query: Why do stocks split?

positive: Stock splits are typically done to increase the liquidity of stock merely by converting every stock of the company into multiple stocks of lower face value. For example, if the initial face value of the stock was $10 and the stock got split 10:1, the new face value of the stock would be $1 each. This has a proportional effect on the market value of the stock also. If the stock was trading at $50, after the split the stock should ideally adjust to $5. This is to ensure that despite the stock split, the market capitalization of the company should remain the same. Number of Shares * Stock Price = Market Capitalization = CONSTANT

negative: "There's no need for an index to have a currency as its purpose is not to act as an asset but rather to signal investors about the performance of a collection of stocks. An index can be price-weighted, meaning that its value equals the (arithmetic) average of the prices of each stock in the index. With no stock splits, the return on this index is the same as the return on a portfolio composed of one share of each stock. If there is a stock split, however instead of dividing by the number of stocks, as you normally would when taking the arithmetic average, you divide it by the number that will make the value of the index pre-stock-split (arithmetic average) equal to the value post stock split. Then use that dividing number for all periods until a new stock split occurs.  An index can be value-weighted, meaning that its changes in value track the percentage changes in total market capitalization of the stocks in the index. Price weighted indexes ignore for ""firm size"" and percentage changes in price weighted indexes are not robust to stock-splits. Value weighted indexes take ""firm size"" into account and are robust to stock-splits. DJIA is price-weighted. S&P 500 is value-weighted."

negative: You can argue that cash dividend is a kind of split as well by this logic. The stock price on ex-dividend gets a hit coincidental with the dividend to be paid, so one can argue that the investor has the same cash value on the day the dividend was paid as if it wouldn't be paid at all. However, for the company to distribute stocks instead of cash may be advantageous if they have low cash reserves but significant amount of treasury stocks, and the stocks are of high liquidity.  It is also a way for the company to release treasury stocks without diluting the current shareholders and creating taxable income to the company, that's an important factor to consider. This is in fact the real answer to your question. The main difference between split and stock dividend is that in split, the stock distributions proportions don't change. With stock dividend - they do. While the outstanding share proportions do not change, total proportions do, because of the treasury stocks being distributed. So company has less stocks in its vaults, but everyone else still has the same proportions of ownership. Compare this to split: company's treasury stocks would be split as well, and it would continue essentially sitting on the same proportion of stocks. That shift of treasury stocks to the outside shareholders - this is what makes it a dividend.

negative: During a stock split the only thing that changes is the number of shares outstanding.  Typically a stock splits to lower its price per share.  Sometimes if a company's value is falling it will do a reverse split where X shares will be exchanged for Y shares.  This is typically done to avoid being de-listed from an exchange if the price per share falls below a certain threshold, usually $1.  Again the only thing changing is the number of shares outstanding.  A 20 for 1 reverse split means for every 20 shares outstanding the shareholder will be granted one new share. Example X Co. has 1,000,000 shares outstanding for a price of $100 per share.  It does a 1 for 10 split.  Now there are 10,000,000 shares outstanding for a price of $10 per share. Example Y Co has 1,000,000 shares outstanding for a price of $1 per share.  It does a 10 for 1 reverse split.  Now there are 100,000 shares outstanding for a price of $10. Quickly looking at the news for ASTI it looks like it underwent a 20 for 1 reverse split.  You should probably look at your statements and ask your broker how the arithmetic worked in your case. Investopedia links for Reverse Stock Split and Stock Split

negative: Companies do both quite often.  They have opposite effects on the share price, but not on the total value to the shareholders.  Doing both causes value to shareholders to rise (ie, any un-bought back shares now own a larger percentage of the company and are worth more) and drops the per-share price (so it is easier to buy a share of the stock).  To some that's irrelevant, but some might want a share of an otherwise-expensive stock without paying $700 for it. As a specific example of this, Apple (APPL) split its stock in 2014 and also continued a significant buyback program: Apple announces $17B repurchase program, Oct 2014 Apple stock splits 7-to-1 in June 2014. This led to their stock in total being worth more, but costing substantially less per share.

negative: Do you realise that the examples you have given are for stock splits not for dividends, that is why the date payable is before the ex-date for the split. The payments for the split occur on 30th June and the first day the stock trades with the new split is on the next trading day, being the ex-date, 1st July.

negative: "I don't have anything definitive, but in general positions in a company are not affected materially by what is called a corporate action. ""Corp Actions"" can really be anything that affects the details of a stock. Common examples are a ticker change, or exchange change, IPO (ie a new ticker), doing a split, or merging with another ticker. All of these events do not change the total value of people's positions. If a stock splits, you might have more shares, but they are worth less per share. A merger is quite similar to a split. The old company's stock is converted two the new companies stock at some ratio (ie 10 shares become 1 share) and then converted 1-to-1 to the new symbol. Shorting a stock that splits is no different. You shorted 10 shares, but after the split those are now 100 shares, when you exit the position you have to deliver back 100 ""new"" shares, though dollar-for-dollar they are the same total value. I don't see why a merger would affect your short position. The only difference is you are now shorting a different company, so when you exit the position you'll have to deliver shares of the new company back to the brokerage where you ""borrowed"" the shares you shorted."

negative: Assuming you plan to buy a whole number of shares and have a maximum dollar value you intend to invest, it may be better to wait for the split if the figures don't quite work out nicely. For example, if you are going to invest $1,000 and the stock pre-split is $400 and the split is 2 for 1, then you'd buy 2 shares before the split unless you have an extra $200 to add. Meanwhile, after the split you could buy 5 shares at $200 so that you invest all that you intend. Aside from that case, it doesn't really make a difference since the split is similar to getting 2 nickels for a dime which in each case is still a total value of 10 cents.

negative: Are you sure you're not just looking at prices that are adjusted for the split, e.g. Yahoo? For example, Gilead Sciences (GILD) split a few months ago, but if you look at a price chart, there isn't an interruption even though the split is clearly marked. (Look in the past six months; it split in January). However, you could also simply be watching companies that happen to not split, for a variety of reasons. This isn't a criticism, but rather just a consequence of whatever stocks you happen to be watching.  However, a quick search for information on stock splits yields a few articles (mainly from the Motley Fool) that argue that fewer companies are performing stock splits in recent years; the articles mainly talk about tech companies, and they make the argument that even though the shares in Google and Apple have a high stock price: Google and Apple aren't all that expensive by traditional valuation   metrics. Google trades at just 15 times next year's projected   profitability. Apple fetches a mere 13 times fiscal 2012's bottom-line estimates. These articles are a bit dated in terms of the stock prices, but the rationale is probably still good. Similar logic could apply for other companies; for example, since May 2009, Panera's stock price has climbed by almost a factor of 4 without splitting. The articles also make the point that stock splits were traditionally seen as bullish signs because: Companies splitting to bring their share prices back down to more   accessible levels were optimistic in building those sand castles back   up. One could make a fair argument that the overall economic climate isn't as bullish as it used to be, although I would only be convinced that this was affecting stock splits if data could be gathered and tested. A stock split can also raise the price of a stock because if small investors feel the stock is suddenly more accessible to them, they purchase more of it and might therefore drive up the price. (See the Investopedia article on stock splits for more information). Companies might not see the necessity in doing this because their stock price isn't high enough to warrant a split or because the price isn't high enough to outprice smaller investors.  One interesting point to make, however, is that even though stock splits can drive small investors to buy more of the stock, this isn't always a gain for the company because professional investors (firms, institutions, etc.) have a tendency to sell after a split. The paper is a bit old, but it's still a very neat read. It's possible that more and more companies no longer see any advantage to splitting because it might not affect their stock price in the long run, and arguably could even hurt it. Considering that large/professional investors likely hold a higher percentage of a company's shares than smaller investors, if a stock split triggers a wave of selling by the former, the increasing propensity to buy of the latter may not be enough to offset the decline in price.  Note: My answer only refers to standard stock splits; the reasons above may not apply to a decrease in the number of reverse stock splits (which may not be a phenomenon; I don't know).

negative: You'd likely be subject to a lock-up period before you could sell the shares along with possibly having other rules about how you could sell your shares as you'd likely be seen as an insider that may have information that gives you an unfair advantage for selling the stock possibly. Depending on how far in advance you hold the shares, you may or may not have adjustments in the valuation and number of shares as some companies may do a split or reverse split when preparing for an IPO. A company I worked for in the late 1990s had an IPO and my stock options had a revised strike price because of a reverse stock split that was done prior to the IPO.

negative: "Ordinarily a stock split increases all shareholders' share counts, so that there is no change in anybody's voting power.  For example, if you owned 1% of the company before the split, after the split you now have twice as many shares, but there are now twice as many shares outstanding, so you still own 1% of the company.  Also, stock splits are not ordinarily ""triggered"".  Usually they happen when the board decides that for one reason or another it's desirable to increase the number of shares in circulation, which causes the price of each share to decrease proportionally.   I'm not familiar with the show, and in particular I don't know what the action is that the character being addressed is thinking of taking, but it sounds like they are describing something akin to a ""poison pill"".  In these arrangements, the ""pill"" is triggered by some predefined condition, say a party acquiring shares in excess of a defined threshold.  What typically happens is that shareholders other than the ones who triggered the pill get a chance to buy shares at a substantial discount, thereby diluting the shares of the party that triggered it.  Because the other shareholders have to buy their additional shares, albeit at a discount, and because it applies only to certain shares, it's not really a split, but it's close enough that the writers of the show may have felt it was worth using the term that is more familiar to the public."

negative: There has been a lot of research on the effects of stock splits. Some studies have concluded that: However note that (i) these are averages over large samples and does not say it will work on every split and (ii) most of the research is a bit dated and more recent papers have often struggled to find any significant performance impact after 1990, possibly because the effect has been well documented and the arbitrage no longer exists. This document summarises the existing research on the subject although it seems to miss some of the more recent papers. More practically, if you pay a commission per share, you will pay more commissions after the split than before. Bottom line: don't overthink it and focus on other criteria to decide when/whether to invest.

negative: This IS a stock split. http://en.wikipedia.org/wiki/Stock_split Ratios of 2-for-1, 3-for-1, and 3-for-2 splits are the most common, but any ratio is possible. Splits of 4-for-3, 5-for-2, and 5-for-4 are used, though less frequently. Investors will sometimes receive cash payments in lieu of fractional shares.

negative: Fully paid up Shares issued in which no more money is required to be paid to the company by shareholders on the value of the shares. When a company issues shares upon incorporation or through an issuance, either initial or secondary, shareholders are required to pay a set amount for those shares. Once the company has received the full amount from shareholders, the shares become fully paid shares.  authorised share capital The number of stock units that a publicly traded company can issue as stated in its articles of incorporation, or as agreed upon by shareholder vote. Authorized share capital is often not fully used by management in order to leave room for future issuance of additional stock in case the company needs to raise capital quickly. Another reason to keep shares in the company treasury is to retain a controlling interest in the company. If so, why not just give the existing shareholders the $500 million, (and do a stock split if desired)? Stock splits, bonus issues doesn't generate any capital for the firm, which it required.

negative: Scrip dividends are similar to stock splits. With a stock split, 100 shares can turn into 200 shares; with scrip dividends they might turn into 105 shares.

negative: No, I think you are misunderstanding the Math. Stock splits are a way to control relatively where the price per share can be for a company as companies can split or reverse split shares which would be similar to taking dimes and giving 2 nickels for each dime, each is 10 cents but the number of coins has varied. This doesn't create any additional value since it is still 10 cents whether it is 1 dime or 2 nickels.  Share repurchase programs though are done to prevent dilution as executives and those with incentive-stock options may get shares in the company that increase the number of outstanding shares that would be something to note.

negative: Simple: Do a stock split. Each 1 Ordinary share now = 100 Ordinary shares (or 100,000 or whatever you choose). Then sell 20 (or 20,000) of them to your third party. (Stock splits are fairly routine occurrence. Apple for example has done several, most recently in 2014 when 1 share = 7 shares). Alternatively you could go the route of creating a new share class with different rights, preferences etc. But this is more complicated.

negative: Imagine that I own 10% of a company, and yesterday my portion was valued at $1 Million, therefore the company is valued at $10 Million.  Today the company accepts an offer to sell 1% of the company for $500 Thousand: now my portion is worth $5 Million, and company is worth $50 Million. The latest stock price sets the value of the company. If next week the news is all bad and the new investor sells their shares to somebody else for pennies on the dollar, the value of the company will drop accordingly.

negative: "I bought 1000 shares of Apple, when it was $5. And yet, while the purchase was smart, the sales were the dumbest of my life.  ""You can't go wrong taking a profit"" ""When a stock doubles sell half and let it ride"", etc.  It doubled, I sold half, a $5000 gain. Then it split, and kept going up. Long story short, I took gains of just under $50,000 as it rose, and had 100 shares left for the 7 to 1 split.  The 700 shares are worth $79,000. But, if I simply let it ride, 1000 shares split to 14,000. $1.4M. I suppose turning $5,000 into $130K is cause for celebration, but it will stay with me as the lost $1.3M opportunity.  Look at the chart and tell me the value of selling stocks at their 52 week high. Yet, if you chart stocks heading into the dotcom bubble, you'll see a history of $100 stocks crashing to single digits. But none of them sported a P/E of 12."

negative: "The share price on its own has little relevance without looking at variations. In your case, if the stock went from 2.80 to 0.33, you should care only about the 88% drop in value, not what it means in pre-split dollar values. You are correct that you can ""un-split"" to give you an idea of what would have been the dollar value but that should not give you any more information than the variation of 88% would. As for your title question, you should read the chart as if no split occurred as for most intents and purposes it should not affect stock price other than the obvious split."

negative: "If I held stock in these companies yesterday, would I have profited by these gains? No.  For DZSI, your 5 shares at $1.10 would now be 1 share at $5.50, so you would have the same total amount.  For SGY, they closed at $6.95, and opened at $32.80, so your five shares at $6.95 would now be one share at $32.80, so you would have actually lost money (not purely because of the split, but because the ""new"" shares are trading lower then the expected 1:5 split price).  A split in general does not affect market cap (how much your total shares are worth) but there may be residual effects that cause the market value to fluctuate after a split that affect the price."

negative: I'm guessing you're conflating bonus share issuance with stock split.  That seems very common to me, from a quick search; there's even some issues of terminology between the US and Europe, I think - it seems some Europeans may use Bonus Shares to mean Stock Split, as opposed to the more common meaning in the US of Stock Dividend. Sometimes a bonus share issuance is (incorrectly) called a stock split, like in this public announcement from STADA in 2004.  It is a 1:1 bonus share issuance (meaning they issue one bonus share to everyone who has one share now), but it is in essence the same thing as a stock split (a 2:1 stock split, namely).  They combined the 1:1 from bonus share with the wording 'split', causing the confusion. Bonus share issuance, also known as a stock dividend, is covered well in this question/answer on this site, or from a search online.  It has no obvious effect initially - both involve doubling shares out there and halving the price - but it has a substantially different treatment in terms of accounting, both to the company and to your tax accountant.

negative: so newscorp is split into two classes of stock, A and B with B having voting power and A non voting. This gives the Murdoch family quite some power however their voting power is 40%, why didnt they make it 50%+1 so they could have full un opposed control of the business?

negative: Calculation. To calculate the DJIA, the sum of the prices of all 30 stocks is divided by a divisor, the Dow Divisor. The divisor is adjusted in case of stock splits, spinoffs or similar structural changes, to ensure that such events do not in themselves alter the numerical value of the DJIA.

negative: "Fama-French would be a couple of names if you want to look at this from a value/growth dichotomy.  A simplified form of this was to take the stocks with a lower Price/Book Value that would be the value stocks while the others would be the growth.  The principle is that some of the beaten-down stocks will appreciate more than the growth stocks will.  6 Ways To Improve Your Portfolio Returns Today also makes note of the ""growth vs value"" split if you want another reference that way.  Historically, growth has been more volatile and produced lower returns, though past performance isn't necessarily always going to hold as some people like to invest in what is known as a ""slice & dice"" portfolio where a portion in invested in each of 4 corners: Large-growth, large-value, small-growth, and small-value.  Some may add in bonds, REITs, and foreign stocks but the idea is that in different years, different parts of the market will do better and this is a way to capture that in a sense."

negative: Aside from the market implications Victor and JB King mention, another possible reason is the dividends they pay. Usually, the dividends a company pays are dependent on the profit the company made. if a company makes less profit, the dividends turn out smaller. This might incite unrest among the shareholders, because this means that they get paid less dividends, which makes that share more likely to be sold, and thus for the price to fall.

negative: I do not fully understand the transactions involved, but it appears that there was a reverse stock split (20:1) and some legal status change as well on June 29th. This seems to be the cause for the change in valuation of the stock as the dates match the drop. https://www.otcmarkets.com/stock/RMSLD/filings

negative: Perhaps someone has an investment objective different than following the market. If one is investing in stocks with an intent on getting dividend income then there may be other options that make more sense than owning the whole market. Secondly, there is Slice and Dice where one may try to find a more optimal investment idea by using a combination of indices and so one may choose to invest 25% into each of large-cap value, large-cap growth, small-cap value and small-cap growth with an intent to pick up benefits that have been seen since 1927 looking at Fama and French's work.

negative: "Stock has value to the buyer even if it does not currently pay dividends, since it is part ownership of the company (and the company's assets). The owners (of which you are now a part) hire managers to make a ""dividend policy decision.""  If the company can reinvest the profits into a project that would earn more than the ""minimum acceptable rate of return,"" then they should do so. If the company has no internal investment opportunities at or above this desired rate, then the company has an obligation to declare a dividend.  Paying out a dividend returns this portion of profit to the owners, who can then invest their money elsewhere and earn more. For example: The stock market currently has, say, a 5% rate of return. Company A has a $1M profit and can invest it in a project with an expected 10% rate of return, so they should do so. Company B has a $1M profit, but their best internal project only has an expected 2% rate of return.  It is in the owners' best interest to receive their portion of their company's profit as a dividend and re-invest it in other stocks. (Others have pointed out the tax deferrment portion of dividend policy, so I skipped that)"

negative: "The Dow Jones Industrial Average (DJIA) is a Price-weighted index.  That means that the index is calculated by adding up the prices of the constituent stocks and dividing by a constant, the ""Dow divisor"".  (The value of the Dow divisor is adjusted from time to time to maintain continuity when there are splits or changes in the roster.)  This has the curious effect of giving a member of the index influence proportional to its share price.  That is, if a stock costing $100 per share goes up by 1%, that will change the index by 10 times as much as if a stock costing $10 per share goes up by the same 1%. Now look at the price of Google.  It's currently trading at just a whisker under $700 per share.  Most of the other stocks in the index trade somewhere between $30 and $150, so if Google were included in the index it would contribute between 5 and 20 times the weight of any other stock in the index.  That means that relatively small blips in Google's price would completely dominate the index on any given day.  Until June of 2014, Apple was in the same boat, with its stock trading at about $700 per share.  At that time, Apple split its stock 7:1, and after that its stock price was a little under $100 per share.  So, post-split Apple might be a candidate to be included in the Dow the next time they change up the components of the index.  Since the Dow is fixed at 30 stocks, and since they try to keep a balance between different sectors, this probably wouldn't happen until they drop another technology company from the lineup for some reason.  (Correction: Apple is in the DJIA and has been for a little over a year now.  Mea culpa.) The Dow's price-weighting is unusual as stock indices go.  Most indices are weighted by market capitalization.  That means the influence of a single company is proportional to its total value.  This causes large companies like Apple to have a lot of influence on those indices, but since market capitalization isn't as arbitrary as stock price, most people see that as ok.  Also, notice that I said ""company"" and not ""stock"".  When a company has multiple classes of share (as Google does), market-cap-weighted indices include all of the share classes, while the Dow has no provision for such situations, which is another, albeit less important, reason why Google isn't in the Dow.  (Keep this in mind the next time someone offers you a bar bet on how many stocks are in the S&P 500.  The answer is (currently) 505!) Finally, you might be wondering why the Dow uses such an odd weighting in its calculations.  The answer is that the Dow averages go back to 1896, when Charles Dow used to calculate the averages by hand.  If your only tools are a pencil and paper, then a price-weighted index with only 30 stocks in it is a lot easier to calculate than a market-cap-weighted index with hundreds of constituents. About the Dow Jones Averages. Dow constituents and prices Apple's stock price chart. The split in 2014 is marked.  (Note that prices before the split are retroactively adjusted to show a continuous curve.)"

negative: "The key difference I've found between a stock split and a stock dividend – of the exact same stock and class, as opposed to a spin-off – seems to be from the company's own accounting perspective.  There doesn't appear to be any actual transfer of value to the shareholder with either kind of transaction; i.e. in theory, each transaction would be immaterial to the value of your holdings. With respect to the company's accounting, a stock split affects the par value of the shares, whereas a stock dividend reduces the retained earnings account in order to increase paid-in or contributed capital. I found a good online source which explains the history behind this accounting difference: McGraw-Hill - Intermediate Accounting eBook, 6/e - Chapter 18 - Stock Dividends and Splits. Small quote: [...]   Besides being based on fallacious reasoning, accounting for stock   dividends by artificially reclassifying “earned” capital as “invested”   capital conflicts with the reporting objective of reporting   shareholders' equity by source. Despite these limitations, this   outdated accounting standard still applies. Since neither the corporation nor its shareholders apparently benefits   from stock dividends, why do companies declare them?23 Occasionally, a   company tries to give shareholders the illusion that they are   receiving a real dividend. Another reason is merely to enable the corporation to take advantage   of the accepted accounting practice of capitalizing retained earnings.   Specifically, a company might wish to reduce an existing balance in   retained earnings—otherwise available for cash dividends—so it can   reinvest the earned assets represented by that balance without   carrying a large balance in retained earnings. [...] There's a lot more on that page, before and after, worth reading. From another book: Google Books - Comparative Income Taxation, a Structural Analysis - page 314 - Stock Dividends. Small quote: The distribution of dividends in the form of stock or ""bonus"" shares   to existing shareholders typically involves a transfer for corporate   law purposes of retained earnings into stated capital.   It can been [sic] viewed as a deemed distribution of a cash   dividend to the shareholders followed by a corresponding contribution   to capital or as solely as an event at the corporate level which has   no effect on the shareholders whose economic interest in the   corporation is unchanged by the receipt of additional shares. The   systems have taken varied approaches to the stock dividend problem.    The treatment is in part a function of the rules dealing with   distributions of stated capital. [emphases above are mine] [... continues w/descriptions of different countries' tax treatments of the kinds of stock dividends. Includes U.S., Sweden, Japan,   Netherlands, Canada, Australia, U.K., France, Germany. ...] As far as why a corporation might want to capitalize earnings and reduce the equity otherwise available for dividends, I can only imagine that, ignoring taxes for a moment, that it may have something to do with capital ratios that need to be maintained for financing or regulatory purposes?  Yet, I remain curious. If I discover more on this then I'll update my answer. Additional resources:"

negative: There are two reasons to do a reverse split.  Those partial shares will then be turned into cash and returned to the investors. For large institutional investors such as mutual funds or pension funds it results in only a small amount of cash because the fund has merged all the investors shares together. If the company is trying to meet the minimum price level of the exchange they have little choice. If they don't do the reverse split they will be delisted. If the goal is to reduce the number of investors they are using one of the methods of going private: A publicly held company may deregister its equity securities when they   are held by less than 300 shareholders of record or less than 500   shareholders of record, where the company does not have significant   assets. Depending on the facts and circumstances, the company may no   longer be required to file periodic reports with the SEC once the   number of shareholders of record drops below the above thresholds. A number of kinds of transactions can result in a company going   private, including:

negative: I was looking at NAT and NAO, NAT owns 20% of NAO.  They trade opposite each other on the price of oil, low is good for NAT, bad for NAO.  In bad times the other company's stock would probably rise, so they could trim excess shares to keep a stable monetary holding.  This would create cash in bad times, in good times they could buy more, creating a floor as well for the other.


query: Can I calculate stock value with Williams%R if I know the last set?

positive: William %R is a momentum indicator used for measuring overbought and oversold levels, it is not used to predict the price of a stock. In fact, William %R, like all momentum indicators, is a lagging indicator - meaning the indicator level changes as the price of the stock changes. It ranges from 0 to -100. Usually when a reading is less than -80 the stock can be considered to be oversold, and when the reading is above -20 the stock can be considered overbought. When viewed together with the price chart, this can help provide a trader with entry and exit points into and out of a trade.

negative: If your APR is quoted as nominal rate compounded monthly, the APR is 108.6 %. Here is the calculation, (done in Mathematica ). The sum of the discounted future payments (p) are set equal to the present value (pv) of the loan, and solved for the periodic interest rate (r).  Details of the effective interest rate calculation can be found here. http://en.wikipedia.org/wiki/Effective_interest_rate#Calculation

negative: What's the present value of using the payment plan? In all common sense the present value of a loan is the value that you can pay in the present to avoid taking a loan, which in this case is the lump sum payment of $2495.  That rather supposes the question is a trick, providing irrelevant information about the stock market. However, if some strange interpretation is required which ignores the lump sum and wants to know how much you need in the present to pay the loan while being able to make 8% on the stock market that can be done. I will initially assume that since the lender's APR works out about 9.6% per month that the 8% from the stock market is also per month, but will also calculate for 8% annual effective and an 8% annual nominal rate. The calculation If you have $x in hand (present value) and it is exactly enough to take the loan while investing in the stock market, the value in successive months is $x plus the market return less the loan payment.  In the third month the loan is paid down so the balance is zero. I.e. So the present value of using the payment plan while investing is $2569.37. You would need $2569.37 to cover the loan while investing, which is more than the $2495 lump sum payment requires.  Therefore, it would be advisable to make the lump sum payment because it is less expensive: If you have $2569.37 in hand it would be best to pay the lump sum and invest the remaining $74.37 in the stock market.  Otherwise you invest $2569.37 (initially), pay the loan and end up with $0 in three months. One might ask, what rate of return would the stock market need to yield to make it worth taking the loan? The APR proposed by the loan can be calculated.   The present value of a loan is equal to the sum of the payments discounted to present value.  I.e. with  ∴ by induction  So by comparing the $2495 lump sum payment with $997 over 3 x monthly instalments the interest rate implied by the loan can be found. Solving for r If you could obtain 9.64431% per month on the stock market the $x cash in hand required would be calculated by This is equal to the lump sum payment, so the calculated interest is comparable to the stock market rate of return.  If you could gain more than 9.64431% per month on the stock market it would be better to invest and take the loan. Recurrence Form Solving the recurrence form shows the calculation is equivalent to the loan formula, e.g. becomes v[m + 1] = (1 + y) v[m] - p where v[0] = pv where In the final month v[final] = 0, i.e. when m = 3 Compare with the earlier loan formula: s = (d - d (1 + r)^-n) / r They are exactly equivalent, which is quite interesting, (because it wasn't immediately obvious to me that what the lender charges is the mirror opposite of what you gain by investing). The present value can be now be calculated using the formula. Still assuming the 8% stock market return is per month. If the stock market yield is 8% per annum effective rate and if it is given as a nominal annual yield, 8% compounded monthly

negative: 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

negative: A bond has a duration that can be easily calculated. It's the time weighted average of all the payments you'll receive and helpful to understand the effect a change in rates will have on that instrument.  The duration of a stock, on the other hand, is a forced construct to then use in other equations to help calculate, say, the summation of a dividend stream. I can calculate the duration of a bond and come up with an answer that's not up for discussion or dispute. The duration of a stock, on the other hand, isn't such a number. Will J&J last 50 more years? Will Apple? Who knows?

negative: The IRR is the Discount Rate r* that makes Net Present Value NPV(r*)==0. What this boils down to is two ways of making the same kind of profitability calculation.  You can choose a project with NPV(10%)>0, or you can choose based on IRR>10%, and the idea is you get to the same set of projects.  That's if everything is well behaved mathematically. But that's not the end of this story of finance, math, and alphabet soup. For investments that have multiple positive and negative cash flows, finding that r* becomes solving for the roots of a polynomial in r*, so that there can be multiple roots.  Usually people use the lowest positive root but really it only makes sense for projects where NPV(r)>0 for r<r* and NPV(r)<0 for r>r*.   To try to help with your understanding, you can evaluate a real estate project with r=10%, find the sum future discounted cash flows, which is the NPV, and do the project if NPV>0.   Or, you can take the future cash flows of a project, find the NPV as a function of the rate r, and find r* where NPV(r*)==0. That r* is the IRR.  If IRR=r*>10% and the NPV function is well behaved as above, you can also do the project. When we don't have to worry about multiple roots, the preceding two paragraphs will select the same identical sets of projects as meeting the 10% return requirement.

negative: "To calculate the balance (not just principal) remaining, type into your favorite spreadsheet program: It is important that the periods for ""Periods"" and ""Rate"" match up.  If you use your annual rate with quarterly periods, you will get a horribly wrong answer. So, if you invest $1000 today, expect 6% interest per year (0.5% interest per month), withdraw $10 at the end of each month, and want to know what your investment balance will be 2 years (24 months) from now, you would type: And you would get a result of $872.84. Or, to compute it manually, use the formula found here by poster uart:   This is often taught in high-school here as a application of geomentric series. The derivation goes like this.  Using the notation :  r = 1 + interest_rate_per_term_as_decimal p = present value a = payment per term eot1 denotes the FV at end of term 1 etc.  eot1: rp + a   eot2: r(rp + a) + a = r^2p + ra + a   eot3: r(r^2p + ra + a) + a = r^3p + r^2a + ra + a ...   eotn: r^np + (r^(n-1) + r^(n-2) + ... 1)a = p r^n + a (r^n - 1)/(r-1)  That is, FV = p r^n + a (r^n - 1)/(r-1).   This is precisely what exel [sic] computes for the case of payments made at the end of each term (payment type = 0). It's easy enough to repeat the calculations as above for the case of payments made at the beginning of each term. This won't work for changing interest rates or changing withdrawal amounts.  For something like that, it would be better for you (if you don't want online calculators) to set up a table in a spreadsheet so you can adjust different periods manually."

negative: The question lacks specificity, i.e. when does the initial investment occur, now or one period from now?  If now then it is a perpetuity due.   I  will consider under 2 scenarios, A and B, relating to the size of the initial investment. A. Assuming that the initial investment (C_0) occurs now and each payment thereafter has the relationship (1+g) with this investment then the relevant base equation is that for the present value of a growing perpetuity due, expressed in terms of C_0, i.e.  PVGPD=  [C_0*(1+g)*(1+i)]/(i-g). Now, to suit the question asked, we can see that i=fixed rate of return (f) and g = expected inflation rate (e) such that we can rewrite the equation as PVGPD = [C_0*(1+e)*(1+i)]/(i-e].   We know that f = is a fixed nominal rate and must be adjusted for e to calculate the real rate (r) according to the equation f=(1+r)*(1+e)-1. Therefore  PVGPD = [C_0*(1+e)(1+(1+r)(1+e)-1)]/((1+r)*(1+e)-1-e] Tidying up  PVGPD = {C_0*(1+r)(1+e)^2}/[r(1+e)] PVGPD = [C_0*(1+r)*(1+e)]/r B. Assuming that the initial investment (X) is not equal to each subsequent perpetual payment (C_1) then the relevant base equation is that for the the initial investment plus the present value of a growing perpetuity, i.e.  PVGP=  X + [C_1/(i-g)] Rewriting  PVGP = X + [C_1/(f-e)]    Substituting PVGPD = X + {C_1/[(1+r)*(1+e)-1-e]} Tidying up  PVGPD = X + C_1/[r*(1+e)]

negative: "This is the best tl;dr I could make, [original](https://www.cnbc.com/2017/09/22/feds-williams-sees-a-calm-market-reaction-to-reducing-its-huge-balance-sheet.html) reduced by 81%. (I'm a bot) ***** > Williams said the Fed could indeed increase rates again this year and three more times next year, but the exact timing was not important, with a gradual increase in interest rates now under way.  > Provided the U.S. economy continues to progress and inflation was on track to reach the Fed&#039;s 2 percent goal, &quot;I would ascribe to a gradual pace of rate increases, which assuming all that&#039;s happening, could have another rate increase this year and three next year,&quot; Williams said.  > Eventually, the Fed would reach a &quot;New normal&quot; of a Fed Funds rate of 2.5 percent, Williams said.   ***** [**Extended Summary**](http://np.reddit.com/r/autotldr/comments/71wsak/feds_williams_sees_a_calm_market_reaction_to/) | [FAQ](http://np.reddit.com/r/autotldr/comments/31b9fm/faq_autotldr_bot/ ""Version 1.65, ~215089 tl;drs so far."") | [Feedback](http://np.reddit.com/message/compose?to=%23autotldr ""PM's and comments are monitored, constructive feedback is welcome."") | *Top* *keywords*: **Fed**^#1 **rate**^#2 **Williams**^#3 **year**^#4 **next**^#5"

negative: "As I understand it, Implied Volatility represents the expected gyrations of an options contract over it's lifetime.  No, it represents that expected movement of the underlying stock, not the option itself.  Yes, the value of the option will move roughly in the same direction the value of the stock, but that's not what IV is measuring. I even tried staring at the math behind the Options pricing model to see if that could make more sense for me but that didn't help. That formula is correct for the Black-Scholes model - and it is not possible (or at least no one has done it yet) to solve for s to create a closed-form equation for implied volatility.  What most systems do to calculate implied volatility is plug in different values of s (standard deviation) until a value for the option is found that matches the quoted market value ($12.00 in this example).  That's why it's called ""implied"" volatility - the value is implied from market prices, not calculated directly. The thing that sticks out to me is that the ""last"" quoted price of $12 is outside of the bid-ask spread of $9.20 to $10.40, which tells me that the underlying stock has dropped significantly since the last actual trade.   If the Implied Vol is calculated based on the last executed trade, then whatever algorithm they used to solve for a volatility that match that price couldn't find a solution, which then choose to show as a 0% volatility.   In reality, the volatility is somewhere between the two neighbors of 56% and 97%, but with such a short time until expiry, there should be very little chance of the stock dropping below $27.50, and the value of the option should be somewhere around its intrinsic value (strike - stock price) of $9.18."

negative: Yep, but it you didn't answer my question (edit: I know it was phrased as a question, but I do know youre supposed to model changes in cash). When bankers calculate all three approaches, how do they compare them? From what I see, the conclusion of each approach gives us:  * Public Company Approach: Enterprise Value * Transaction Approach: Enterprise Value * Discounted Cash Flow Approach: Enterprise Value + Minimum Level of Operating Cash  Does an investment banker subtract out that minimum level of operating cash at the end of the calculation to get to a value that he can then compare?

negative: Value investing is an investment approach that relies on buying securities below their intrinsic values. There are two main concepts; one is the Intrinsic Value and the other is Margin of Safety.  Intrinsic value is the value of the underlying business - if we are talking about stocks - that can be calculated through carefully analyzing the business looking at all aspects of it. If there is an intrinsic value exists for a company then there is a price tag we can put on its shares as well. Value investing is looking to buy shares well below its intrinsic value.  It is important to know that there is no correct intrinsic value exists for a company and two people can come up with different figures, if they were presented the same data. Calculating the intrinsic value for a business is the hardest part of value investing.  Margin of Safety is the difference between the buying price of a stock and its intrinsic value. Value investors are insisting on buying stocks well below their intrinsic value, where the margin of safety is 20%-30% or even more. This concepts is protecting them from poor decisions and market downturns. It is also providing a room for error, when calculating the intrinsic value.  The approach was introduced by Benjamin Graham and David Dodd in a book called Security Analysis in 1934. Other famous investor using this approach is Warren Buffet Books to read:  I would start to read the first two book first.

negative: The 1.140924% is calculated by taking 13.69%/12 = 1.140924%. Dividing this number by 100 gives you the answer 1.140924 / 100 = .01140924. When dealing with decimals it's important to remember the relationship between a decimal and a percent. 1% = .01 To return .01 to a percent you must multiple that number by 100.  So .01 x 100 = 1% In order to get a decimal from a percent, which is what is used in calculations, you must divide by 100. So, here if we are trying to calculate how much interest you are paying each month we can do this: 9800 * .1369 = $1341.62 (interest you will pay that year IF the principal balance never changed) 1341.62 / 12 = ~111.81 Now, month two 9578.34 * .1369 = 1311.274746 1311.274746 / 12 = 109.28 In order to get your monthly payments (which won't change) for the life of the loan, you can use this formula: Monthly payment = r(PV) / (1-(1+r)^-n) Where:  r= Interest Rate (remember if calculating monthly to do .1369/12) PV= Present Value of loan n=time of loan ( in your case 36 since we are talking monthly and 12*3 = 36) from here we get: [(.1369/12)*9800]/(1-(1+.1369/12)^-36) = $333.467 when rounding is $333.47 As far as actual applied interest rate, I'm not even sure what that number is, but I would like to know once you figure out, since the interest rate you're being charged is most definitely 13.69%.

negative: I want to know why my investment is having loss in 4 to 5 months. As the funds invest in stock markets, the Pakistan stock market is going down in last 4-5 months from all time high. Should I liquidate my investment or wait in hope that it will grow again? This is opinion based and one cannot predict what will happen in future. The funds may grow or may loose value. If I loose all my investment value, is it insured. OR do I loose everything? The growth fund I understand is not guaranteeing any returns. in theory you can loose all the money, however practically there will be some value. If you need guaranteed returns maybe EFU Guaranteed Growth fund will be better choice.

negative: "Beta is the correct answer.  It is THE measure of the risk relationship of a stock with the broad market. R squared is incorrect unless you mean something very odd by ""co-efficiency.""  A stock that goes up each time the market goes down has very low co-efficiency (negative risk as you have defined it) but very high R squared.  A stock that goes the same direction as the market but twice as far (with a lot of noise) has a very low R squared but contains a lot of market risk.  A stock that always goes in the same direction as the market but only a 100th as far is very safe but has a very high R squared. You can calculate beta using ""slope"" in excel or doing a regression, but the easiest thing is just to look up the beta in yahoo finance or elsewhere.  You don't need to calculate it for yourself normally."

negative: "I don't know why there is so much confusion on such a simple concept. The answer is very simple. A stock must eventually pay dividends or the whole stock market is just a cheap ponzi scheme. A company may temporarily decided to reinvest profits into R&D, company expansion, etc. but obviously if they promised to never pay dividends then you can never participate in the profits of the company and there is simply no intrinsic value to the stock. For all of you saying 'Yeah but the stock price will go up!', please people get a life. The only reason the price goes up is in anticipation of dividend yield otherwise WHY would the price go up?  ""But the company is worth more and the stock is worth more"" A stocks value is not set by the company but by people who buy and sell in the open market.  To think a stock's price can go up even if the company refuses to pay dividends is analogous to : Person A says ""Hey buy these paper clips for $10"". But those paper clips aren't worth that. ""It doesn't matter because some fool down the line will pay $15"". But why would they pay that? ""Because some fool after him will pay $20"" Ha Ha!"

negative: On closer look, it appears that Google Finance relies on the last released 10-k statement (filing date 10/30/2013), but outstanding shares as of last 10-Q statement. Using these forms, you get ($37,037M / 5.989B ) = $6.18 EPS. I think this is good to note, as you can manually calculate a more up to date EPS value than what the majority of investors out there are relying on.

negative: From InvestingAnswers, the price of a bond is equal to the present value of its future cash flows, as shown in the following formula:  Where: By induction, this is equivalent to: or, using more familiar formulae, it is equivalent to the formula for the present value of an ordinary annuity to represent the coupon payments, plus a term for the discounted value at maturity: For example, a 10 year semiannual bond with coupon payment 10%, priced at 1095 with maturity value 1000. Solving for r yields 0.0428332 or 4.28% semi-annually. (8.75% per annum) The solution can be found by plotting or using a solver, which many pocket calculators have.  Plot of p as a function of r, intersecting with p = 1095 when r = 0.0428   Checking on Investopedia

negative: Mutual funds don't work like stocks in that way. The price of a mutual fund is set at the end of each day and doesn't fluctuate during the day. So no matter when you put in your order, it will be filled at the end of the day at whatever the closing price is for that day. Here is some good information on that There is no continuous pricing of fund shares throughout the trading   day. When an investor places an order to buy or sell a fund's shares,   the order is executed based on the NAV calculated at the end of that   trading day, regardless of what time during the day the order was   placed. On the other hand, if the investor were to check the price of   his or her fund shares halfway through the business day, the price   quoted would be the previous day's NAV because that was the last time   the fund calculated and reported the value. -http://www.finweb.com/investing/how-mutual-funds-are-priced.html

negative: In this case, it looks like the interest is simply the nominal daily interest rate times number of days in the period. From that you can use a spreadsheet to calculate the total payment by trial and error. With the different number of days in each period, any formula would be very complicated. In the more usual case where the interest charge for each period is the same, the formula is: m=P*r^n*(r-1)/(r^n-1) where * is multiplication ^ is exponentiation / is division (Sorry, don't know if there's a way to show formulas cleanly on here) P=original principle r=growth factor per payment period, i.e. interest rate + 100% divided by 100, e.g. 1% -> 1.01 n=number of payments Note the growth factor above is per period, so if you have monthly payments, it's the rate per month. The last payment may be different because of rounding errors, unequal number of days per period, or other technicalities. Using that formula here won't give the right answer because of the unequal periods, but it should be close. Let's see: r=0.7% times an average of 28.8 days per period gives 20.16% + 1 = 1.2016. n=5 P=500 m=500*1.2016^5*(1.2016-1)/(1.2016^5-1) =167.78 Further off than I expected, but ballpark.

negative: "You can use the 6900 to make an investment.  Or to buy something.  That's why people keep reminding you that you could make interest.  Because most people think of either 7200 now or paying the same 7200 over time.  So you could just be storing the 7200 under the mattress until you pay it out.  Obviously in that case, inflation doesn't matter (""is not applicable"").  You've given up the use of the 7200 from the beginning.   Think of it instead as 7200 now and twenty-three payments of 300 each.  So 14,100 total.  Then you can spend 6900 on something else at the beginning or spend 300 a month on other things.  The difference between spending 6900 now and 300 in each of twenty-three months would be measured in inflation.  Of course, this requires you to have both 7200 now and an income stream producing at least 300 a month.   Another way of doing things is to take 6900 and invest it.  Each month you remove 300 and use it to make a payment.  We're now back to just one 7200, plus the interest over time.  I would argue that this is still an inflation advantage.  It's just that instead of spending the money, you invested it.  And that of course is your prerogative.   The point being that you would not have that opportunity if you paid up front.   Now to calculate the difference in monthly payments of 300 euro using the above webpage what should I do?   As already said, you would have to calculate twenty-three values and then sum them with the 300 you pay up front in the monthly.   There are other ways to calculate it, if you are not using that particular tool.  For example, there are formulas to calculate the net present value of an annuity.  E.g. see Investopedia.   Where: P = the present value of an annuity stream PMT = the dollar amount of each annuity payment r = the inflation rate n = the number of periods in which payments will be made Investopedia talks about interest rates, but you can put inflation there for this purpose.  In that case, r might better be called the ""discount rate"".   PMT is 300. r is whatever estimate you are using for inflation.  E.g. .003 per period. n is 23.   Note that the monthly inflation rate is smaller than the annual rate.  So .003 is about 3.66% annually.  3.04% annually is more like .0025 a month.   I found calculators for this with search terms ""present value of annuity calculator"".  Some of the calculators will take the annual rate (3.66%) and number of periods per year as input.  Or the calculator may take a monthly rate as a percentage (.3%) rather than as a decimal (.003).  So be careful of the inputs.   This gives me a net present value (NPV) of 6,657.69 for the 23 payments of 300, assuming .3%.  Or 6957.69 is the NPV of the monthly payments and 7200 is the NPV of the 7200 up front.   Obviously if you can pay less than 6957.69 up front rather than 7200, then it makes more sense to pay up front.   Even without a discount though, it still may make more sense to pay up front.   How much those intangibles are worth is up to you."

negative: From Wikipedia -  To calculate the value of the S&P 500 Index, the sum of the adjusted   market capitalization of all 500 stocks is divided by a factor,   usually referred to as the Divisor. For example, if the total adjusted   market cap of the 500 component stocks is US$13 trillion and the   Divisor is set at 8.933 billion, then the S&P 500 Index value would be   1,455.28. From a strictly mathematical perspective, the divisor is not canceling out the units, and the S&P index is dollar denominated even though it's never quoted that way. A case in point is that the S&P is often said to have a P/E, and especially an E, the earnings attributed to one 'unit' of S&P. And if you buy a mutual fund sporting a low expense ratio, you can invest exactly that much money (the current S&P index value) and see the dividends accrue to your account, less the fee.

negative: "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."

negative: Sometimes, but it was more common for the 'presentation' leg of the project to use Excel as the last step before passing the data on to the next team or pushing things into a powerpoint. For new projects, those were much more likely to be R end to end and yes, I often used an organization like you mention, extract and transform -> Fit Model and export predictions -> produce visuals and explanatory data.   I did have a few examples where I used R to build on top of excel models, e.g. passing data that was already being calculated into a regression or producing a plot that excel couldn't easily do. In my case we had 10+ people who were good with excel and only 1 or 2 being proficient with R. If the majority of people were strong R users, I'm sure it would have had more predominance in our work.

negative: "Of course it can. This is a time value of money calculation. If I knew the maturity date, or current yield to maturity I'd be able to calculate the other number and advise how much rates need to rise to cause the value to drop from 18 to 17. For a 10 year bond, a rise today of .1% will cause the bond to drop about 1% in value. This is a back of napkin calculation, finance calculators offer precision. edit - when I calculate present value with 34 years to go, and 5.832% yield to maturity, I get $14.55. At 5.932, the value drops to $14.09, a drop of 3.1%.  Edit - Geo asked me to show calculations. Here it goes - A) The simplest way to calculate present value for a zero coupon bond is to take the rate 5.832%, convert it to 1.05832 and divide into the face value, $100. I offer this as the ""four function calculator"" approach, so one enters $100 divided by 1.05832 and repeat for the number of years left. A bit of precision is lost if there's a fractional year involved, but it's close. The bid/ask will be wider than this error introduced.  B) Next - If you've never read my open declaration of love for my Texas Instruments BA-35 calculator, here it is, again. One enters N=34 (for the years) FV = 100, Rate = 5.832, and then CPT PV. It will give the result, $14.56.  C) Here is how to do it in Excel -  The numbers in lines 1-3 are self evident, the equation in cell B4 is =-PV(B3/100,B1,0,B2) - please note there are tiny differences in the way to calculate in excel vs a calculator. Excel wants the rate to be .05832, so I divided by 100 in the equation cell.  That's the best 3 ways I know to calculate present value. Geo, if you've not noticed, the time value of money is near and dear to me. It comes into play for bonds, mortgages, and many aspect of investing. The equations get more complex if there are payments each year, but both the BA-35 and excel are up to it."

negative: You need the Present Value, not Future Value formula for this. The loan amount or 1000 is paid/received now (not in the future). The formula is $ PMT = PV (r/n)(1+r/n)^{nt} / [(1+r/n)^{nt} - 1] $  See for example http://www.calculatorsoup.com/calculators/financial/loan-calculator.php With PV = 1000, r=0.07, n=12, t=3 we get PMT = 30.877 per month

negative: I don't know how long run but this last week people have been talking about McDonalds a lot.  I think the trick is to set a limit and have it auto sell when it is met. There is no need to hold forever and therefor what is 'long term' can be variable.

negative: "Do not reinvent the wheel! Historical data about stock market returns and standard deviations suffer from number of issues such as past-filling and mostly survivorship bias -- that the current answers do not consider at all. I suggest to read the paper ""A Century of Global Stock Markets"" by Philippe Jorion (UC Irvine) and William Goetzmann (Yale), here. William Bernstein comments the results here, notice that rebalancing is sometimes a good option but not always, his non-obvious finding where the low SD did not favour from rebalancing:  Look at the final page of the paper,  ""geometric returns -- represent returns to a buy-and-hold strategy"" and the ""arithmetic averages -- give equal weight to each observation interval."", where you can find your asked ""historical effect of Rebalancing on Return and Standard Deviation"". The paper nicely summarizes the results to this table:  The results in the table are from the interval 1921-1996, it is not that long-time but even longer term data has its own drawbacks. The starting year 1921 is interesting choice because it is around the times of social-economical changes and depressing moments, historical context can be realized from books such as Grapes Of Wrath (short summary here, although fiction to some extent, it has some resonance to the history). The authors have had to ignore some years because of different reasons such as political unrest and wars.  Instead of delving into marketed spam as suggested by one reply, I would look into this search here. Look at the number of references and the related papers to judge their value.  P.s. I encourage people to attack my open question here, hope we can solve it!"

negative: "4) Finally, do all companies reduce their stock price when they pay a dividend? Are they required to? There seems to be confusion behind this question.  A company does not set the price for their stock, so they can't ""reduce"" it either.  In fact, nobody sets ""the price"" for a stock. The price you see reported is simply the last price that the stock was traded at.  That trade was just one particular trade in a whole sequence of trades.  The price used for the trade is simply the price which the particular buyer and particular seller agreed to for that particular trade.  (No agreement, well then, no trade.)  There's no authority for the price other than the collection of all buyers and sellers. So what happens when Nokia declares a 55 cent dividend?  When they declare there is to be a dividend, they state the record date, which is the date which determines who will get the dividend: the owners of the shares on that date are the people who get the dividend payment.  The stock exchanges need to account for the payment so that investors know who gets it and who doesn't, so they set the ex dividend date, which is the date on which trades of the stock will first trade without the right to receive the dividend payment.  (Ex-dividend is usually about 2 days before record date.)  These dates are established well before they occur so all market participants can know exactly when this change in value will occur. When trading on ex dividend day begins, there is no authority to set a ""different"" price than the previous day's closing price.  What happens is that all (knowledgeable) market participants know that today Nokia is trading without the payment 55 cents that buyers the previous day get.  So what do they do?  They take that into consideration when they make an offer to buy stock, and probably end up offering a price that is about 55 cents less than they would have otherwise.  Similarly, sellers know they will be getting that 55 cents, so when they choose a price to offer their stock at, it will likely be about that much less than they would have asked for otherwise."

negative: 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.

negative: I don’t disagree that housing prices are important and vital to the economy, but I think they are a separate issue to inflation, requires a different set of tools to deal with, and has completely different outcomes from policies.   First and foremost, they are almost the only item purchased that can be resold at a higher value. So even though house prices may have risen 1000%, who ever had bought a house exits with a 1000% increase in equity. How would account for that when calculating inflation?

negative: "As a rental, this is not an ideal set of numbers. You manage to show a $255 'gain' but $275 is from payment to principal. So, from the start, you're out $20/wk.  This ignores the $170K down payment, which has an opportunity cost, however you calculate it. You can assign the same rate as the mortgage, and it's nearly $10K/yr. Or the rate you feel your choice of stock market or alternate investment would rise. Either way, you can't ignore this money.  Your mortgage rate isn't fixed. A 1% rise and it would jump to $1663 ($842/week) Ideally, a rental property is cash positive without counting principal paydown or even the tax refund. It's a risky proposition to buy and count on everything going right. I didn't mean to scare you off with ""1%"" but you should research the costs of repair and maintenance. Last year my Heat/AC system needed replacement. US$10K. This year, it's time to paint, and replace rotting trim, $7000.  In the US we have property tax that can range from 1-2% of the house value. If you don't have this tax, that's great, just please confirm this."

negative: Thanks for this, great in depth answer. I had previously calculated a WACC and have used it for my discount rate.   As part of your last point on revenue vs. cash, I've set a accounts receivable period of 30 days, and then applied a factor of 30/365 * revenue to understand what portion of my revenue is not cash in hand. Does that make sense?