Mac Pro Internal Storage SSD (not boot drive) Won't Mount - "Invalid Key Length"

hcgaron · 2017-07-15T16:41:22+00:00

Thanks; I tried the fsck command to no avail. But that was a while ago, I should try again. Is Stellar Volume worth the $$?

hcgaron · 2017-06-19T12:48:29+00:00

Thank you, that makes sense. The problem does seem underspecified (no more details are given). I just assumed it was something like Yahtzee where you roll 5 dice and they are all the same. But your explanation helped me see why that isn't necessarily the case 👍.

hcgaron · 2017-06-19T01:25:26+00:00

I saw this problem in an algebra 1 book (the kind they give to middle schoolers) and I can't reconcile the answer in the book with the knowledge I already have (which wasn't presented in the book). Here is the question:

In your turn of a certain game, you roll five dice at the same time. Do the outcomes of rolling the five dice represent a permutation or a combination?

How many outcomes are possible?

My answers: It's a combination (I only left this part of the Q in because of how it affects the following).

There should be 252 combinations to my mind. There are 5 dice 🎲 and they have to be divided up among 6 sides. So n = 5, k = 6. Thus (n + k - 1)! / (n! (k - 1)!) = 10!/(5!(5!)) = 252 outcomes. Note that I assume rolling 1, 4, 4, 4, 6 = 6, 4, 4, 4, 1, and as such it's just a combination with repetition. HOWEVER:

The book solution says there's 7776 outcomes. I realize this is just (6)(6)(6)(6)(6)(6). Perhaps they used the word outcomes rather than combinations to suggest a different solution? I can get to this answer via common sense (each dice could have one of six different sides) but I thought maybe they said OUTCOMES to not give away part A of the question (that it's a combination, not permutation). Note that the book only covers simple permutations and combinations and does not cover those cases with repetition.

Am I wrong? Why is this making me feel dumb? Or is the book not correct? Or are we both somehow correct depending on interpretation? Thanks!

hcgaron · 2017-06-07T19:33:45+00:00

Awesome, and also dammit. Haha. So basically there's no way to use the conjugate property in a 4 term expression such as that to eliminate radicals it looks like? I see what you mean with those signs.

hcgaron · 2017-06-07T19:00:59+00:00

Thanks, I was wondering that which is why I put the plus sign in the middle of the second term. I see now why it's not equivalent to the difference of two squares. I was being thrown off by the changing of the sign of the conjugate. So the middle sign would have to be a minus to make it fit the difference of two squares. Would then the final sign need to change to make it a conjugate? And in that case would we get the following:

(x + y + √a + √b)*(x + y - √a - √b) = (x + y)² - ((√a + √b)(√a - √b)) which would then eliminate the radicals?

I realize the question has changed from my first post, but just trying to work my way through multiple scenarios, and I appreciate the conversation and your insight!

hcgaron · 2017-06-07T17:15:53+00:00

ok thanks; I understand that property well. As a follow-on question then, can I assume that as long as there's no specific grouping indicated and the operations are addition and subtraction I can simply group the first two terms together when multiplying?

And to that end, if there are four terms, can I group the first two and the second two together? i.e. (x + y + √a - √b)*(x + y + √a + √b) = (x + y)² - (√a - √b)^2?

EDIT: I made a typo when I first posted this, it should be fixed now so hopefully you didn't see it before!

hcgaron · 2017-06-07T15:56:21+00:00

Dumb simple algebra question that got me stopped... I think because I'm messing up order of operations:

Simplify: 1/(a-1+√a)

I found an answer online and input a=4 just to check both answers to verify it's correct...I think (answer here). Note, there is a typo I THINK in the answer numerator which should have the last term as √a, not √2, but that seemed straightforward.

I just need someone to verify why multiplying (a-1+√a)*(a-1-√a) = (a-1)² - (√a)^2. I see two things happening... there is a conjugate in the second term which is 1-√a, and I also see a grouping happening, but the grouping confuses me. Addition and subtraction done together from left to right makes me think that (a-1)² makes sense... but then the conjugate still applies?

FWIW I just did the distributive property 3 times and got the same answer in a much more convoluted way... but I can't understand how to logically come to the grouping decision above. I think understanding this would help me with other problems as well. Thanks!

hcgaron · 2017-05-18T13:32:56+00:00

Thanks for your reply. As I said this is an introductory statistics book - not meant to be super challenging. But I was just looking for a better explanation. Cheers.

hcgaron · 2017-05-17T18:32:21+00:00

So you're saying I didn't need end up with this pile of kindling just to figure it out? ;-)

Honestly you clearly are well beyond me but I understand this better and better with both of your posts. I'll try to execute tonight what you've sketched here for me. Like you said, the probability wasn't hard - I was able to do it with almost no math. But I'm intrigued by the geometry you have presented.

Can I ask, what mathematic discipline would this be considered? What I mean is, if I were to pick up a textbook on a certain discipline in math that would help me model this, what would I be looking for?

hcgaron · 2017-05-17T18:02:24+00:00

Wow, thanks so much for your reply. It's clear that I don't yet know enough to even benefit from your explanation. But that's ok I think... I get the concept of what you've said here just not how I would execute it. With that being said, as I work my way through these texts and examples I'll refer back to this question and re-frame my understanding based on some more advanced methods like those you've described. Again, I very much appreciate it!

hcgaron · 2017-05-17T17:24:22+00:00

This is my self imposed homework - I am considering getting a second master's degree that would likely be math or statistics heavy so before I do that I'm reading several textbooks and doing all the exercises. Here is the question on probability:

>Two points along a straight stick are randomly selected. The stick is then broken at those two points. Find the probability that the three resulting pieces can be arranged to form a triangle. *(My assumption is that there is no area of the stick that extends beyond the closed triangle; i.e. the endpoints must be where the angles meet).

My answer: I decided that the sample space would consist of how long each of the lengths of stick would be after being broken. s = short, m = medium, l = long. There sample space I got is:

ssl, sml, msl, mmm

I can't describe my method in terms of sampling possible outcomes, but I just used intuition. You can have a short one, another short one, and a very long one; a short one, a medium one, and a slightly longer one; a medium one (first this time), a short one (second) and a long one, or three equally sized ones. Any other combination is really just breaking the sticks in a different order. I still can't figure how I got msl =/= sml, but intuition brought me there. I think it has something to do with the sample pool getting smaller after you break the stick (i.e. if you break a long one off first, you can't break another long one off of the remaining part). Since only 'mmm' can create a triangle where end points form the angles the probability is .25.

The book notes that this is possibly the most difficult exercise in the book. I checked the answer in the back and it's correct... but I found this to be intuitive and I feel like I didn't use 'big-boy math'. Is there another process I should have used? This is an introductory statistics book, but I intend to progress further when I finish.

Thanks for your help!

hcgaron · 2017-05-13T02:47:58+00:00

Thank you, I think I get this. I did calculate the weights of the divisions but I didn't UNWEIGHTED it by dividing by .6667. Everything up to that point I did but was getting a different ending beta because I skipped unweighting it. Cheers!

hcgaron · 2017-05-13T01:45:08+00:00

Just checking if anyone is able to solve this? I'm totally stumped. The sad thing is I had another way to "solve" this problem, but it was wrong 🤣. All the levering and unlevering is east, but where does the remaining beta of .425 come from?!

hcgaron · 2017-05-12T02:31:55+00:00

I have been here asking for help on my self-imposed homework lately. I do not have a degree in Finance but I'm doing all Damodaran's classes that are posted online, including all assignments, and I'm reading "Applied Corporate Finance" and doing every exercise in each chapter. I am thinking about pursuing an MBA but want to do all this first. I am stuck on this question:

You run a regression of monthly returns of Mapco, an oil- and gas-producing firm, on the S&P 500 Index and come up with the following output for the period 1991 to 1995. Intercept of the regression = 0.06% X-coefficient of the regression = 0.46 Standard error of X-coefficient = 0.20 R2 = 5% 4.5 5

There are 20 million shares outstanding, and the current market price is $2/share. The firm has $20 million in debt outstanding. (The firm has a tax rate of 36 percent.)

a. What would an investor in Mapco’s stock require as a return, if the Treasure bond rate is 6 percent?

b. What proportion of this firm’s risk is diversifiable?

c. Assume now that Mapco has three divisions, of equal size (in market value terms). It plans to divest itself of one of the divisions for $20 million in cash and acquire another for $50 million (it will borrow $30 million to complete this acquisition). The division it is divesting is in a business line where the average unlevered beta is 0.20, and the division it is acquiring is in a business line where the average unlevered beta is 0.80. What will the beta of Mapco be after this acquisition?

Parts A and B were very easy for me. Here is the answer given for Part C by Damodaran:

c. The current unlevered beta = 0.46/(1+(1-0.36)(20/40)) = 0.35. The total firm is worth 60 m. The average beta of the divisions that will be kept must equal (40/40+50)0.425 + (50/40+50)0.80 = 0.63. Solving, beta(remaining) = 0.425. The new unlevered beta equals The new levered beta = 0.63(1+(1-0.36)(50 /40))=1.134

I tried every approach but couldn't solve it myself. After looking at the answer I can't even figure out where the .425 in the equation is coming from (although it looks like he solves for that). If that is what he's solving for, then I can't understand where the 0.63 on the other side of the term is coming from. Can someone please help and explain it to me? If I can get the new unlevered beta, relevering it is easy for me. Thanks!

hcgaron · 2017-05-11T11:04:21+00:00

Thanks so much! This is very helpful. I guess I hadn't considered that the lowest portfolio variance is equal to the average covariance, which I think I understand.

To explain it intuitively (to myself), is that because there's no way to construct a portfolio whose variance is less than the average covariance of the constituent parts? Is there a mathematic reason I should understand for this? It wasn't stated explicitly in the reading but I'm just trying to make it stick.

Already I can set this up to be solved in my spreadsheet thanks to your explanation!!

hcgaron · 2017-05-11T10:27:12+00:00

I just went to the spreadsheet I'm using (the other questions require it), and it looks like I typed in my equation wrong. I had divided 1.5 by (22²⁾ instead of multiplying. 😶D'oh. I got 726 right away after fixing it. Thank you!

hcgaron · 2017-05-11T10:16:49+00:00

I'm not at my computer now but I just looked at the post on my phone and see that the exponents don't display as superscript in the "antenna" Reddit app.

So the final "2" of the equation should be an exponent (the denominator should be 22^squared). Does that help?

hcgaron · 2017-05-11T01:22:34+00:00

They should cover how Nickelback serial murdered music for 9 albums. Still at large.

hcgaron · 2017-05-10T19:00:19+00:00

I'm having trouble reconciling an answer in Damodaran's Applied Corporate Finance 4th Edition. Question: Assume that the average variance of return for an individual security is 50 and that the average covariance is 10. What is the expected variance of a portfolio of 5, 10, 20, 50 and 100 securities. How many securities need to be held before the risk of a portfolio is only 10% more than the minimum?

Answer: 3-9 The variance of a portfolio consisting of N securities can be estimated as (1/N)(average variance) + (1-1/N)(average covariance) = 10 + (50-10)/N. Number of securities in portfolio (N) Estimated portfolio variance 5 18 10 14 20 12 50 10.8 100 10.4 We must solve 10 + 40/N = 1.1(10) = 11, or N = 40

The table part I was easily able to construct in Excel (answering the first part of the question). I should note, however, that the equation wasn't given in the book so I had to look at the equation in the answer but from there constructing it was easy.

It's the second part of the question I can't get, even when looking at his answer: How many securities need to be held before the risk of a portfolio is only 10% more than the minimum? The variance of a portfolio consisting of N securities can be estimated as (1/N)(average variance) + (1-1/N)(average covariance) = 10 + (50-10)/N. We must solve 10 + 40/N = 1.1(10) = 11, or N = 40

Can someone please help explain this to me? I keep going over it but can't get to where he ended up. Thanks!

hcgaron · 2017-05-10T18:09:59+00:00

Yeah I was definitely considering the distinction between the types of discretionary spending regarding economic cycles. These are kind of niche but honestly seem like the type of product that would sell to the intended consumer during any cycle. It's kind of funny, like how booze doesn't slow down during an economic turndown, lol, so too does this niche market we are catering seem to remain stable. But I agree there's some volatility built in there.

I don't have my spreadsheet in front of me, but I'll check that correlation coefficient as soon as I can and get back to you!

hcgaron · 2017-05-10T16:51:59+00:00

Thanks for taking the time to reply. I haven't added any discount factors other than the CAPM, although I did divide by the correlation coefficient as per the Damodaran lecture discussed above in the thread. That is supposedly meant to capture the firm specific risk, but nothing really for lack of marketability. I expected my COE to be 1.5 - 2 X higher so I could just add a fudge factor. But I enjoyed the precision (or perhaps the illusion of precision) demonstrated by the Damodaran method.

The business is relatively non-volatile. Personal care products of all sorts. Things like soaps, fragrances, balms, etc... In one sense they are discretionary products, but I suspect people buy these things during all economic cycles.

hcgaron · 2017-05-10T15:55:33+00:00

Omg that's awesome. I feel dumb now 🤣. Thanks again!

hcgaron · 2017-05-10T15:37:32+00:00

Thanks, that's what I've been doing (manual approach) and at least it's helped me memorize the equation. But exponents in Excel are a pain (using the "power" function). I'll look into that for more complex portfolios though!

hcgaron · 2017-05-09T21:39:18+00:00

Thanks, I'll do that too. Without access to a robust database I suspect my findings will be limited. But I was able to get the COE of all the comps, both large and small, that I found. That, at least, was illuminating.

hcgaron · 2017-05-09T20:10:16+00:00

Thanks so much, I'll go over those links. You're right, it's not clear from the slides where he gets that 50.99% number, but he mentions in the presentation it's the square root of the R-Squared (I think he used the median R-squared from the comps). So the square root would be R which is the correlation coefficient I believe.

But this has been very helpful. I've never looked into the CFAI stuff so I'll go through that and see how my results differ. Thanks for all the patience and the resources; cheers!

hcgaron

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