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This work presents an analysis regarding returns of stocks per business cycle periods/phases; volatility, risks, and risk-adjusted returns are also examined. Furthermore, returns of stocks in the first part of the business cycles are compared to the late stages of cycles to determine whether stocks provide better returns in the early stages of the cycle compared to the late stages.
Business cycle (BC) dating provided by the National Bureau of Economic Research's committee on BC is utilized in this work for the numerical analysis.
*values in tables are monthly, with the exception of the yearly VaR values.
Table 1. Business cycles and returns of S&P 500 (half century of data analyzed):
Table 2. The first part of the cycle (33% of cycles' months from the start):
Table 3. The late part of the cycle (33% of final months of the innings):
Do stages of the business cycle affect stock/S&P 500 returns & risk?
The answer is somewhat multifaceted. On the face of it, the mean returns of stocks in the first period (33% of first months) of the cycles in the last half-century have been slightly higher than returns in the late stages. A statistical test on the value also confirms that the difference is statistically significant  (results available at the end).
However, when a controversial period of 5 months (July 1980-Oct 1980) is excluded from the data as an early-cycle period & a trimmed mean is calculated, the mean return of the early period declines by -38.5% to 0.91%; volatility, on the other hand, isn't affected much.
Once the controversial period is excluded, the returns of the two periods don't exhibit much difference; statistical testing  also confirms that the difference that remains after the controversial period is excluded isn't statistically significant, and the two values (means) are statistically comparable (not different).
As far as the comparability of the total cycle periods with the early & late stages is concerned, there is no statistical difference (,) when it comes to returns of the early/late periods of the cycle and the total periods of all BCs.
Are stocks/S&P 500 more or less risky in different business-cycle stages?
It seems reasonable to assume that there may be a difference between the overall level of market risk, depending on the stage of the BC. Nonetheless, to test this notion scientifically, F-tests have been conducted in this work.
The results confirm that volatility in both periods (early/late) isn't statistically different from the entire/total BCs examined. Thus, it is erroneous to assume that the volatility of stocks changes as per different stages of the business cycle.
While it is true that volatility rises to very high levels at the very end of the BC—during a market crash—and the very early phase of the BC, an overall assessment, however, confirms that the late and early stages of the BC don't exhibit a different level of market volatility (risk) compared to the overall BC.
So, is there any element of significance under this analysis that investors & traders can use/be aware of?
While the rudimentary elements analyzed in this work (returns & risk) don't hold any relation of statistical significance with BCs, there is one more factor (perhaps more important) that we must examine: risk-adjusted returns/performance (RAP); this is best, and most simply, examined through the Sharpe ratio:
The assessment of Sharpe ratios (excluding the controversial 1980-1981 period) divided by phases (total, early, & late) confirms that the Sharpe ratio of the stock market (S&P 500) is higher in the late stages of the BC compared to the entire cycle; statistical testing also confirms this difference to be of statistical significance .
Fundamentally, this means that the returns stocks offer, minus the risk-free rate (interest that can be earned by investing in government bonds), when compared to the risk, is highest in the later periods of the BC.
On the face of it, investors would assume that as the economy inches more & more towards the overheating phase, interest rates should rise, and as the FED increases policy rates & utilizes the monetary transmission mechanism to influence rates upwards with a hawkish outlook, the net returns offered by stocks (stock returns – the risk-free rate, which is the numerator of the Sharpe ratio) should reduce (if we assume that stocks returns don't fluctuate very much as per the phases of the BC).
However, the findings are contrary to the common supposition stated above & the data reveals that the S&P 500 has had a higher Sharpe ratio in the late phase of the BCs, as per data from the last half-century.
What factor can explain this finding?
In the final phase of the cycle—typically—economic confidence is high; the economy has had healthy growth for some periods, which reduces apprehensions or fears in the minds of the market participants. The most important consequence of such improved or stabilized outlooks is a comparative reduction in volatility. As investors are more confident due to the economic performance of previous years, there is less panic trading and selling of stocks, leading to comparatively lower levels of volatility.
Both parameters of risk (volatility & VaR) are at reduced levels during the late phase. This effect, i.e., the power of the denominator in the Sharpe ratio, overrides the power of marginally higher interest/risk-free rate during such period, resulting in higher risk-adjusted returns in the late innings of the cycle.
Nevertheless, investors/traders should also know that possibility of a major market-related crash is also at a heightened level in the late phase of the BC. Thus, logically, the higher Sharpe ratio in the late-innings can be thought of as compensation for exposure to a heightened possibility of a crash, i.e., returns are high in a period of low volatility due to the pricing in of the stage of the BC and the probability of an adverse market event (crash), or put another way, a sharp rise in future volatility. This line of reasoning rationalizes the condition observed.
Results of statistical tests
Tests for returns/risk
Tests for Sharpe ratio