Quiz motivated from Avi's post

[retaker]

Quiz:

T or F. A stocks Beta measures systematic (market) risk?



"..that means that the stock is 20% more volatile than the market average and that if the stock market index increases by 10% the expected move in this firm's stock would be a 12% increase. Higher betas imply higher risk.."

Higher Beta's imply higher risk and higher return, since
r= r_f+B(r_m - r_f) right.

T or F So if a stock's return has a S.D. (risk) greater than that of the market's, then that stock's expected return, r, is greater than the markets?

[sunshine]

Okay, I'm not 100% sure about this, but...

I think its generally true, but not always.
Generally true, because: Beta = Cov(r_stock, r_mkt)/Var_mkt
And Cov = rho*SD_stock*SD_mkt where rho is the correlation coeff.
Most stocks have a strong pos correlation coeff.
If SD_stock is large, then Cov is large, then Beta is large, then r_stock is large.

But: perhaps SD_stock is large, but the correlation coeff between the stock and the market is very low. So the stock price varies a lot, but not in step with the market.
Then the Cov is small, so Beta is small, so r is small.

To try to justify this verbally, by contradiction: if you had a stock with high variance which you think gives high r, but low correlation to the market, you could make a lot of money by holding half stock and half market portfolio, because both have high r, but since they are not correlated, your total portfolio variance falls dramatically. So this drives the price up of the stock, and r drops.

[retaker]

I'm not sure about all you wrote (that I understand it, that is, not if it is correct) but I can tell you what the old CAS questions and ACTEX think the answers are.
First, I don't think the (correct) definition of Beta you used is helpful.

1) True. I think this is bad wording. When I think of Beta it is usually in the context of an individual stock, and measures the stocks sensitivity to the market. Market risk is just something that exists due to all the many stocks in the market and their interaction. Beta doesn't measure that.
When they say "Beta measures market risk" I think they mean Beta measures as stock's sensitivity to market risk.

2)False. Remember, Beta measures "market" risk. High SD could be a result of high unique aka unsystematic aka diversifiable risk and hence not high market risk and so Beta will not be larger.


I don't think they will use these types of words - systematic etc - or ask concept questions along this line, but the old 220 and 4B, 5A did.
This is probably overkill.


How about this? The risk of a well-diversified portfolio mainly depends on covariance.

[sunshine]

1. I agree with you, that Beta actually measures a stock's sensitivity to market risk.

I find your last statement technically true but misleading.
My claim: the risk of ANY portfolio depends on covariance.

For any portfolio, well-diversified or not, r depends on beta, which depends on covariance (from my suggested formula).

Formula for covariance: Cov=rho*SD_stock*SD_mkt*

For a well-diversified portfolio, the correlation coeff (rho) is about 1, so this leaves SD_stock as the only important influnce on Cov.
Therefore, for a well-diversified portfolio, r depends on covariance, but to be more specific, r depends on SD_stock.

For a not well-diversified portfolio, r stil depends on beta, which still depends on covariance.
But in this case, we can make no remarks about rho, or any other part of the formula for cov, so the best we can say is that r depends on covariance.

Hope this makes sense- I know I can be verbose.

[retaker]

I didn't like the statement that a well-diversified portfolio mainly reflects covariance, since if it is well diversified the variances should some what cancel out, right, and you should approach the market portfolio?

Again, I think you have a better understanding of the details. I am just sticking to my current understanding, which is probably too much, too.[/i]

[Macroman]

retaker,

You are right, this is overkill.

What you want to take with to the exam about Beta is that it is the contribution of market risk to the total risk level of a specific company. That specific company will also have risk factors which are specific to that company.

[sunshine]

Retaker, you are right, I think I made a couple of mistakes in my explanation. For one thing I was mixing up the stock and the portfolio.
1. If a portfolio is well-diversified, then you are right, the variances cancel out, and then beta for a well-diversified portfolio must only depend on rho, the portfolio's correlation to the market, which can take on a wide range of values.

Just curious - are you working? I'm supposed to be working but I'm so nervous about the test I can't get anything else done.

[retaker]

"If a portfolio is well-diversified, then you are right, the variances cancel out, and then beta for a well-diversified portfolio must only depend on rho, the portfolio's correlation to the market, which can take on a wide range of values."

I don't remember that, but it sounds good.

Did they mean to say: The risk of a well diversified portfolio mainly depends on the portfolio's covariance with the market??

When they say the risk of a well diversified portfolio depends on covariance, I think about the covariance of the actual stocks in the portfolio, and in that case their statement doesn’t make sense, since if it is well diversified the co variances cancel out, and get rid of the unique risk and leave almost only the market risk, right?

I actually may not have this completely straight, but I bet it once again is the language which is messing me up.


Yes, I am working. Just writing in between. Took the 7th actex sample test today. I forgot about changing the clock and was panicking (is that spelled right) after 3 hours when I thought my time was up and I only answered 40 of the questions and didn't feel 100% on all of them.




[/i]

[sunshine]

Okay, I thought I'd actually *read the book* (what a novel idea!) instead of continuing to pull BS out of you-know-where. Check out bottom of page 175 and top of 176.
I think that they say for a well-diversified portfolio,rho is about 1, and that rho measures unique risk. If its overall a risky (but well-diversified) portfolio, then the SD will be a lot higher than the market SD.
So Beta for the well-diversified portfolio depends on the SD of the portfolio.

So if its well diversified, then the SD's do NOT cancel like we thought, rather, rho=1.

Whaddya think?

[retaker]

I don't even know what rho is, and to tell you the truth, I don't care at this point. I think we know too much already.

Nothing seems clearer to me, and I'm not spending any more time on this topic. We already have Course 6 or Course 8 level knowledge of this material.

Like you said before B_p = sigma_p/sigma_m, so yeah it depends on the SD of the portfolio.

Don't forget about interest theory- the speed necessary to solve the problems, that is, not the actual ability to solve them - that's part of what got me last time. I neglected interest theory at the end.

[sunshine]

I agree. 'Nuff said.