# Thread: Same variable on both sides - how to resolve this?

1. ## Same variable on both sides - how to resolve this?

I have a regression which is supposed to capture the effect of R&&D expenditures on stock returns, given some controllers X1, X2 and volatility, i.e. my model looks like this:

$ln(Return) = \beta_0 + \beta_1*ln(RDEXP)+\beta_2*X_1 + \beta_3*X_2+\beta_4*volatility$

I want to use volatility as a measure of riskiness of the respective stock. The problem with all risk measures is that they somehow depend on the stock price or returns, i.e. I have the same variable on the RHS and LHS. In this case,

$Return = 1+ (p_1-p_0)/p_0$

and

$volatility = \sigma_r/(tradingdays)$

where $\sigma_r$ is the standard deviation of the natural logarithmic stock returns

As I said, I run into the same problem with all other risk measurements but I feel that this is an important determinant. Any ideas how to solve this? The correlation matrix in Stata shows only a correlation of 0.08 between volatility and stock returns and -0.1 between volatility and ln(stock returns).

2. ## Re: Same variable on both sides - how to resolve this?

Typically, in models like yours, the volatility is a function of returns on the previous days. It is either an estimate of the standard deviation using a rolling window (with potential exponential smoothing), or an estimate from the GARCH(1,1) model, or an estimate from a Hidden Markov Model, or something else.

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