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I know about CAPM. My question is if this method is also viable:

Calculate monthly logReturns

sym  date       open   high   low    close  volume   logReturns  
-----------------------------------------------------------------
AAPL 2019.08.09 201.3  202.76 199.29 200.99 24423000 -0.0252867  
AAPL 2019.07.31 216.42 221.37 211.3  213.04 69281400 0.03197147  
AAPL 2019.06.28 198.68 199.5  197.05 197.92 31110600 0.05327795  
AAPL 2019.05.31 176.23 177.99 174.99 175.07 27043600 -0.05927072 

Extract the frequency table

logReturns| frq
----------| ---
-0.09     | 1  
-0.07     | 1  
-0.06     | 1  
-0.055    | 2  
-0.05     | 1  
...

Calculate the probability of a return occurring by taking the frq and divide by sum of frq

logReturns| frq prb       
----------| --------------
-0.09     | 1   0.01515152
-0.07     | 1   0.01515152
-0.06     | 1   0.01515152
-0.055    | 2   0.03030303
...

calculate returns and their sum

logReturns| frq prb        ret          
----------| ----------------------------
-0.09     | 1   0.01515152 -0.001363636 
-0.07     | 1   0.01515152 -0.001060606 
-0.06     | 1   0.01515152 -0.0009090909
-0.055    | 2   0.03030303 -0.001666667 

return: 0.003787879

Is this a valid way? I know for the expected returns of a portfolio we assume a bad, stagnant or strong economy and we calculate the returns by doing that. I couldn't find anywhere something about the expected returns of a single stock.

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  • 1
    $\begingroup$ Why do you need a frequency table, why not take the log returns from the first step and calculate the average directly? $\endgroup$ – Alex C Aug 11 at 22:47
  • $\begingroup$ I thought it might be a more accurate depiction of what could happen if I check how often a certain return occurs in a series of past returns and somehow project that in the future. My brain goes back to something I did in uni about step forecasts or something like that in which we calculated the probability of a certain state occurring ... but I cannot remember the exact technique. $\endgroup$ – Alex Aug 11 at 22:53
  • $\begingroup$ ohh. I was looking for regime switching models but not sure if they can help me much. $\endgroup$ – Alex Aug 11 at 23:02
  • $\begingroup$ The only problem with this method is that unless you have humongous amount of data (decades), the standard error of estimate is going to be fairly large... $\endgroup$ – Alex C Aug 11 at 23:12
  • $\begingroup$ I see. I will take that into account. Thank you very much! $\endgroup$ – Alex Aug 11 at 23:25
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One of the best ways I came across to estimate the expected return of a stock (even with limited time-series data), is Martin and Wagner (2019): What is the expected return on a stock?.

From their paper:

Second, our formula provides conditional forecasts at the level of the individual stock. Rather than asking, say, what the unconditional average expected return is on a portfolio of small value stocks, we can ask, what is the expected return on Apple, today?

Our approach [...], as we will show, [...] performs better empirically than the CAPM.


In a nutshell they use options data to compute the expected return on any given stock:

\begin{equation} \frac{E_t R_{i,t+1}-R_{f,t+1}}{R_{f,t+1}} = SVIX^2 + \frac{1}{2} (SVIX^2_{i,t} - \bar{SVIX}^2) \end{equation}

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