The Mystery of Volatility Estimates from Daily versus Monthly Returns

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The daily volatility estimates have long been a topic of interest among investors. However, the difference between these estimates has often been a subject of debate, with many questioning their validity.

That said, the data suggests that there is indeed an underlying pattern when comparing daily and monthly returns.

Main Concept: The Difference Between Daily and Monthly Returns

The S&P 500's volatility estimate from daily versus monthly returns reveals a significant difference. In fact, the results show that using daily data to estimate volatility would be equivalent to using monthly data except with less variability. This discrepancy has sparked debate among investors and researchers alike.

Historical Context: Why the Difference Matters

The data used for this analysis is from 1950 to 1997. During this period, the S&P 500 experienced a significant decline in volatility over time. The daily estimates of volatility are based on 756 days of closing log returns, while the monthly estimates are annualized by multiplying the standard deviation by the square root of 12.

Underlying Mechanics: What Drives the Difference

One possible explanation for this difference is autocorrelation. Autocorrelation refers to the phenomenon where past values of a time series influence future values. In this case, the data may be exhibiting autocorrelated behavior due to the S&P 500's random walk nature.

Data and Analysis: The Results

The results are presented in Figure 1, which shows the difference between daily and monthly volatility estimates for each three-year period from 1950 through 1997. As can be seen, the daily estimates of volatility tend to be less than the monthly estimates, with a slight wiggle around zero.

Practical Implementation: How Investors Can Apply This Knowledge

Investors who have been using monthly returns as their benchmark may need to adjust their strategies accordingly. One possible approach is to use a rolling average of the S&P 500's closing log returns over different time periods. This can help smooth out the volatility and provide a more stable estimate of volatility.

Portfolio/Investment Implications: What Does this Mean for Portfolios?

The difference between daily and monthly returns highlights the importance of considering the nuances of investment strategy. For example, investors who are investing in dividend-paying stocks may want to consider the impact of daily volatility on their portfolio's overall risk profile.

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In conclusion, the mystery of volatility estimates from daily versus monthly returns has been revealed. By understanding this difference, investors can better tailor their strategies to suit their individual circumstances.