29 January 2025
By Zeshu Xu
When we look at how many people enter or exit the stock market each year, one striking observation is how much it varies over time, and how responsive entry and exit is to recent returns. For example, data from Finland and Norway suggest that people exhibit a tendency to enter the stock market when recent returns are high and exit the stock market when recent returns are low. It therefore seems that people learn from stock returns and that they trade accordingly. However, are they entering and exiting at the right time? And what are the implications of such a trading pattern for asset prices and welfare?
Figure 1: Stock market entry and exit in Finland and Norway. Sources: Statistics Finland, Statistics Norway.
Fluctuations in stock market entry and exit lead to fluctuations in the stock market participation rate. When we plot the time-series of detrended participation rates against the price-dividend ratio in Finland, Germany, Norway and the USA, we see that they move up and down hand in hand. Investors tend to enter the stock market in exuberance during episodes of high prices, which coincide with the episodes of low expected returns, and leave the stock market in disappointment when prices are low and expected returns are high.
Consequently, and not surprisingly, we observe in data that participation rates negatively predict both total stock returns and excess returns at different horizons. That is, trend-chasing investors earn low returns when they participate in the stock market, while miss high returns when they are out of the stock market, implying large welfare losses.
Figure 2. Participation rates and price-dividend ratio in Finland, Germany, Norway and the US. Participation rates are detrended using country-specific trends. The correlation between the participation rate and lagged PD-ratio in Finland, Germany, Norway and the US are 0.63, 0.10, 0.22, and 0.78 respectively. Sources: Statistics Finland, Deutsches Aktieninstitut, Statistics Norway, US Internal Revenue Services, Amit Goyal’s website, and Ken French’s website.
In my paper titled “Beliefs-driven Stock Market Entry and Exit”, joint with Paul Ehling and Christian Heyerdahl-Larsen, we study how beliefs about returns influence decisions related to entering, exiting, and re-entering the stock market, and how these decisions subsequently impact expected stock returns and welfare.
Within the framework of our model, the distribution of beliefs determines the asset pricing quantities, including the interest rate, the market price of risk, and the volatility. In turn, investors enter or exit the stock market upon crossing the cutoff belief. The investors who are more optimistic than the cutoff belief are stock market participants, while the others are nonparticipants.
Through extrapolative beliefs, our model reproduces the time-series dynamics of stock market participation, entry and exit. We feed our model with shocks extracted from the stock market and generates implied time-series of participation rates for Finland, Germany, Norway and the USA. For Finland and Norway, where entry and exit data are available, we further generate the model-implied entry and exit rates. Compared to the actual time-series of stock market participation, entry and exit in these countries, our model captures the fluctuations to a large extent.
Figure 3. Data and model implied stock market participation rates in Finland, Germany, Norway and the US. Participation rates are detrended using country-specific trends. n is the length of the initial window for the prior belief and T is the t-statistics on the actual participation rate from regressing the model participation rate on a constant and the actual participation rate. Sources: Statistics Finland, Deutsches Aktieninstitut, Statistics Norway, and Internal Revenue Services.
Figure 4. Data and model implied stock market exit rates in Finland and Norway. n is the length of the initial window for the prior belief and T is the t-statistics on the actual participation rate from regressing the model participation rate on a constant and the actual participation rate. Sources: Statistics Finland and Statistics Norway.
In our analysis, the one thing that stands out is the short sample of returns investors seem to use to produce the large swings in participation, entry and exit. Using such short samples leads to large bias, volatile portfolio, and large welfare costs. We formally measure the welfare loss due to extrapolative beliefs-driven entry and exit using a benchmark economy with complete information. With a two-year learning window over which an investor observes before she starts trading, the welfare loss is equivalent to an over 60% reduction in the aggregate growth rate, or an over 4 times increase in the growth volatility. Such a large magnitude in welfare loss highlights the importance of financial education, especially for the young and unexperienced investors.