# Estimating Beta from unevenly spaced price history

I have a certain non-stock asset that has 1 transaction every 1 to 8 months.
I also have a price index of that class of asset compiled by another party on monthly basis.
If I regress $price = \alpha' + \beta' index$, the $R^2$ is 0.975 to 0.999 for every asset.

How do I obtain an estimate of $\beta$ of CAPM $R_i = R_f + \beta(R_m-R_f)$

Right now, I am blindly guessing it through the following steps:
1. Regress $price = \alpha' + \beta' index$, obtain $\alpha'$ and $\beta'$
2. Generate interpolated monthly price $\widehat{price}_t$ by plugging in the monthly index
3. Generate monthly asset return $\hat{R}_{t+1}=\frac{\widehat{price}_{t+1}}{\widehat{price}_t}-1$
4. Generate monthly market return $\hat{R}_{m_{t+1}}=\frac{index_{t+1}}{index_t}-1$
5. Regress $\hat{R_{t}}$ on $\hat{R}_{m_{t}}$ and obtain $\beta$ of CAPM

Is this method valid? If not, what would be the proper convention?

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There's really no proper convention here. There are a lot of different options that might be better in some cases than others. Also, how much effort you put in might depend on what you're trying to do and what your boss wants. –  John Apr 21 at 17:11