Calculating Stock Beta Against the FTSE 100 Benchmark
Summary
The document addresses unexpectedly low beta estimates for stocks in the FTSE 100. It explains beta as the slope in a regression of a stock’s returns on benchmark returns: stock return is the dependent variable, and index return is the independent variable. In spreadsheet terms, the stock-return series belongs in the first, or y-value, argument and the FTSE 100 return series in the x-value argument. Reversing those inputs estimates a different slope and can produce misleading results.
A second answer gives the covariance-over-variance definition using returns in excess of the risk-free rate. It notes that a low beta generally indicates lower sensitivity to benchmark movements, but beta is not identical to total volatility or risk. The answers provide calculation guidance and an example estimate from supplied data, but the discussion does not assess whether one year of daily observations is sufficient or address other estimation choices such as benchmark composition and sampling error.
Key ideas
- Beta is the slope from regressing a stock’s returns on benchmark returns.
- In a spreadsheet slope function, stock returns are the dependent-variable series and index returns are the independent-variable series.
- Beta can also be calculated as covariance with benchmark excess returns divided by benchmark excess-return variance.
- A low beta indicates less sensitivity to benchmark moves, but beta is not the same as total volatility.
- The document does not assess how the sample period or other estimation choices affect the result.
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# Beta of FTSE100 stocks against benchmark index FTSE100
# Beta of FTSE100 stocks against benchmark index FTSE100
first post so if I write something silly don't hold it against me.
I calculated beta for almost all the stocks that compose the FTSE100. All have beta < 1. This, as far as I understand it, means that they are all less volatile than the benchmark index.
But, how can it be? Shouldn't some of the stocks that compose the index be more volatile??
--EDIT--
I downloaded 1 year long historical data for FTSE100 and for several stocks.
I calculated the daily movements (% returns) with the formula:
```
(close_price_today - close_price_yesterday) /close_price_yesterday
```
for each day except the last naturally. Did the same for both FTSE100 and all the stocks.
Then used slope function using FTSE100 using:
```
=SLOPE(array%ret_stock , array%ret_FTSE100)
```
the values are all above 0 and all below 1 (highest is approximately 0.6)
Here is a sample of what I did: https://docs.zoho.com/file/egrja03b89e74f3ca4dac91e8a02b0d950156
## Answer by Artur Silva (score 2, accepted)
https://quant.stackexchange.com/a/12709
Beta is calculated as Rstock = alpha + beta*Rindex. When you use slope in excel the first value is for the y's so you are doing it wrong, you should have slope(Stock returns, Index returns). While that is the formula you use above it is not the one in the excel, with the data you provide I get a beta of 0.96.
## Answer by Simon (score 0)
https://quant.stackexchange.com/a/12790
The computation of Beta is rather simple. Please try using my following procedures:
$$ ret_i = ret_{i} - ret_{rf} $$ $$ ret_b = ret_{benchmark} - ret_{rf} $$ then $$ \beta_{i} = \frac{cov(ret_p, ret_b)}{var(ret_b)} $$
where $ ret_b $ is the benchmark return net of risk-free rate, $ret_i$ is the stock return net of risk-free rate, $ cov $ is the covariance operator and $var$ is the variance operator. $\beta_{i}$ is the beta of the $i_{th}$ stock in the portfolio.
In this case benchmark return is FTSE100 Index, and stock return is the return of a given component stock in this universe. And risk-free rate can be taken as 0 given the low-interest environment of developed markets.
Generally low beta stocks are less volatile than high beta stocks. Usually large cap stocks tend to have lower beta than small-cap stocks. Beta can be used as a proxy for volatility and riskiness of a security, although they are not equivalent.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.