vania-janet/multiturn-rag-retrieval-data huggingface dataset:
In reading the Moody's report I found it funny that 2 notches worth of Morgan Stanley's rating id due to the benefit from implied TBTF protection.  So here we are 4 years after the crisis and Morgan Stanley still has 2 notches of creditworthiness due to still being TBTF.  So without that MS would be one notch above junk.
I don't expect you to remember the area for the surface of a sphere; I do expect you to be able to take a derivative of a volume. Especially if you are a PhD. Believe it or not, it IS faster than looking it up on the internet. And abilities to do quick back of the napkin estimations are very handy in my field (CS).  Also, I noticed that meetings with people who are in command of basic facts are usually faster and more productive than with people who are constantly looking things up on the internet.
It also works the same way if you take out a loan rather than depositing money. Tax effects (capitals gains taxes or interest expense deductions) may make the actual amount paid or received different, but that does not change the fundamental aspect of how to calculate interest. Do CD's make more money with higher interest rates, or is it the other way around? Usually fixed interest rate instruments such as certificates of deposit, or loans with fixed rates, pay a higher interest rate for longer terms. This is because it is harder to judge credit risk in a longer term, so whoever gives the loan usually wants a premium for the additional risk. So a 6-month CD will normally pay a smaller percentage interest per year than a five-year CD. Note that this is not always the case; the technical term for when this does not hold is inverted yield curve. Interest rates are almost always formally specified in terms of percent per year, which makes it easy to compare rates. If you buy a $100 6-month CD paying 1% (I told you these were only examples :)) and then reinvest the money at the end of the term in another 6-month CD also paying 1%, the total amount paid will be ($100 * 1 + (1% * 6/12)) = $100.50 for the first term, then ($100.50 * 1 + (1% * 6/12)) = $101.0025 at the end of the second term. As you can see, the compounding of the interest makes this return slightly more than a single $100 12-month CD ($100 * 1 + 1% = $101), but unless you are dealing with large amounts of money, the difference is small enough to be negligible. If you were to put $100 in a 2% one-year CD, you'd get back $102 at the end of the year. Put the same amount in a 5% one-year CD, and you get back $105. So yes, higher interest rates means more interest money paid, for loans as well as deposits. Keep in mind that loans and deposits really are essentially the same thing, and interest calculations work the same way for both.
"As a former consumer credit counselor, who worked with struggling homeowners and first time homebuyers I would argue that it is a mistake for lenders to rely on gross income and assumptions on what an applicant spends their income on. I think lenders do this because they believe it is efficient and may not understand the long term ramifications for the stakeholders, e.g. the borrower, the lender, the servicer, the investor, the broker, the taxpayer, the marshall, the foreclosure lawyers etc. Or lenders do know the impact of a superficial mortgage screening, and intentionally want to enrich themselves in the short term while harming other stakeholders in the long term. Developing a budget that reflects what a person can realistically spend on their mortgage takes much longer than signing up for a Rocket mortgage. I would say an hour minimum for the first appointment to get a baseline, and at least two follow up appointments to make adustments soon after or whenever a borrower's financial situation changes dramatically. Credit counselors factor in all of the factors mentioned above, i.e. take home pay, future pay vs current pay, the ability to adjust deductions, seasonal expenses, multiple sources of income and their frequency, debt load etc. Budgets are always fluctuating, but when it is done right by a qualified professional the result is a much more accurate financial picture. The consequences for not doing this type of old-school due diligence, or for willfully choosing to skip it, are varied. First off, mortgages will be given to homeowners who should never have qualified in the first place, and likewise denied to homeowners who should qualify. This will result in market distortion and this distortion was a primary contributor to the 2008 subprime mortgage crisis and the wave of foreclosures that came with it. Another consequence is the stripping of wealth from minority communities since they are often targeted by the most unscrupulous of lenders. Additionally, the securitization of mortgages based on poor diligence at the loan officer level means loan portfolio ratings are questionable, investors will lose money, and small banks who are heavily invested will fail as they did in the past.
tl;dr: The CNN Money and Yahoo Finance charts are wildly inaccurate. The TD Ameritrade chart appears to be accurate and shows returns with reinvested dividends. Ignoring buggy data, CNN most likely shows reinvested dividends for quoted securities but not for the S&P 500 index. Yahoo most likely shows all returns without reinvested dividends. Thanks to a tip from Grade Eh Bacon, I was able to determine that TD Ameritrade reports returns with reinvested dividends (as it claims to do). Eyeballing the chart, it appears that S&P 500 grew by ~90% over the five year period the chart covers. Meanwhile, according to this S&P 500 return estimator, the five year return of S&P 500, with reinvested dividends, was 97.1% between July 2012 to July 2017 (vs. 78.4% raw returns). I have no idea what numbers CNN Money is working from, because it claims S&P 500 only grew about 35% over the last five years, which is less than half of the raw return. Ditto for Yahoo, which claims 45% growth. Even stranger still, the CNN chart for VFINX (an S&P 500 index fund) clearly shows the correct market growth (without reinvesting dividends from the S&P 500 index), so whatever problem exists is inconsistent:  Yahoo also agrees with itself for VFINX, but comes in a bit low even if your assume no reinvestment of dividends (68% vs. 78% expected); I'm not sure if it's ever right.  By way of comparison, TD's chart for VFINX seems to be consistent with its ABALX chart and with reality:  As a final sanity check, I pulled historical ^GSPC prices from Yahoo Finance. It closed at $1406.58 on 27 Aug 2012 and $2477.55 on 28 Aug 2017, or 76.1% growth overall. That agrees with TD and the return calculator above, and disagrees with CNN Money (on ABALX). Worse, Yahoo's own charts (both ABALX and VFINX) disagree with Yahoo's own historical data.
This article makes claims and fails to back *any* of them up with actual data. Showing your work is rather important here.  [This is the official table from the BLS, showing a seasonally-adjusted U-6 number of 15.6%, down 0.6% from last month and down 1.4% year-over-year.](http://www.bls.gov/news.release/empsit.t15.htm)
Oh, I missed that in a follow-up comment you say you are paying 4% on a mortgage which you are adjusting to 3% because of tax implications. Probability based on mean and SD you gave of getting less than 3% is 26%. I didn't read the article you cite. I assume the standard deviation given is for the rate of return for one year. If you stretch that over many years, the SD goes down, as many factors tend to even out. So while the probability that money in a given, say, mutual fund will grow by less than 3% in one year is fairly high -- the 25 - 35% we're talking here sounds plausible to me -- the probability that it will grow by an average of less than 3% over a period of 10 or 15 or 20 years is much less. Further Thought There is, of course, no provably-true formula for what makes a reasonable risk. Suppose I offered you an investment that had a 99% chance of showing a $5,000 profit and a 1% chance of a $495,000 loss. Would you take it? I wouldn't. Even though the chance of a loss is small, if it happened, I'd lose everything I have. Is it worth that risk for the modest potential profit? I'd say no. Of course to someone who has a billion dollars, this might be a very reasonable risk. If it fails, oh well, that could really cut in to what he can spend on lunch tomorrow."
It is an action movie, but it begins with a dice game. Consider adopting a Bayesian perspective on probability as it would be a healthier perspective based on how you are thinking about this problem. A ""frequency"" approach always assumes the null model is true, which is what you are doing. Had you tried this will real money, your model would have been falsified, but you still wouldn't know the true model. Yes, you can do much worse than 1/6th of the time. Even if you are trying to be ""fair,"" you have not accounted for the variance. Extending that logic, then for an inexperienced trader, is it right to say then that it's equally difficult to purposely make a loss then it is to purposely make a profit? Because if I can purposely make a loss, I would purposely just do the opposite of what I'm doing to make a profit. So in the dice example, if I can somehow lower my chances of winning below 16.6667%, it means I would simply need to bet on the other 5 numbers to give myself a better than 83% chance of winning. If the game were ""fair,"" but for things like forex the rules of the game are purposefully changed by the market maker to maximize long-run profitability. Under US law, forex is not regulated by anything other than common law. As a result, the market maker can state any price, including prices far from the market, with the intent to make a system used by actors losing systems, such as to trigger margin calls. The prices quoted by forex dealers in the US move loosely with the global rates, but vary enough that only the dealer should make money systematically. A fixed strategy would promote loss. You are assuming that only you know the odds and they would let you profit from your 83.33 percentage chance of winning. So then, is the costs of trading from a purely probabilistic point of view simply the transaction costs? No matter what, my chances cannot be worse than random and if my trading system has an edge that is greater than the percentage of the transaction that is transaction cost, then I am probabilistically likely to make a profit? No, the cost of trading is the opportunity cost of the money.
Your analysis is wrong for a few reasons. One, the consolidated margins of Nflx are being weighed on by international expansion. US EBIT margins were 24% in 2016, and even that is an underestimating of steady state margin profile because nflx runs a subscription model where CAC is paid up front. US marketing was 7% of US streaming revenue in 2016, so in a mature sub-replacement growth profile you could easily see that coming down to 4-5%, accretion that delta to the US EBIT margin, leaving you around 26-27% margins. Stead state international margins should be higher because in local markets Netflix only wants to have 20% of the content library be local, with the remainder leveraged from the US library.   Haven't read the Bernstein report, but I think you misunderstood it. The point was that the analyst calculated net customer LTV and valued the company based on that times his sub estimate... The value additive part of the note is the LTV Calc, which I haven't seen but I imagine is probably based on the above margin analysis and some churn assumptions.
Nobody outside of the credit scoring agencies know exactly what goes into the scoring formula. That said, I don't think there is any evidence that keeping a fixed loan (car or mortgage) open is necessary to keep its effect on your score. It doesn't improve your utilization ratio like an open revolving credit line would. And depending on the exact details of how your specific lender reports the loan, it might appear detrimental to your debt-to-income ratio.  I would simply pay it off.
Perhaps there is no single formula that accounts for all the time intervals, but there is a method to get formulas for each compound interest period. You deposit money monthly but there is interest applied weekly. Let's assume the month has 4 weeks.  So you added x in the end of the first month, when the new month starts, you have x money in your account. After one week, you have x + bx money. After the second week, you have x + b(x + bx) and so on. Always taking the previous ammount of money and multiplying it by the interest (b) you have. This gives you for the end of the second month:  This looks complicated, but it's easy for computers. Call it f(0), that is: It is a function that gives you the ammount of money you would obtain by the end of the second month. Do you see that the future money inputs are given with relation to the previous ones? Then we can do the following, for n>1 (notice the x is the end of the formula, it's the deposit of money in the end of the month, I'm assuming it'll pass through the compound interest only in the first week of the next month):  And then write:  There is something in mathematics called recurrence relation in which we can use these two formulas to produce a simplified one for arbitrary b and n. Doing it by hand would be a bit complicated, but fortunately CASes are able to do it easily. I used Wolfram Mathematica commands: And it gave me the following formula:  All the work you actually have to do is to figure out what will be f(0) and then write the f(n) for n>0 in terms of f(n-1). Notice that I used the command FullSimplify in my code, Mathematica comes with algorithms for simplyfing formulas so if it didn't find something simpler, you probably won't find it by yourself! If the code looks ugly, it's because of Mathematica clipboard formatting, in the software, it looks like this:  Notice that I wrote the entire formula for f(0), but as it's also a recurrence relation, it can be written as:  That is: f(0)=g(4). This should give you much simpler formulas to apply in this method.
Will the investor beat the benchmark for a given period will follow a Bernoulli distribution -- each period is a coin toss, and heads mean the investor beat the market for that period.   I can't prove the negative that there is no investor ever whose probability function p = 1, but you can statistically expect a number of individual investors with p ~ 0.5 to have a sequence of many heads in a row, as a function of the total population.   By example, my father explained investment scams and hot-hand theory to me this way when I was younger:  Imagine an investor newsletter which mails out to a mailing list of 1024 prospects (or alternately, a field of 1024 amateur investor bloggers in a challenge).  Half the letters or bloggers state AAPL will go up this week, half that AAPL will go down this week.  In the newsletter case, next week ignore the people we got wrong.  In the blogger case, they're losers, so we don't pay attention to them.  Next week, similar split: half newsletters or bloggers claim GOOG go up, half GOOG go down.  This continues for a 10 week cycle.   Now, in week 10: the newsletter has a prospect they have hit correct 10x in a row: how much will he pay for a subscription?  Or, one amateur investor blogger has been on a 10 week winning streak and wins the challenge, so of course let's give her a CNBC show after Jim Cramer.  No matter what, next week, this newsletter or investor is shooting 50-50.   How do you know this person is not the statistically expected instance backed up by a pyramid of 1023 Bernoulli distribution losers?  Alternately, if you think you're going to be the winner, you've got a 1/1024 shot.
http://en.wikipedia.org/wiki/Black%E2%80%93Scholes  Start there, the black scholes formula is used to calculate the value of a call or put option and it incorporates the risk free rate in the formula.  I am currently a bit busy but I will write up a better answer later if I get time.
Yeah and Doctor Oz has a medical degree. There's a whole lot of skepticism and critique of the outdated and abandoned methods he's using. A quick google search will say from plenty of other experts from MIT and other name dropping schools that his data isn't and cannot be realistic.   I'm anticipating a market correction, but I'm also not a conspiracy theorist.
"My experience is in economics, so it may differ from an accounting or personal finance perspective somewhat; that being said, I find it perfectly acceptable to use a term like CAGR when the rate is positive or negative. Economists talk about negative growth rates all the time, and it's universally assumed that growth rates can be positive or negative.1 Ideally, the actual magnitude and sign of the value should be specified by the value itself. The term, whether it's ""growth rate"", some modified version of it like CAGR, or any label in a table or on a graph, should describe the calculation or source used obtain the value. I shouldn't need the name to indicate the sign of the number if the number is present; the name is only there to help me understand the value. Unfortunately, I don't know of any specific term that represents the geometric averaging nature of CAGR and also eliminates the minor potential for semantic confusion. However, I think the minor problem of semantics needs to be balanced against the tradeoff of using a different term that isn't as common, if one were to exist. CAGR is a standard, well-known term that a) allows someone who is familiar with the term to instantly understand the procedure you're using, and b) allow someone who isn't familiar with it to quickly search and find an explanation, since searching for CAGR will numerous simple explanations of how it's calculated. 1. This is different from the concept of economic growth, which is usually assumed to be positive in informal discussions. In economic modeling, many of the first steps in creating a model are symbolic anyway, so ""growth rate,"", ""change in output"", and ""economic growth"" are used interchangeably to describe changes in GDP because the values either aren't known, irrelevant until later in the project, or pulled from data that describes it using one or several of the previously stated terms."
Set your xirr formula to a very tall column, leaving lots of empty rows for future additions. In column C, instead of hardcoding the value, use a formula that tests if it's the current bottom entry, like this: =IF(ISBLANK(A7),-C6, C6) If the next row has no date entered (yet), then this is the latest value, and make it negative. Now, to digress a bit, there are several ways to measure returns. I feel XIRR is good for individual positions, like holding a stock, maybe buying more via DRIP, etc. For the whole portfolio it stinks. XIRR is greatly affected by timing of cash flows. Steady deposits and no withdrawals dramatically skew the return lower. And the opposite is true for steady withdrawals. I prefer to use TWRR (aka TWIRR). Time Weighted Rate of Return. The word 'time' is confusing, because it's the opposite. TWRR is agnostic to timing of cashflows. I have a sample Excel spreadsheet that you're welcome to steal from: http://moosiefinance.com/static/models/spreadsheets.html (it's the top entry in the list). Some people prefer XIRR. TWRR allows an apples-to-apples comparison with indexes and funds. Imagine twin brothers. They both invest in the exact same ideas, but the amount of cash deployed into these ideas is different, solely because one brother gets his salary bonus annually, in January, and the other brother gets no bonus, but has a higher bi-weekly salary to compensate. With TWRR, their percent returns will be identical. With XIRR they will be very different. TWRR separates out investing acumen from the happenstance timing of when you get your money to deposit, and when you retire, when you choose to take withdrawals. Something to think about, if you like. You might find this website interesting, too: http://www.dailyvest.com/
"I think your very long list of possible assumptions makes a tacit point of your own:  to state ""15%"" as a general value is bogus.  I think, in most cases, the ""15%"" is merely a popular meme.   To give any fixed number or percentage of income saved is insufficient without expanding things in the way you show.  Therefore, a formula, in which at least a handful of variables can be plugged into it, seems like the right approach.  (And this is what is being discussed here with the Monte Carlo method)."
The periodic rate (here, the interest charged per month), as you would enter into a finance calculator is 9.05%. Multiply by 12 to get 108.6% or calculate APR at 182.8%. Either way it's far more than 68%.  If the $1680 were paid after 365 days, it would be simple interest of 68%. For the fact that payment are made along the way, the numbers change.  Edit - A finance calculator has 5 buttons to cover the calculations:  N = number of periods or payments %i = the interest per period PV = present value PMT = Payment per period FV= Future value In your example, you've given us the number of periods, 12, present value, $1000, future value, 0, and payment, $140. The calculator tells me this is a monthly rate of 9%. As Dilip noted, you can compound as you wish, depending on what you are looking for, but the 9% isn't an opinion, it's the math. TI BA-35 Solar. Discontinued, but available on eBay. Worth every cent.  Per mhoran's comment, I'll add the spreadsheet version.  I literally copied and pasted his text into a open cell, and after entering the cell shows,  which I rounded to 9.05%. Note, the $1000 is negative, it starts as an amount owed.  And for Dilip - 1.0905^12 = 2.8281 or 182.8% effective rate. If I am the loanshark lending this money, charging 9% per month, my $1000 investment returns $2828 by the end of the year, assuming, of course, that the payment is reinvested immediately. The 108 >> 182 seems disturbing, but for lower numbers, even 12% per year, the monthly compounding only results in 12.68%
The solution is x = 8.92. This assumes that Chuck's six years of deposits start from today, so that the first deposit accumulates 10 years of gain, i.e. 20*(1 + 0.1)^10.  The second deposit gains nine years' interest: 20*(1 + 0.1)^9 and so on ...    If you want to do this calculation using the formula for an annuity due, i.e. http://www.financeformulas.net/Future-Value-of-Annuity-Due.html  where  (formula by induction) you have to bear in mind this is for the whole time span (k = 1 to n), so for just the first six years you need to calculate for all ten years then subtract another annuity calculation for the last four years.  So the full calculation is:  As you can see it's not very neat, because the standard formula is for a whole time span.  You could make it a little tidier by using a formula for k = m to n instead, i.e.  So the calculation becomes  which can be done with simple arithmetic (and doesn't actually need a solver).
Average rates of return usually assume compounding, so your formula would be for annual compounding ,or for continuous compounding.