vania-janet/multiturn-rag-retrieval-data huggingface dataset:
I have answered your question in detail here https://stackoverflow.com/questions/12396422/apr-calculation-formula The annuity formula in FDIC document is at first finding PVIFAD present value annuity due factor and multiplying it with annuity payment and then dividing it by an interest factor of (1+i) to reduce the annuity to an ordinary annuity with end of period payments They could have simply used PVIFA and multiplying it with annuity payment to find the present value of an ordinary annuity In any case, you should not follow the directions in FDIC document to find interest rate at which the present value of annuity equals the loan amount. The method they are employing is commonly used by Finance Professors to teach their students how to find internal rate of return. The method is prone to lengthy trial and error attempts without having any way of knowing what rate to use as an initial guess to kick off the interest rate calculations So this is what I would suggest if you are not short on time and would like to get yourself familiar with numerical methods or iterative techniques to find internal rate of return There are way too many methods at disposal when it comes to finding interest rates some of which include All of the above methods use a seed value as a guess rate to start the iterative calculations and if results from successive calculations tend to converge within a certain absolute Error bound, we assume that one of the rates have been found as there may be as many rates as the order of the polynomial in this case 36 There are however some other methods that help find all rates by making use of Eigenvalues, but for this you would need a lengthy discourse of Linear Algebra One of the methods that I have come across which was published in the US in 1969 (the year I was born :) ) is called the Jenkins Traub method named after the two individuals who worked jointly on finding a solution to all roots of a polynomial discarding any previous work on the same subject I been trying to go over the Jenkins Traub algorithm but am having difficulty understanding the complex nature of the calculations required to find all roots of the polynomial In summary you would be better of reading up on this site about the Newton Raphson method to find IRR
Yea, like others are saying -- it's legitimate.  Just insurance.  In fact, as far as derivatives go -- weather futures are probably one of the least crazy.  FYI, all derivative and exotic securities are legitimate -- just a matter of price.  CDS? Fine.  CDOs? Yep.  Even the CDO^2 -- They're all fine as long as the price is set right.  A truly efficient market would shun some of these as they are too hard to untangle and understand what the real risks are.  However, we don't have a truly efficient market (nor a particularly free one -- but that's another discussion).
If the cash flow information is complete, the valuation can be determined with relative accuracy and precision. Assuming the monthly rent is correct, the annual revenue is $1,600 per year, $250/mo * 12 months - $1,400/year in taxes. Real estate is best valued as a perpetuity where P is the price, i is the income, and r is the rate of interest.  Theoreticians would suggest that the best available rate of interest would be the risk free rate, a 30 year Treasury rate ~3.5%, but the competition can't get these rates, so it is probably unrealistic. Anways, aassuming no expenses, the value of the property is $1,600 / 0.035 at most, $45,714.29. This is the general formula, and it should definitely be adjusted for expenses and a more realistic interest rate. Now, with a better understanding of interest rates and expenses, this will predict the most likely market value; however, it should be known that whatever interest rate is applied to the formula will be the most likely rate of return received from the investment. A Graham-Buffett value investor would suggest using a valuation no less than 15% since to a value investor, there's no point in bidding unless if the profits can be above average, ~7.5%.  With a 15% interest rate and no expenses, $1,600 / .15, is $10,666.67.  On average, it is unlikely that a bid this low will be successful; nevertheless, if multiple bids are placed using this similar methodology, by the law of small numbers, it is likely to hit the lottery on at most one bid.
The equation is the same one used for mortgage amortization.  You first want to calculate the PV (present value) for a stream of $50K payments over 20 years at a10% rate.  Then that value is the FV (future value) that you want to save for, and you are looking to solve the payment stream needed to create that future value. Good luck achieving the 10% return, and in knowing your mortality down to the exact year. Unless this is a homework assignment, which need not reflect real life.  Edit - as indicated above, the first step is to get that value in 20 years:  The image is the user-friendly entry screen for the PV calculation. It walks you though the need to enter rate as per period, therefore I enter .1/12 as the rate. The payment you desire is $50K/yr, and since it's a payment, it's a negative number. The equation in excel that results is: =PV(0.1/12,240,-50000/12,0) and the sum calculated is $431,769 Next you wish to know the payments to make to arrive at this number:  In this case, you start at zero PV with a known FV calculated above, and known rate. This solves for the payment needed to get this number, $568.59 The excel equation is: =PMT(0.1/12,240,0,431769) Most people have access to excel or a public domain spreadsheet application (e.g. Openoffice). If you are often needing to perform such calculations, a business finance calculator is recommended. TI used to make a model BA-35 finance calculator, no longer in production, still on eBay, used.  One more update- these equations whether in excel or a calculator are geared toward per period interest, i.e. when you state 10%, they assume a monthly 10/12%. With that said, you required a 20 year deposit period and 20 year withdrawal period. We know you wish to take out $4166.67 per month. The equation to calculate deposit required becomes - 4166.67/(1.00833333)^240= 568.59  HA! Exact same answer, far less work. To be clear, this works only because you required 240 deposits to produce 240 withdrawals in the future.
As has been said before, going from nothing to something is an infinite percent increase! It is not 100%. Maybe you had a dollar and now have $101 that is a 10000% increase! Quite remarkable. I often work with symmetrized percent changes like: spc = 100 * (y2-y1)/(0.5 * (y1+y2)) Where I compute the percent with respect to the average. First this is more stable as often measurements can have noise, the average is more reliable.  Second advantage is also that this is symmetric. So going from 95 to 105 is a 10 % increase while going from 105 to 95 a 10% decrease. Of course you need to explain what you show.
Two ways to solve this.  Look at the answer. If the answer says 3 months, then using ceiling for similar questions. You have to act according to the exam conventions, not according to own feelings. Whether or not the answer is reasonable and applicable in real life is out of the question.  Ask yourself, did the investment double after 14 years 2 months? i.e. FV >= 2PV. Does a person who ran 99.72 meters in a 100-meter dash counted as touching the finish line?
The author is using the simple Dietz method, (alternatively the modified Dietz), with the assumption that the net cash-flow occurs halfway through the time period.  Let's say the time period is one year for illustration, so the cash-flow would be at the end of the second quarter. The money-weighted method gives a more accurate return, but has to be solved by trial-and-error or using a computer.  The money-weighted return is 11.2718 % and the simple or modified Dietz return is 11.2676 %.  When the sums are done backwards to check, the Dietz is half a dollar out with a final value of $11,999.50 while the money-weighted return recalculates exactly $12,000. It is worth pointing out that the return changes if the cash-flow is not in the middle of the time period.  A case with the cash-flow at the end of Q3 is added to illustrate.
"It does depend, but in the effort to be efficient we usually just add back Depreciation, Amortization, and Stock Based Comp.  [Although adding back SBC is hotly debated](https://www.wallstreetprep.com/blog/stock-based-compensation-treatment-dcf-almost-always-wrong/), we usually still add it back at my firm.  Keep in mind I'm in M&amp;A, so we don't really concern ourselves with creating the ""purest"" valuation...  * EBIAT * Add Depreciation * Add Amort * Add SBC * Subtract Capex * Add the decrease in NWC * Subtract the increase in NWC * = FCFF"
This is the sum of discounted periodic payments as if we replace 1/1+i with x then this turns out to be geometric series of the form This simplifies to replacing (1/1+i) for x we get which is the present value of periodic payment in amount of $1 The future value of periodic payments in amount of $1 can be arrived at multiplying the PVIFA by (1+i)^n giving Once again the interest is compounded per annum and for intra-year compounding you would have to at first find the annual effective yield AEY to use as the effect rate is the PVIFA and FVIFA calculation for continuous compounding All the calculation discussed thus far did not take inflation into consideration, if we were to adjust the amounts for a growth of g% then the present value of a $1 would be as follow Once again you would have to use AEY if compounding frequency of interest is intra-year Now assume that each loan repayment increases or decreases by an extra amount Q per period. To find the present value of series of payments P that increase or decrease per period by an amount Q we would do the following calculations Here and All of these calculations have been available in tadXL add-in for finance and incrementally being offered as JavaScript financial functions library tadJS. Please note that the tad series of the financial functions library for various environments such as Excel, JavaScript, PHP, Ruby, Microsoft.net and others are property of the author writing this post. All of these libraries except one for Excel are available for FREE for public use. And the future value of such payments with increments may be found by multiplying the PV by (1+i)^n as follows Here"
There's no standard formula. You can compare the going rates on the market for unsecured LOCs and take that as the starting anchor. Unsecured lines of credit run in the US at about 8-18%. Your risk should be reflected in the rate, and I see no reason why the rate would change throughout the loan. As to the amount of principal changing? Just chose one of the standard compounding options - daily (most precise, but most tedious to calculate), monthly average balance, etc.
TWRR = (2012Q4 x 2013Q1 x 2013Q2) ^ (1/3) = ?? (1.1 * .809 * 1.29) ^ (1/3) = 1.047 or 4.7% return. No imaginary numbers needed.  But. Your second line there is wrong $15,750 - $15,000 - $4,000 ? The $15K already contains the $4k, why did you subtract it again?  This a homework problem?
Is my math correct? The Math is correct, however Dividends don't work this way. The Yield is Post Facto. i.e. Given the dividend that is declared every quarter, once calculates the yield. The dividends are not fixed or guaranteed. These change from Quarter to Quarter or at times they are not given at all. The yield is 3.29% and the value is $114 per share. Assuming that the price remains exactly the same for an entire year, and that I purchase only one share, then this should be the math for calculating the yield: 114 x 0.0329 = 3.7506 What the Link is showing is that last dividend of MCD was 0.94 for Q3; that means total for a year will be 0.94*4 [3.76], this means yield will be 3.29%. Note this year there were only 3 Dividend was 0.89 on 26-Feb, 0.89 on 2-Jun and 0.94 on 29-Nov. It is unlikely that there will be one more dividend this year. So for this year the correct post facto calculation would be 0.89+0.89+.94 = 2.72 and hence an yield of 2.38%  Also, are there any fees/deductions, or would I receive the amount in full, which should be $3.75? There are no fee deducted. Not sure about US tax treatment on Dividends.
Yes, the entire financial system is based on trust. As we have seen repeatedly, even the ratings agencies can be wrong and in collusion. You need to understand what products have any insurance/contingency/recourse if things don't go as planned. A lot of people were surprised when they found out SIPC didn't ensure futures when MF Global declared bankruptcy last fall.
Since nobody does this with investment returns, it's not very useful, but it can be used to compare the yield on a zero-coupon bond to the yield on a coupon bond if you treated both the same way, or to compare a coupon bond to a CD or other compound-interest-bearing account that you planned to buy into and not touch for its lifetime. The Yield to Maturity, which IS seen, is the true yield percentage of the bond in time-valued terms, assuming you buy the bond now, hold it to maturity and all coupon payments are made on time and reinvested at a similar yield. This calculation is based on the simple APY, but takes into account the fact that most of the coupon payments will be made prior to maturity; the present value of these will be higher because they happen sooner. The YTM is calculated by summing the present values of all payments based on when they'll occur; so, you'll get one $4 payment a year from now, then another $4 in two years, then $4 in 3 years, and $104 at maturity. The present value of each of those payments is calculated by flipping around the future value formula: PV = FV/(1+r)t. The present value of the entire bond (its current price) is the sum of the present value of each payment: 114.63 = 4/(1+r) + 4/(1+r)2 + 4/(1+r)3 + 104/(1+r)4. You now have to solve for r, which is difficult to isolate; the easiest way to find the rate with a computer is to ""goal seek"" (intelligently guess and check). Based on the formula above, I calculated a YTM of .314% for the first bond if you bought on Sept 7, 2012 (and thus missed the upcoming coupon payment). Buying today, you'd also be entitled to about 5 weeks' worth of the coupon payment that is due on Sept 07 2012, which is close enough to the present day that the discounted value is a rounding error, putting the YTM of the bond right at .40%.
Real-world score range: 309 to 839 (as shown on page 16 of this Transunion document) Equifax Official name: Equifax FICO Score 5 (also known as Equifax Beacon 5.0) Common name: EQ-04 Available directly to consumers: from myFICO as described here. Also available from Equifax when buying FICO score (as a one-time purchase with the ""Score Power"" product available here, or as part of credit monitoring available here). Some credit unions such as DCU provide it free each month to members. Real-world score range: 334 to 818 Experian Official name: Experian FICO Score 3 (also known as Experian FICO Risk Model v3) Common name: EX-04 Available directly to consumers: from myFICO when buying a product that includes all 19 available scores (as described here). Real-world score range: 325 to 850 (as shown on this Experian document) Transunion Official name: Transunion FICO Score 8 (also known as Transunion FICO 8 Risk Score or FICO Risk Score Classic 08) Common name: TU-08 Available directly to consumers: from myFICO as described here. Some credit card issuers such as Discover, Barclays, and Walmart provides it free each month. Real-world score range: 341 to 850 (as shown on page 15 of this Transunion document) Equifax Official name: Equifax FICO Score 8 (also known as Equifax Beacon 09) Common name: EQ-08 Available directly to consumers: from myFICO as described here. Real-world score range: 300 to 850 Experian Official name: Experian FICO Score 8 (also known as Experian FICO Risk Model v8) Common name: EX-08 Available directly to consumers: from myFICO as described here. Real-world score range: 316 to 850 (as shown on this Experian document) How FICO Score 8 differs from previous versions is explained here. In May 2014, a poster named android01 received 850 scores from all three credit agencies, as described in this post. In June 2014, a poster named fused received 850 scores from all three credit agencies, as described in this post.
It's a bit below the 10% long term S&P return, and a good round number. The Rule of 72 says 9 years to double, so, 18 years is 4X, and 36 years is 8X. For my initial calculation, I'll use 40 years. The 40th root of 10. I get 5.925% (Again the precise rate that gives 10 fold over 40 years) and multiplying this by 40, I get a ""Rule of 237"" which I'm tempted to round to 240. At 6%, 237/6= 39.5 yrs, 1.06^39.5 = 9.99 At 6%, 240/6= 40.0 yrs, 1.06^40.0 = 10.29 You can see that you lose some accuracy for the sake of a number that's easier to remember, and manipulate. 72 to double is pretty darn accurate, so I'll stick with ""Rule of 237"" to get 10X my money. To close, the purpose of these rules is to create the tool that lets you perform some otherwise tough calculations away from any electronic device. Of course I know how to use logs, and in real life I'm paid to explain them to students who are typically glad when that chapter is over. I've shown above how the ""Rule of X"" can be formulated with a power/root key, which, for most people, is simpler. Ironically, log calculations as @jkuz offered, force a continuous compounding which may not be desired at all. It would give a result of 230 for my 10X return example, and the following (using the first equation he offered) - At 6%, 230/6= 38.3 yrs, 1.06^38.3 = 9.31 which is further away from the desired 10X than my 237 or rounded 240."
"This chart concerns an option contract, not a stock. The method of analysis is to assume that the price of an option contract is normally distributed around some mean which is presumably the current price of the underlying asset. As the date of expiration of the contract gets closer the variation around the mean in the possible end price for the contract will decrease. Undoubtedly the publisher has measured typical deviations from the mean as a function of time until expiration from historical data. Based on this data, the program that computes the probability has the following inputs: (1) the mean (current asset price) (2) the time until expiration (3) the expected standard deviation based on (2) With this information the probability distribution that you see is generated (the green hump). This is a ""normal"" or Gaussian distribution. For a normal distribution the probability of a particular event is equal to the area under the curve to the right of the value line (in the example above the value chosen is 122.49). This area can be computed with the formula:  This formula is called the probability density for x, where x is the value (122.49 in the example above). Tau (T) is the reciprocal of the variance (which can be computed from the standard deviation). Mu (μ) is the mean. The main assumption such a calculation makes is that the price of the asset will not change between now and the time of expiration. Obviously that is not true in most cases because the prices of stocks and bonds constantly fluctuate. A secondary assumption is that the distribution of the option price around the mean will a normal (or Gaussian) distribution. This is obviously a crude assumption and common sense would suggest it is not the most accurate distribution. In fact, various studies have shown that the Burr Distribution is actually a more accurate model for the distribution of option contract prices."
To that last bit, I just went through the textbooks I have on hand, and this concept is not mentioned in either of the undergraduate statistics/probability textbooks I own, nor in the one undergraduate finance textbook I have. I'm in machine learning and compsci, not finance, but it is mentioned in just one of the four graduate-level texts I have on applied statistics and probability - once on one page in a textbook on Bayesian statistics. And the wikipedia page is terrible. In short, while this is an interesting little experiment and write-up, I think the analysis and conclusions are inappropriate and not supported by the evidence the authors provide. That doesn't mean that their conclusions are incorrect, just that I disagree with the notion that this paper corroborates them. ...This response ended up being way long...
I don't know of any books, but there are a lot of good white papers on the subject if you take the time to look for them. For example, Moody's has a white paper on their LGD model (LossCalc) that explains their calibration methodology.   Searching for academic papers on the subject is really the only way to go, because credit risk is a field that really is just being explored. Really only since 2006 have banks started to actively try to use a risk rating model that incorporates PD and LGD. This is because of data insufficiency - banks just didn't keep active and centralized loan level data that is required to calibrate the models.  tl;dr: Use the internet - it is your friend.
"Using the following equations from the book a stab at the correlation can be made.   Calculating the residual volatilities from equation 2.4 The correlation of stock A with stock B is 0.378 and stock B has the higher residual volatility. However, the correlation is given as a ""simple model"", which may suggest that it is an approximation.  If I have applied it correctly, some testing shows that it is only approximate. Also of interest"
I have never seen a backtest showing that prices tended to be attracted by / to revert around Fibonacci levels. The fact that many people use them doesn't mean that they can be turned into a profitable system... I have on the other hand seen many backtests showing that they don't do anything, such as the one described in this article: At least in this sample of market data, using this particularly specification for swings, we find no evidence that Fibonacci ratios are significant in the market.   Perhaps I have missed something significant, or perhaps I am merely completely wrong in my analysis, but one thing should be clear—the burden of proof should lie on the people offering arcane and complex methodologies, when simpler methods work just as well or better in the marketplace. If Fibonacci ratios are the key to the markets, where are the quantitative tests? Where’s the proof?
I don't see how anyone could give you a hard-and-fast formula, unless they know where to get some applicable statistics. Because several factors here are not a straight calculation. If you don't replace the tires but keeping driving the car, what is the increased probability that you will get into an accident because of the bald tires? How much will bald tires vs new tires affect the selling price of the car? Presumably the longer you drive the car after getting new tires, the less increase this will give to the market value of the car. What's the formula for that? If you keep the car, what's the probability that it will have other maintenance problems? Etc. That said, it's almost always cheaper to keep your current car than to buy a new one. Even if you have maintenance problems, it would have to be a huge problem to cost more than buying a new car. Suppose you buy a $25,000 car with ... what's a typical new car loan these days? maybe 5 years at 5%? So your payments would be about $470 per month. If you compare spending $1000 for new tires versus paying $470 per month on a new car loan, the tires are cheaper within 3 months. The principle is the same if you buy with cash. To justify buying a new car you have to factor in the value of the pleasure you get from a new car, the peace of mind from having something more reliable, etc, mostly intangibles.
The first thing I did when I read this was compute how many people on just those two bus lines traveled on a yearly basis. It computes to about 0.02% chance of death when traveling by bus. Which is exactly the same as what the National Safety Council says your one-year odds of dying in a car accident is (1:6500)  Can we question the safety of our cars too?