macrocephalopod on Twitter: "They are both true by definition if the weights are market cap weights and the index you are measuring beta to is a market cap weighted index. No data analysis required, it is just math.… https://t.co/KCi8MKmjv0"

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Robot James ‏ @therobotjames 16 Mar 2021

Replying to @breakingthemark @macrocephalopod and

I'm not sure... I'd need to run the numbers.

2 replies 0 retweets 1 like

Matt Hollerbach‏ @breakingthemark 16 Mar 2021

Replying to @therobotjames @macrocephalopod and

Ok, run the numbers. Back of the envelope its easy to see it's at least close. Equity risk premium is about 8%. Stock vol around 28%= 8% variance.

2 replies 0 retweets 1 like

Robot James ‏ @therobotjames 16 Mar 2021

Replying to @breakingthemark @macrocephalopod and

Daily returns on R1000 stocks since 1999. Point-in-time (no survivorship bias). Removed obvs with price < $5 or volume < 0. Observations: 5,541,053 AR Mean: 0.055% Geo Mean: 0.020% Stdev: 2.625%

3 replies 0 retweets 3 likes

Robot James ‏ @therobotjames 16 Mar 2021

Replying to @therobotjames @breakingthemark and

Avg risk free rate (3 month bills) was 0.589% over that period. Which is 0.002% per day. I'm not 100% sure what you're expecting to see here so I haven't tried to interpret this for you.

1 reply 0 retweets 2 likes

Robot James ‏ @therobotjames 16 Mar 2021

Replying to @therobotjames @breakingthemark and

Here's the annualised arithmetic return plotted against the annualised variance for each stock. (Each point is a unique stock ticker.) I've truncated axes a bit...pic.twitter.com/wKiETH1zgN

2 replies 0 retweets 2 likes

Robot James ‏ @therobotjames 17 Mar 2021

Replying to @therobotjames @breakingthemark and

Here is the data summarised by ticker. https://filebin.net/ctycg7t0rgpozadj/byticker.csv?t=ek9bfpdq … Note the observations column... Stocks go in and out of the index so some stocks have lots of observations and others much fewer.

1 reply 0 retweets 1 like

Matt Hollerbach‏ @breakingthemark 17 Mar 2021

Replying to @therobotjames @macrocephalopod and

Thanks. I've done two things. I calculated the OL for each stock and then averaged them, weighted by the # of observations. Its 1.16 And I calculated the weighted avg of return and st. dev. (my st. dev was a bit lower than yours, return was same). and then the OL. Its 0.85pic.twitter.com/xFIGI5Ol6M

1 reply 0 retweets 0 likes

Matt Hollerbach‏ @breakingthemark 17 Mar 2021

Replying to @breakingthemark @therobotjames and

So somewhat near 1. I'm not sure if 20 years is enough to get a full convergence. I used 70 years of data in my post. I think its a coincidence that the two meathods nearly equally flank 1 on each side.

1 reply 0 retweets 0 likes

Adam Goldstein‏ @goldstein_aa 17 Mar 2021

Replying to @breakingthemark @therobotjames and

Well, using your method of corroborating a theory CAPM has been corroborated 100% perfectly. Weighted average beta for all stocks=1, weighted average excess return = market excess return. But that's not how people judge CAPM, and it's not how people will judge your theory.

3 replies 0 retweets 1 like

Matt Hollerbach‏ @breakingthemark 17 Mar 2021

Replying to @goldstein_aa @therobotjames and

"Weighted average beta for all stocks=1, weighted average excess return = market excess return" Are either of these true? I sent you a screen last week which made is seem like the first certainly wasn't true.

2 replies 0 retweets 0 likes

macrocephalopod‏ @macrocephalopod 17 Mar 2021

Replying to @breakingthemark @goldstein_aa and

They are both true by definition if the weights are market cap weights and the index you are measuring beta to is a market cap weighted index. No data analysis required, it is just math.

7:03 AM - 17 Mar 2021

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