Estimating Individual Stock Returns with Options-Based Volatility
Summary
The document asks whether an individual stock’s historical monthly return frequencies can provide a valid expected return estimate. The proposed method groups observed log returns, treats each frequency as an estimated probability, multiplies returns by those probabilities, and sums the products. This is a sample-based estimate, but the post does not establish that it is a reliable forecast of future returns.
The answer points instead to an options-based approach from Martin and Wagner. In outline, it estimates a stock’s conditional expected return using risk-free returns, aggregate option-implied variance, and the difference between the stock’s implied variance and a market-wide average. The cited paper is described as finding stronger empirical performance than CAPM, though the document provides no supporting details, sample design, or caveats about that comparison. The formula is presented without definitions for all terms or implementation guidance, so readers would need to consult the original research before applying it.
Key ideas
- A frequency-weighted average of historical returns estimates a sample mean, not necessarily a dependable forecast.
- The cited alternative estimates conditional stock returns using option-implied variance measures.
- The method compares a stock’s implied variance with a market-wide variance benchmark.
- The post reports an empirical comparison with CAPM but gives no supporting study details.
- The formula requires further definitions and the original paper for practical implementation.
Tags
Full text
# How to calculate the expected stock returns for an individual stock?
# 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.
## Answer by phdstudent (score 5)
https://quant.stackexchange.com/a/47082
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}Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.