Replicating a Three-Year Monthly Equity Beta Estimate

Summary

The document concerns reproducing a published equity beta using monthly stock returns and the S&P 500 as a market proxy. Beta is estimated as the covariance between market and stock returns divided by the variance of market returns. The questioner reports a result far from the expected range after calculating returns from downloaded price data, and asks why the estimate differs.

The accepted response points to two possible data issues: calculating 36 monthly returns requires prices from 37 months, and the index closing-price series may need to be used. It also flags a suspicious observation in the downloaded data and reports that interpolating it brought the estimate closer to the stated reference. This is a troubleshooting example, not a general validation of Yahoo’s methodology; the suggested interpolation and data-source assumptions should be checked independently before relying on the resulting beta.

Key ideas

• A three-year sample of monthly returns requires 37 monthly price observations.
• Equity beta can be estimated from stock and market returns using covariance divided by market-return variance.
• Price-series conventions and erroneous observations can materially affect a beta estimate.
• The proposed interpolation is a case-specific repair and should be independently validated.

Tags

# Flow Variable and Stock Variable


# Flow Variable and Stock Variable












I am new to stochastic control and I need your help! Suppose that we are a trader and we are trading based two sources of signal. One comes from the stock's flow of dividends as well as another trader's demand. Assume that the dividend flow moves as $$ dD_t = \mu_D dt + \sigma_D dZ^1_t $$ where $Z^i_t$ denotes a standard Wiener process. Also suppose that the other trader trades randomly and demands on the interval $[t,t+dt)$ the amount $dY_t$. Indeed $Y_t$ denotes the cumulative purchased shares the other trader holds. Also assume that

$$ dY_t = \mu_Z dt + \sigma_Z dZ^2_t $$

For me it is both intuitive and technically robust to assume that we can trade as a function of the other trader's demand. I mean if we trade like $dX_t = -dY_t$ then we are spanning the filtration made by the other trader's movements. That is to say, my demand has an increment with $dZ^2_t$ in it. Am I able to do a trade based on the "flow" variable $D_t$ as well? What is the intuition? What technical assumption makes it possible?

For example if I trade just the opposite direction of the other trader and just the magnitude of dividends paid then my trade at $[t,t+dt)$ will be $$D_t dt-dY_t$$. But can I reach a trading policy which has the form $$KdZ_t^1$$?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.