vania-janet/multiturn-rag-retrieval-data huggingface dataset:
We have log(1 billion - 20k) on the insured side, and 1%*log(999 million) + 99% * log(1 billion) on the uninsured side. The logs of each side are 21.42 vs 20.72. (Note that the base of the logarithm doesn't matter; so long as you use the same base on each side). According to Kelly, we have found a case where insurance isn't worth it. The Kelly Criterion roughly tells you ""if I took this bet every (period of time), would I be on average richer after (many repeats of this bet) than if I didn't take this bet?"" When the answer is ""no"", it implies self-insurance is more efficient than using external insurance. The answer is going to be sensitive to the profit margin of the insurance product you are buying, and the size of the asset relative to your total wealth. Now, the Kelly Criterion can easily be misapplied. Being worth financially zero in current assets can easily ignore non-financial assets (like your ability to work, or friends, or whatever). And it presumes repeat to infinity, and people tend not to live that long. But it is a good starting spot. Note that the option of bankruptcy can easily make insurance not ""worth it"" for people far poorer; this is one of the reasons why banks insist you have insurance on your proprety. You can use Kelly to calculate how much insurance you should purchase at a given profit margin for the insurance company given your net worth and the risk involved. This can be used in Finance to work out how much you should hedge your bets in an investment as well; in effect, it quantifies how having money makes it easier to make money."
I would use neither method.  Taking a short example first, with just three compounding periods, with interest rate 10%.  The start value y0 is 1. So after three years the value is 1.331, the same as y0 (1 + 0.1)^3. Depreciating (like inflation) by 10% (to demonstrate) gets us back to y0 = 1 Appreciating and depreciating by 10% cancels out: Appreciating by 10% interest and depreciating by 3% inflation: This is the same as y0 (1 + 0.1)^3 (1 + 0.03)^-3 = 1.21805 So for 50 years the result is y0 (1 + 0.1)^50 (1 + 0.03)^-50 = 26.7777 Note You can of course use subtraction but the not using the inflation figure directly.  E.g. (edit: This appears to be the Fisher equation.) 2nd Note Further to comments, here is a chart to illustrate how much the relative performance improves when inflation is accounted for.  The first fund's return is 6% and the second fund's return varies from 3% to 6%.  Inflation is 3%.
Agree with the above poster regarding causation vs. correlation. Unless you can separate out the variables questions like this are somewhat impossible to answer.  Additionally, one of the fundamental issues is the Agency Problem. Depending on the fee structure the advisor might be more interested in their own self benefit then yours.
My thinking is that since the last time a drop like that happened was back in the early 1930's, calling a drop of that magnitude, even if off by 2 years, is still an impressive feat. That's equivalent today to calling the SP500 to be under 400 by a certain date. Sheer insanity to make that kind of call.   Not saying either of us is correct, I think we just have different perspectives on accuracy.
"Johnny.  I recently bought my first home as well, and I have worked in the credit business (not mortgage), so I think I can answer some of your questions.  Disclaimer first that I'm in NY, and home buying does vary from state to state. In my experience, pre-qual is not too different from pre-approval.  Neither represents any real committment on the part of the bank (i.e. they can still deny approval at any point), and both are based on pulling your credit bureau and calculating ratios based on your stated (probably not documented) financial information.  It's theoretically possible that a seller would choose a pre-approved buyer over a pre-qualified buyer, all other things being equal, but all other things are seldom equal. Remember also that you don't need to ultimately get a mortgage from the same bank that you use for the pre-qual.  The pre-qual just shows that you are probably credit-worthy and serves to give you some credibility with sellers.  Once you have an accepted offer and need to find a real mortgage, you can shop around for the best rate and best loan structure.  Banks don't need to have pulled your credit to quote rates, but they will need to have a general idea of your FICO range.  Once you find the bank you like with the best rate and actually apply for the loan, they will pull a hard bureau, and if your scores are different from what you said before, the rate may change, but within the same range, you'll generally be ok.  Also, banks do not necessarily pull all 3 bureaus; they may only pull 1, as it costs them for each pull. 2 potential downsides to this approach: Also, make sure you have a mortgage/funding clause in your contract, as banks are unpredictable, and make sure you have a great real estate lawyer, not a legal ""factory"" - the extra few hundred $ are worth it. Don't overthink this credit stuff too much.  Find a good house for a good price, and get a no-nonsense mortgage that you fully understand - no exotic stuff.  Good luck!"
Although I understand the gut reaction to feel that way, I disagree that women with ovarian cancer can't prove it was the talc.  The plaintiffs in these cases have accused Johnson and Johnson of deliberately covering up their own research showing a connection between repeated use of talc and an increase in ovarian cancer rates and the massive punitive damages awards in this recent case suggests the jury believed there was a cover up.  This recent study suggested a 33% increased risk.  https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4820665/#!po=79.8387.  Very much like the tobacco lawsuits, the crime is in the coverup.  Tobacco companies knew cigarettes were linked to cancer and promised its customers they were completely safe.  They simply needed to warn consumers once they knew this risk existed.  Instead buried their own research demonstrating the risk under the rug in the name of profits.  The jury in this recent case believed Johnson and Johnson did the same
This is crude and inaccurate because in one year, the bond will be a year closer to maturity and will return one less coupon payment; therefore at the same rate of return the present value of the remaining payout of the bond will only be $110.99 (which makes a lot of sense if you think about it; the bond will only pay out $112 if you bought it a year from now, so why would you pay $114 for it?). Another measure, not seen in the list, is the ""simple APY"". Quite simply, it is the yield that will be realized from all cash flows from the bond (all coupon payments plus the face value of the bond), as if all those cash flows happened at maturity. This is calculated using the future value formula: FV = PV (1+r/n)nt, where FV is the future value (the sum of the face value and all coupon payments to be made before maturity), PV is present value (the current purchase price), r is the annual rate (which we're solving for), n is the number of times interest accrues and/or is paid (for an annual coupon that's 1), and t is the number of years to maturity. For the first bond in the list, the simple APY is 0.2974%. This is the effective compound interest rate you would realize if you bought the bond and then took all the returns and stuffed them in a mattress until maturity. 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.
"Well it depends. I doubt the professor is looking for the ""basic"" answer as you described it. He's mostly likely looking for the above answers (i.e. the Rf is used to value a call in the B-S model).   Like in all classes, you need to know what the prof is really looking for, because many questions can be interpreted many different ways and unfortunately most teachers aren't clear in asking what they want."
"Given the exact formula that goes into the 'Fair Issac"" calculation is a closely guarded trade secret, AND that each agency has their own formula, I'm not sure there's really any 100% for sure authoritative answer to the question in terms of which option would be best.  There are a lot of balancing factors, like how long you've had accounts, payment history over time, etc.  Stuff that is known to HURT a score can include things like closing a longstanding account.   If you have a very low interest loan (like some car companies offer now and then) I'd just make the normal payments.  If you have something at a higher interest rate, especially above 6-7%, then I'd worry less about credit score and more about how much I'm going to pay in interest and pay it off as rapidly as I could. The big key is 'never pay late' more than anything else,  Followed by how much of your debt capacity is used (which paying down any account, loan or credit card, will help), and long standing relationships (length of history)  See this (approximate) chart and notice that any early payoff is basically going lower your 'capacity used', possibly reduce the types of credit used (if it's the last loan of that type), all of which should help your score."
I took it in my Junior year and scored 99th percentile. Two years later, I've had dozens of resume requests without any results. Personally, now that you can take it multiple times and from anywhere, I think it has lost any value it may have provided.
It would be difficult, but it's a statistical task, and you'd need to refer to a competent statistician to really get a sense of what sort of certainty could be derived from the available data.  I believe that you'd start by looking over your state-by-state data on a granular level to try to find if there was any persistent correlation between Amazon's market penetration in a particular area and employment data from the retail industry.  With regards to Ma &amp; Pa's complaint, you're sort of wrong and sort of right.  Obviously they have no direct knowledge that online retail was responsible for the decline in sales that they saw.  In terms of sustainability and mismanagement, however, they can show you their books.  If the business had been established from some time it would be easy to see whether it had indeed been a sustainable business model in prior years.  Sustainability and mismanagement, however, are Scotsmen when it comes to reasoning about causes.  In measuring the effect of Amazon's entry into the market on local businesses, we can just as easily use a model that assumes a perfect market, that inefficiencies on the part of Ma^1 &amp; Pa^1 would lead them to be displaced by Ma^2 &amp; Pa^2, and that on average Ma^x &amp; Pa^x manage their business sufficiently well to extract an optimal return on effort.    If circumstances are such that the role of vendor is not fungible, and the supply of Mas and Pas does not respond to the demand for family stores, then I don't actually know how to do the math, but on the other hand I do recognize a smoking gun.
Edit 2 OK, so I've had a look at what JoeTaxpayer is saying in the comments below, and now I agree: The CAGR should be 4%. Where I want wrong was to assume that the $50 per month payments over the five years are worth $50 * 5 * 12 = $3000. This neglects the ""time value of money"" --- having small amounts of money periodically, rather than all of it in a lump sum. Including this makes the ""effective"" value of the monthly $50 payments $2714.95 written as =PV(0.04/12,60,-50) in Excel or Google Docs. I've added a tab to the original spreadsheet to show the different calculations. Note that it still doesn't quite come to 4%, but I guess it's a minor error in the sheet. NB: I know, I'm leaving out mortgage interest tax relief, costs for selling etc. etc."
"The Dividend Discount Model is based on the concept that the present value of a stock is the sum of all future dividends, discounted back to the present. Since you said: dividends are expected to grow at a constant rate in perpetuity ... the Gordon Growth Model is a simple variant of the DDM, tailored for a firm in ""steady state"" mode, with dividends growing at a rate that can be sustained forever. Consider McCormick (MKC), who's last dividend was 31 cents, or $1.24 annualized. The dividend has been growing just a little over 7% annually. Let's use a discount, or hurdle rate of 10%. MKC closed today at $50.32, for what it's worth. The model is extremely sensitive to inputs. As g approaches r, the stock price rises to infinity. If g > r, stock goes negative. Be conservative with 'g' -- it must be sustainable forever.  The next step up in complexity is the two-stage DDM, where the company is expected to grow at a higher, unsustainable rate in the early years (stage 1), and then settling down to the terminal rate for stage 2. Stage 1 is the present value of dividends during the high growth period. Stage 2 is the Gordon Model, starting at the end of stage 1, and discounting back to the present. Consider Abbott Labs (ABT). The current annual dividend is $1.92, the current dividend growth rate is 12%, and let's say that continues for ten years (n), after which point the growth rate is 5% in perpetuity. Again, the discount rate is 10%. Stage 1 is calculated as follows: Stage 2 is GGM, using not today's dividend, but the 11th year's dividend, since stage 1 covered the first ten years. 'gn' is the terminal growth, 5% in our case. then... The value of the stock today is 21.22 + 51.50 = 72.72 ABT closed today at $56.72, for what it's worth."
I would like to know how they calculated such monthly payment The formula is:  Your values would come out to be: r = (1+3.06/(100*365))^31-1=0.002602 (converting your annual percentage to a monthly rate equivalent of daily compounded interest) PV = 12865.57 n = 48 Inserting your values into the formula: P = [r*(PV)]/[1-(1+r)^(-n)] P = [0.002602*(12865.57)]/[1-(1.002602)^(-48)] P = 285.47
The Finance functions in spreadsheet software will calculate this for you.  The basic functions are for Rate, Payment, PV (present value), FV (Future value), and NPER, the number of periods.  The single calculation faces a couple issues, dealing with inflation, and with a changing deposit. If you plan to save for 30 years, and today are saving $500/mo, for example, in ten years I hope the deposits have risen as well. I suggest you use a spreadsheet, a full sheet, to let you adjust for this.  Last, there's a strange effect that happens. Precision without accuracy. See the results for 30-40 years of compounding today's deposit given a return of 6%, 7%, up to 10% or so. Your forecast will be as weak as the variable with the greatest range. And there's more than one, return, inflation, percent you'll increase deposits, all unknown, and really unknowable.  The best advice I can offer is to save till it hurts, plan for the return to be at the lower end of the range, and every so often, re-evaluate where you stand. Better to turn 40, and see you are on track to retire early, than to plan on too high a return, and at 60 realize you missed it, badly.  As far as the spreadsheet goes, this is for the Google Sheets -  Type this into a cell =nper(0.01,-100,0,1000,0) It represents 1% interest per month, a payment (deposit) of $100, a starting value of $0, a goal of $1000, and interest added at month end. For whatever reason, a starting balance must be entered as a negative number, for example - =nper(0.01,-100,-500,1000,0) Will return 4.675, the number of months to get you from $500 to $1000 with a $100/mo deposit and 1%/mo return. Someone smarter than I (Chris Degnen comes to mind) can explain why the starting balance needs to be entered this way. But it does show the correct result. As confirmed by my TI BA-35 financial calculator, which doesn't need $500 to be negative.
well there are many papers on power spot price prediction, for example. It depends on what level of methodology you would like to use. Linear regression is one of the basic steps, then you can continue with more advanced options. I'm a phd student studying modelling the energy price (electricity, gas, oil) as stochastic process. Regarding to your questions: 1. mildly speaking, it's really hard, due to its random nature! (http://www.dataversity.net/is-there-such-a-thing-as-predictive-analytics/)  2. well, i would ask what kind of measure of success you mean? what level of predicted interval one could find successful enough? 3. would you like me to send you some of the math-based papers on? 4. as i know, the method is to fully capture all main characteristics of the price. If it's daily power price, then these are mean-reversion effect, high volatility, spike, seasonality (weekly, monthly, yearly).  Would you tell me what kind of method you're using? Maybe we can discuss some shared ideas? Anna
(In theory, a series of one-month options would be higher time value, but there are frictional costs, and no guarantee that today's ""good deal"" will be repeatable twelve time per year.) When comparing various strikes and expirations, compare time value per day. To compare the same statistic across multiple companies, use time value per day as a percent of capital at risk. CaR is the price of the stock less the premium received. If you already own the stock, track it as if you just bought it for this strategy, so use the price on the day you wrote the call. Along with time value per day, compare the simple annualized percent return, again, on capital at risk, measuring the return if a) the stock is called away, and b) the stock remains unchanged. I usually concentrate more on the second scenario, as we get the capital gain on the stock regardless, without the option strategy. Ideally, you can also calculate the probability (based on implied volatility) of the stock achieving these price points by expiration. Measuring returns at many possible stock prices, you can develop an overall expected return. I won't go into further detail, as it seems outside the scope here. Finally, I usually target a minimum of 25% annualized if the stock remains unchanged. You can, of course, adjust this up or down depending on your risk tolerance. I consider this to be conservative."
"I think you're on the wrong track. Getting more and more samples from the real world does not make your backtest more accurate, it just confirms that your strategy can withstand one particular sample path of a stochastic process. The reason why you find it simple to incorporate fees, commissions, taxes, etc. is because they're a static and constant process -- well they might change over time but most definitely uncorrelated to the markets. Modelling overnight returns or the top levels of the order book the next day is serious work. First you have to select a suitable model (that's mostly theoretical work but experience can help a lot). Then, in order to do it data-driven, you'd have to plough through thousands of days of sample data on a set of thousands of instruments to get a ""feeling"" (aka significant model parameters). Apropos data mining, I think Excel might be the wrong tool for the job. Level-2 data (even just the first 10 levels) is a massive blob. For example, the NYSE OpenBook historical data weighs in at a massive 15 TB compressed (uncompressed 74 TB) for the last 10 years, and costs USD 200k. Anyway, as for other factors to take into account: So how to account for all this in a backtest? Personally, I would put in some penalty terms (as % on a return basis) for every factor you want to consider, don't hardcode them. You can then run a stress test by exploring these parameters (i.e. assign some values in the range of 0 to whatever fits). Explore them individually (only set one penalty term at a time) to get a feeling how the strategy might react to stress from that factor. Then you can run the backtest with typical (or observed) combinations of penalty factors and slowly stress them altogether. Edit Just to avoid confusion about terminology. A backtest in the strict sense (had I implemented this strategy X years ago, what would have happened?) won't benefit from any modelling simply because the real-world ""does the sampling"" for us. However, to evaluate a strategy's robustness you should account for the additional factors and run some stress tests.
Ditto Bill and I upvoted his answer. But let me add a bit. If everyone knew exactly what the risk was for every investment, then prices would be bid up or down until every stock (or bond or derivative or whatever) was valued at exactly risk times potential profit. (Or more precisely, integral of risk times potential profit.) If company A was 100% guaranteed to make $1 million profit this year, while company B had 50% change to make a $2 million profit and 50% to make $0, and every investor in the world knew that, then I'd expect the total price of all shares of the two stocks to stabilize at the same value. The catch to that, though, is that no one really knows the risk. The risk isn't like, we're going to roll a die and if it comes up even the company makes $1 million and if it comes up odd the company makes $0, so we could calculate the exact probability. The risk comes from lack of information. Will consumers want to buy this new product? How many? What are they willing to pay? How capable is the new CEO? Etc. It's very hard to calculate probabilities on these things. How can you precisely calculate the probability that unforeseen events will occur? So in real life prices are muddled. The risk/reward ratio should be roughly sort of approximately linear, but that's about the most one can say.
"The worth of a credit score (CS) is variable.  If you buy your stuff outright with 100% down then your CS is worthless. If you take a loan to buy stuff then it is worth exactly what you save in interest versus a poor score. But there is also the ""access"" benefit of CS where loans will no longer be available to you, forcing you to rent. If you consider rent as money down teh tiolet then this could factor in. The formula for CS worth is different for everyone. Bill Gates CS is worth zero to him. Walking away from a mortage is not the same as walking away from a loan.  A mortage has collateral. There are 2 objects: the money, and the house. If you walk away the bank gets the house as a fair trade. They keep all money you put against the house to boot! Sometimes the bank PROFITS when you walk away.  So in a good market you could consider walking away to be the Moral Michael thing to do. :)"
http://www.calcamo.net/loancalculator/simulation/fixed-rate-loan.php5 This website is a calculator only and has some extra features that take into account late payments, paying extra to reduce principal, and has the ability to export amortization table to excel that you could use to keep track of the loan.   If you are looking for a web site to manage and keep track of the whole process, reminder emails, accepting credit card payments, etc.. paybaq.com may be right for you.
That might be a generational difference. For us, as long as we know where to find the equations, what's the point in knowing a formula if you're not using it on a regular basis. It's much more prudent to know where to find the formulas you might need in the future or where to find the methods to derive them, and have the ability to do this as opposed to remembering the steps or the formulas by rote. The information is usually seconds away, the skills are not.