Independent vs Dependent Regression correlation?

Question

I am trying to look at stock tickers. For example "MSFT" is the stock ticker for Microsoft. Using the package quantmod, an R package, I can get the latest 365 days of stock prices.

Each quarter a company will release their financial statements. The balance sheet, income statement, and cash flow documents. Now using these documents I can calculate certain financial ratios, such as the P/E ratio (Price/Earnings ratio). I would like to see how these ratios correlate to stock price. I will have four different P/E ratio calculations, because the financial statements are released quarterly.

My problem is I have way more than four stock prices since these are released on a daily basis. If I only use the latest four quarters stock prices as shown below, I know I will run into an error of not having enough data points to make a significant statistical prediction:

Dependent Variable-Stock Price: $2.00, $3.00, $3.50, $3.25

Independent Variable 1-# Days: 90, 180, 270, 360

Independent Variable 2-PE Ratio: 36, 48, 41, 51

But, if I use a different stock price on a daily basis, I run into having to repeat four different PE ratios a great many times as shown below. I feel like this will spit out a better p-value, but doubt you should even do this. I've learned regression on my own, so I don't know if the below is valid and the consequences of doing this:

Dependent Variable-Stock Price: $2.00, $2.05,..., $3.00, $2.97,..., $2.50, $2.60,..., $3.25, $3.28

Indpendent Variable 1-# Days: 90, 91,..., 180, 181,..., 270, 271,..., 360, 361

Indpendent Variable 2-PE Ratio: 36, 36,..., 48, 48,..., 41, 41,..., 51, 51

Would there be any way to work around either problem of not having enough data to make a significant prediction or not having to repeat values in the independent variable PE ratio?

Answer 1

If one carries back the dividend as adding value to a stock settlement price on a prorated basis one is doing the same thing as any other investor and usually the stock price on any give day already reflects that value as an estimate based on the expected future dividend. It then stands to reason that one should discount the prorated dividend from the stock price. Keeping this simple, one can say that at dividend day just after dividend issue, the stock is the market settlement value plus zero credited accumulated dividend. The P/E for that day is clearly $P/Div_{Q0}$. Now, since we have truth data for the next dividend, a simple (if slightly inaccurate) model of dividend discounted settlement value would be for elapsed day one $\frac{P_1-Div_{Q1}/90}{Div_{Q1}}=\frac{P_1}{Div_{Q1}}-\frac{1}{90}$ or in general for $0<n<90$ days is $P/E=\frac{P_n}{Div_{Q1}}-\frac{n}{90}$, which we can recalculate for each $j^{th}$ dividend, $Div_{Qj}$.

Mind you, that type of calculation works more accurately for bond issues where the payments out are better known in advance. However, the same model applies to stocks, if with more inherent noise. Also, note in the stocks link, the Microsoft share price example, just like you asked about.