Understanding Beta and its benchmark (CAPM)

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I understand that Beta=Cov (i,mkt)/ VAR (mkt). And is measuring a securities excess return in comparison to the markets excess returns. However, what do we actually mean by “Market”? Are we talking about the collective group of securities like the S&P 500 market index, or are we talking about a sector in which a company operates in? I’m really just having a hard time understanding the intuition behind the “Market” benchmark.
Thanks,
 
The S&P 500 is used as the market return by all of the major data providers here in the US.
 
Just to elaborate a little further… you’ve run into an essential question in the CAPM. What is the market and how can we measure its return? That’s a question for which there is no universally correct and practical answer. Basically, you can get a theoretical “correct” answer and a practical answer (based on the real world use of the model, which depends on the scope or context [international vs traded in the US only, for example]). The only reason I bring this up is because you won’t be necessarily correct to put “S&P 500” as an answer choice on an exam.
 
In theory, the market portfolio would be a value-weighted one consisting of ALL risky assets (even assets like human capital). But that’s not feasible.
In practice, the S&P is used more often than anything else.
 
busprof wrote:
In theory, the market portfolio would be a value-weighted one consisting of ALL risky assets (even assets like human capital). But that’s not feasible.
In practice, the S&P is used more often than anything else.
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It is not feasible and there is one more reason why we use some certain stocks instead of the whole market. The research made about this reveal that when you put something like S&P 500 you still get an accurate estimate so you dont need the whole market. If you read the portfolio management section of CFA level 1 books you will understand better on your own.
 
Wallkahn:
The point I was trying to make (albeit unsuccessfully) is that the true market portfolio (according to the papers that started the whole CAPM thing back in the day) is unobservable. I’m not aware about research indicating that the S&P gives an “accurate” estimate, because in order to get one, we’d have to know the “correct” estimate. And since the “Correct” estimate is unknowable, I don’t know how you’d make that judgement.
The key point is that the S&P is often used in practice as a proxy for the market. And as far as the CFA exam is concerned, when choosing between the “theoretically correct” answer and the “CFA answer”, only the latter one matters.
 
busprof wrote:
Wallkahn:
The point I was trying to make (albeit unsuccessfully) is that the true market portfolio (according to the papers that started the whole CAPM thing back in the day) is unobservable. I’m not aware about research indicating that the S&P gives an “accurate” estimate, because in order to get one, we’d have to know the “correct” estimate. And since the “Correct” estimate is unknowable, I don’t know how you’d make that judgement.
The key point is that the S&P is often used in practice as a proxy for the market. And as far as the CFA exam is concerned, when choosing between the “theoretically correct” answer and the “CFA answer”, only the latter one matters.
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It’s ironic that he points you to the curriculum when the curriculum is based on the papers (or on texts based on the papers). The point was that the model was derived under certain assumptions, which may or may not be realistic or practical. I think you were clear on the topic…(and you seem to have a good point about being unable to compare an S&P500 estimate with the true parameter since we don’t know the true value…)
 
If you take a look at various proxies for “the market” – the S&P 500, the DJIA, the Russell 3,000 – you’ll find that their correlations of returns are incredibly high: on the order of 0.95+. I haven’t looked at market (i.e., equity) indices outside the US, but I suspect that you’ll see similarly high correlations of returns.
The upshot is that if you use virtually any broad market (equity) index, the beta that you calculate will be nearly the same as the one that you would get by using any other index. So, while it’s true that you cannot observe the entire “true” market, you can observe enough of it for practical purposes.
 
If I can put on my “academic nerd” hat one last time, the correlations between different broad indexes are high enough that using one is pretty much as good as using another. But the “theoretical” problem is that none of them contain the non-market-index assets like human capital, intellectual property, and so on (which the original CAPM theory assumed would be in the “market” portfolio).
If these assets are highly correlated with the indexes, the error in using an index as a proxy for the “true” market portfolio will be small. Unfortunately, we can’t easily tell, because these assets are unobservable.
Theory is clean. Reality is messy. Unfortunately, it’s reality we’ve got.
 
I will keep it simple to explain my point of view here. The aim of the beta is to see an asset or a specific portfolio’s movement with the “market risk”. So lets say an asset or a portfolio with 0.8 beta. We expect this asset to decrease by 0.8 unit when the market decreases by 1 unit. (We only expect that doesnt mean it will %100 occur).
So the point is how we reach the market risk right? According to the portfolio theory if we put every single risky asset which includes stocks, bonds, real estate, gold etc etc etc any asset in the whole world, we reduce the unsystematic risk to 0 and we will reach to the pure systematic risk which is market risk.
I am not a researcher or an acedemic person but I rely on acedemic people’s research.
So when I was reading the Schweser book it was written that “a research” made by acedemic people shows that if you only put 12 to 18 stocks you can reduce the unsystematic risk by 90% and I rely on those research.
I dont get why you make a debate on we cant see see the true parameter which is the whole market while I already mention that the whole market is not “feasible” for application. We cant observe a lot of population parameters but by using statistical tools we make “inference” that with some confidence intervals we can rely on our findings.
 
busprof wrote:
If I can put on my “academic nerd” hat one last time, the correlations between different broad indexes are high enough that using one is pretty much as good as using another. But the “theoretical” problem is that none of them contain the non-market-index assets like human capital, intellectual property, and so on (which the original CAPM theory assumed would be in the “market” portfolio).
If these assets are highly correlated with the indexes, the error in using an index as a proxy for the “true” market portfolio will be small. Unfortunately, we can’t easily tell, because these assets are unobservable.
Theory is clean. Reality is messy. Unfortunately, it’s reality we’ve got.
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That was what I believe the other poster missed. The derivation has specific assumptions, the real world doesn’t change what assumptions were used to derive the model.
 
Thank you everyone for adding your input! A lot of good information came out of this thread. From what I have inferred, the benchmark that is being utilized in the Beta calculation really doesn’t matter. As long as the benchmark for the market is a representation of the market as a whole (S&P 500, DJIA, R 3,000) the beta calculation for a given company should come out relatively the same.
 
Akeg wrote: Thank you everyone for adding your input! A lot of good information came out of this thread. From what I have inferred, the benchmark that is being utilized in the Beta calculation really doesn’t matter. As long as the benchmark for the market is a representation of the market as a whole (S&P 500, DJIA, R 3,000) the beta calculation for a given company should come out relatively the same.
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They’ll be quite close generally.
It would be an interesting experiment to check this for yourself. On Yahoo! Finance you can download historical prices for a variety of securities and indices. You should try downloading monthly prices on several stocks, mutual funds, and ETFs, as well as several indices (S&P 500, DJIA, Russell 3000, Wilshire 5000). Calculate the monthly returns for each security and each index for, say, 5 years (60 months of returns), then compute beta for each of those securities vs. each index. Excel has a SLOPE function that will give you just what you want. Take a look at the different estimates of beta for each security, depending on the particular market proxy you use.
 
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