center is stable at around 10 times PE, and the current market valuation is 5 times PE. Then, the odds of buying and holding until the company's valuation is restored would be 1 times.

The strongest assumption in this example is that the company's valuation mean-reverts and the center is 10 times PE (with an implied annual return rate equal to 10%, meaning the principal is recovered in ten years without interest). But we all know that valuations are not stable mean-reverting at different stages of a company's operating life and under different macro policy environments. Taking the Wind All A Index as an example, valuations before 2010 were significantly higher than after 2010, and the statistical distributions obtained from different sample intervals are completely different and even incomparable.

A common explanation is that as economic growth slows and interest rates decline, valuations in emerging markets will gradually decrease. Therefore, the equity risk premium has gradually become a consensus in characterizing the odds of the stock market in recent years. There are many ways to calculate it, and there are many details to handle, but the core consideration is to use the market-implied equity yield (the reciprocal of PE_TTM or the dividend yield) minus the bond yield to obtain the premium reward for investors actively taking on the risk of stock market fluctuations.

Under the premise that the equity risk premium (equity-bond yield difference) is an effective proxy variable for characterizing the relative cost-effectiveness of equity, or the equity odds indicator. How to construct a generalized and highly referable proxy variable has become our main task, and we have made some new thoughts and innovations on this point.

Firstly, regarding stock returns, the valuation implied yield (the reciprocal of PE_TTM) is a more comprehensive indicator than the dividend yield. According to data from the China Listed Companies Association, as of the end of 2023, among the 4,022 Shanghai and Shenzhen A-share listed companies that have been listed for three years, 2,181 have consecutively paid cash dividends in the past three years, accounting for about 54%. This proportion would only be lower before, as the total number of cash dividend companies in 2023 has increased by more than double digits compared to 2022. That is, if we use the dividend yield to measure the return on stocks, the coverage of A-shares is only about half. However, as long as the company's profit is positive, the reciprocal of PE_TTM can be used to characterize the implied yield, and the coverage of this indicator was about 80% in the mid-2024 report.

Of course, the valuation implied yield is not universally applicable. Apart from targets with negative profits, the effectiveness of this indicator for equity assets with high valuations will be relatively poor. For example, if the minimum value of the PE_TTM for a certain innovative industry is 50 times and the maximum value is 100 times, the corresponding range of valuation implied yields is roughly between [1-2%], while the historical range of bond yields is much larger than 100bps. Therefore, the equity risk premium, as the difference between the two, mainly reflects the fluctuations in the bond market.Next, we turn to bond yields. Currently, most equity risk premium calculations refer to the long-term government bond interest rates used in the classic paper "The Equity Premium Puzzle" by Mehra and Prescott (1985), specifically the yield to maturity of 10-year U.S. Treasury bonds. As an imported concept, domestic risk premium calculations also essentially adopt the yield to maturity of our country's 10-year government bonds as the subtracted term in the formula. However, for both investors and financiers, the difference between equity returns and long-term national debt should not only include the risk premium brought by equity volatility but also the credit premium for the possibility of bankruptcy of the entity. Therefore, when constructing the equity risk premium, we will use the yield of credit bonds to more purely isolate the size of the equity risk premium (when benchmarking broad-based indices, we use the yield to maturity of the China Bond Corporate Bond AAA-rated 2-year term).

After determining the calculation formula, the historical trend of the risk premium of the Wind All A is shown. We can understand that even after subtracting the bond yield, the risk premium of A-shares also shows a relatively volatile upward trend, indicating that the speed of the implied yield increase in the Chinese stock market (historical valuation correction) is faster than the speed of the decline in bond yields. Therefore, we will also apply an HP filter to the calculated ERP, of course, what needs to be filtered here is the longer-term trend, making the ERP series more stable. Of course, the rolling window method can also be used to smooth the series, but the cost is sacrificing the data distribution outside the window, focusing the observation perspective on a more recent time range, with the risk of being like a blind man touching an elephant.

The stability of data is a very important premise in statistical analysis. Theoretically, non-stationary series do not have the characteristics of mean reversion, which greatly reduces the usability of the indicator (similar to the situation we discussed in the first article of this series, "Decomposing Quantitative Asset Allocation Model Series 1 - What is a Good Trading Congestion Indicator in Our Eyes?" published on April 19, 2024). And the familiar "2sigma" rule, the premise of application is that the sample conforms to the normal distribution. However, from the results, the historical sequence of ERP before and after filtering does not meet the premise of the normal distribution assumption, so using percentiles as a description of relative high and low statistics is better than the Z-statistic (N times Sigma above and below the median).