3
$\begingroup$

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.

Improve this question
$\endgroup$
5
  • 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 '19 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. $\endgroup$
    – user91991993
    Aug 11 '19 at 22:53
  • $\begingroup$ ohh. I was looking for regime switching models but not sure if they can help me much. $\endgroup$
    – user91991993
    Aug 11 '19 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 '19 at 23:12
  • $\begingroup$ I see. I will take that into account. Thank you very much! $\endgroup$
    – user91991993
    Aug 11 '19 at 23:25
4
$\begingroup$

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}

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.