# How to calculate the expected stock returns for an individual stock?

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.

• Why do you need a frequency table, why not take the log returns from the first step and calculate the average directly? Aug 11 '19 at 22:47
• 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. Aug 11 '19 at 22:53
• ohh. I was looking for regime switching models but not sure if they can help me much. Aug 11 '19 at 23:02
• 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... Aug 11 '19 at 23:12
• I see. I will take that into account. Thank you very much! Aug 11 '19 at 23:25

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