What exactly is the profit and loss of a portfolio?
When we 'delta-hedge', we make the value of a portfolio 0.  No - you make the risk relative to some underlying 0.  The portfolio does have a value, but if whatever underlying you're hedging against changes slightly the value of your portfolio should not change. But, what is the derivative of a portfolio?  It's the instantaneous rate of change of the portfolio) relative to some underlying phenomenon.  With a portfolio of many stocks, there's not one single factor that drives the value of your portfolio. You have sensitivity to each underlying stock (price and volatility), interest rates, the market as a whole, etc. For simplicity, we might imagine a portfolio that has holdings in .... a call .... a stock .... and a bank account (to borrow and lend money).  You will have a delta relative to the stock and a delta relative to the underlying instrument on the option, etc.  Those can only be aggregated for each factor (e.g. if the call is an option on the same stock) Theta is the only one you can calculate for the portfolio as a whole - it will be the aggregate theta of all of your positions (since change in time is constant across all investments).  All of the others are not aggregatable since they are measuring sensitivities to different phenomena.
"So it seems like a lot of people here aren't exactly sure about why this works and its financial implications.   So what you are referring to is in Finance something called Funds Transfer Pricing or FTP (often referred to as just Transfer Pricing). Like anything else, FTP has its place. Most companies; however, don't use it properly. FTP, theoretically, has one primary purpose (although it's developed a second): to properly allocate opportunity costs across divisions.  Let's say Company A produces widgets. They sell these widgets for $200 at a TOTAL COST of $150 and book profits of $50. Now to produce the widget Division 1 makes a computer chip at a cost of $50 that it then ""sells"" to Division 2 for $60. Division 1 then books a profit of $10. Division 2 then makes some plastic stuff and assembles the device. This is labor intensive so Division 2's costs are $100. Company A sells the completed device for $150. Division 2 subsequently books profits of $40, and appears much more profitable than Division 1, on the surface.  The problem arises when Division 1 could sell the chip to the open market for $125. Now it costs them $50 to produce, and they could make a theoretical profit of $75. This is MORE than the company makes AS A WHOLE on the entire device. By having Division 2 pay effectively ""fair market price"" for that chip, you realize that Division 2 is really operating at a loss (the *opportunity cost* of not selling the chip to market is greater than producing the completed device). Company A would be better off getting rid of Division 2 and solely focusing on Division 1. In a good FTP system, Division 2 would pay the fair market price of $125. If done properly, management would  hopefully realize it should divest Division 2.  That's the ***fundamental premise*** behind FTP. In actuality things get much more complicated because of economics, the company itself, branding, IT, operations, management, PPE, labor laws, etc. Thats why most companies screw it up. All that other stuff falls under whats called cost allocation accounting. It gets VERY complex and entire masters courses are dedicated to it (different methods, etc.)   The other thing you can do with FTP is get crazy tax breaks due to various tax laws. The simplified explanation is that divisions pay taxes on profits to the government ***that division*** is located in (this works on the state level, too btw.). GE does a lot of this and it's a big part of why they pay almost no-taxes. Again, it gets more complicated when you involve audits as there's some grey area legally.   For simplicity, assume tax rates are 40% in the US and 10% in India. So let's say GE makes an airplane engine in the US but ""finishes"" manufacturing in India. These specific engines costs $5,000,000 for the US division to make, up to a certain point.  The US division can then sell the engine at a break even to India. So India ""pays"" $5,000,000 for the engine. The US division then books no profit. India finishes the manufacturing with additional costs of $1,000,000. The India division then sells the engine to the open market for $9,000,000 . Therefore, the India division books a profit of $3,000,000 and pays taxes of $300,000. Now GE as a whole makes a profit of $3,000,000 less taxes of $300,000 = net profit of $2,700,00.  Further, let's say the fair market value of the engine, as is, when the US sells to India is $7,000,000. That would mean US ***should*** book profits of $2,000,000 and India ***should*** book profits of $1,000,000. Total taxes by GE are now $800,000 (US) + $100,000 (India) = $900,000. However, what's important is that NET PROFIT is now $2,100,000. ***GE just saved $600,000 in taxes by doing this***. The beauty of this is, divisions are supposed to charge fair market value for products FTP'd internationally; however, it's REALLY hard for the IRS to say what the value of an unfinished product really is (heck, you could be offering bulk discounts, etc.)...  The fact is, often, US divisions have skilled labor that is difficult to replicate elsewhere. They just show US divisions operating at losses to make the company as a whole better. The problem, again, arises when top management don't fully appreciate or understand the reasoning behind this stuff. They end up making cuts to US labor because it's ""unprofitable"" without thinking about the entire story.   I know this is very long winded but hope it helps!  ***tldr; companies FTP to recognizes profitability and opportunity costs of divisions as well as use it for overseas tax breaks.***  Side note: Politically speaking, people who know how this works are pissed off about it in the U.S. (don't worry though, most politicians on both sides don't have a clue). We have high corporate tax rates relative to other countries and IRS loopholes allow this kind of thing (lobbying $$). It's also why, economically, you can't just raise ***corporate*** tax rates to increase domestic tax reciepts as more companies will just implement this process (it's complicated to do properly). Also, please don't say 50 years ago tax rates were higher and raising taxes increased receipts. The fact is most companies couldn't even FATHOM doing this 50 years ago, no less even 20.  edit: some clarification in wording" "According to the following links, it is commonly pronounced ""Cecil"".   https://kaufmanrossin.com/blog/bank-ready-meet-cecil/ The proposed model introduces the concept of shifting from an incurred   loss model to the current expected credit loss model commonly referred   to as CECL (pronounced “Cecil”). http://www.gonzobanker.com/2016/02/cecl-the-blind-leading-the-blurry/ [...] and its name is CECL (Current Estimated Credit Losses, pronounced like   the name “Cecil”). The name Cecil means “blind,” which is ironic, because FASB’s upcoming   guidance will push FIs to clarify the future performance of their loan   portfolios by using models to predict CECL of all loan portfolios. https://www.linkedin.com/pulse/operational-financial-impact-cecl-banks-nikhil-deshmukh Termed as Current Expected Credit Loss (CECL, or Cecil, as some call   it), [...]" Well it would appear that you had a wash sale that canceled out a loss position.  Without seeing the entire report, I couldn't tell you exactly what was happening or how you triggered § 1091.  But just from the excerpted images, it appears as though your purchase of stock was layered into multiple tranches - perhaps you acquired more of the stock in the 61-day period than you sold (possibly because of a prior holding).   If in the 61-day period around the sale of stock (30 days before and 30 days after), you also acquire the same stock (including by contract or option), then it washes out your loss.  If you held your stock for a while, then in a 61-day period bought more, and sold some, then any loss would be washed out by the acquisition.  Of course it is also a wash sale if your purchase of the stock follows your sale, rather than precedes it.  Your disallowed loss goes into the basis of your stock holding, so will be meaningful when you do have a true economic sale of that stock. From IRS Pub 550: A wash sale occurs when you sell or trade stock or securities at a loss and within 30 days before or after the sale you: Buy substantially identical stock or securities, Acquire substantially identical stock or securities in a fully taxable trade, Acquire a contract or option to buy substantially identical stock or securities, or Acquire substantially identical stock for your individual retirement account (IRA) or Roth IRA. If you sell stock and your spouse or a corporation you control buys substantially identical stock, you also have a wash sale. Looking at your excerpted account images, we can see a number of positions sold at a loss (sale proceeds less than basis) but each one is adjusted to a zero loss.  I suspect the fuller picture of your account history and portfolio will show a more complicated and longer history with this particular stock.  That is likely the source of the wash sale disallowed loss notations. You might be able to confirm that all the added numbers are appearing in your current basis in this stock (or were reflected upon your final exit from the stock). "There are some good answers about the benefits of diversification, but I'm going to go into what is going on mathematically with what you are attempting. I was always under the assumption that as long as two securities are less than perfectly correlated (i.e. 1), that the standard deviation/risk would be less than if I had put 100% into either of the securities. While there does exist a minimum variance portfolio that is a combination of the two with lower vol than 100% of either individually, this portfolio is not necessarily the portfolio with highest utility under your metric.  Your metric includes returns not just volatility/variance so the different returns bias the result away from the min-vol portfolio. Using the utility function: E[x] - .5*A*sig^2 results in the highest utility of 100% VTSAX. So here the Sharpe ratio (risk adjusted return) of the U.S. portfolio is so much higher than the international portfolio over the period tracked that the loss of returns from adding more international stocks outweigh the lower risk that you would get from both just adding the lower vol international stocks and the diversification effects from having a correlation less than one. The key point in the above is ""over the period tracked"".  When you do this type of analysis you implicitly assume that the returns/risk observed in the past will be similar to the returns/risk in the future.   Certainly, if you had invested 100% in the U.S. recently you would have done better than investing in a mix of US/Intl.  However, while the risk and correlations of assets can be (somewhat) stable over time relative returns can vary wildly! This uncertainty of future returns is why most people use a diversified portfolio of assets.  What is the exact right amount is a very hard question though." "My knowledge relates to ETFs only. By definition, an ETF's total assets can increase or decrease based upon how many shares are issued or redeemed.  If somebody sells shares back to the ETF provider (rather than somebody else on market) then the underlying assets need to be sold, and vice-versa for purchasing from the ETF provider.  ETFs also allow redemptions too in addition to this. For an ETF, to determine its total assets, you need to you need to analyze the Total Shares on Issue multipled by the Net Asset Value.  ETFs are required to report shares outstanding and NAV on a daily basis. ""Total assets"" is probably more a function of marketing rather than ""demand"" and this is why most funds report on a net-asset-value-per-share basis. Some sites report on ""Net Inflows"" is basically the net change in shares outstanding multiplied by the ETF price. If you want to see this plotted over time you can use a such as: http://www.etf.com/etfanalytics/etf-fund-flows-tool which allows you to see this as a ""net flows"" on a date range basis." "The standard measure of risk is the variance of the asset. The return on investment of the asset is understood as a random variable with a particular distribution. One can make inferences about the underlying distribution using historical data. As you say, this is what the quants do. There are other, more sophisticated measures of risk that allow for such things as skewed distributions and Markov switching. If you are interested in learning more, I suggest starting with the foundations of Modern Portfolio Theory: ""Portfolio Selection"" by Harry Markowitz and ""Capital Asset Prices"" by William Sharpe." "Selling short is simply by definition the selling, then later re-buying of stock you don't initially own. Say you tally your entire portfolio balance: the quantity of each stock you own, and your cash assets. Let's call this your ""initial position"". We define ""profit"" as any increase in assets, relative to this initial position. If you know a particular stock will go down, you can realize a profit by selling some of that stock, waiting for the price to go down, then buying it back. In the end you will have returned to your initial position, except you will have more cash. If you sell 10 shares of a stock valued at £1.50, then buy them back at £1.00, you will make a £5.00 profit while having otherwise returned to your previous position. If you do the same, but you initially owned 1000 shares, sold just 10 of those, then bought 10 back, that's still a profit of £5.00. Selling short is doing the same thing, but with an initial and ending balance of 0 shares. If you initially own 0 shares, sell 10, then buy 10 back, you return to your initial position (0 shares) plus a profit of £5.00. (And in practice you must also pay a borrowing fee to do this.) The advantage of selling short is it can be done with any stock, not just those currently owned." "Bob should treat both positions as incomplete, and explore a viewpoint which does a better job of separating value from volatility. So we should start by recognizing that what Bob is really doing is trading pieces of paper (say Stocks from Fund #1 or Bonds from Fund #2, to pick historically volatile and non-volatile instruments.*) for pieces of paper (Greenbacks).  In the end, this is a trade, and should always be thought of as such.  Does Bob value his stocks more than his bonds?  Then he should probably draw from Fund #2.  If he values his bonds more, he should probably draw from Fund #1. However, both Bob and his financial adviser demonstrate an assumption: that an instrument, whether stock bond or dollar bill, has some intrinsic value (which may raise over time).  The issue is whether its perceived value is a good measure of its actual value or not. From this perspective, we can see the stock (Fund #1) as having an actual value that grows quickly (6.5% - 1.85% = 4.65%), and the bond (Fund #2) as having an actual value that grows slower (4.5% - 1.15$ = 3.35$).  Now the perceived value of the stocks is highly volatile.  The Chairman of the Fed sneezes and a high velocity trader drives a stock up or down at a rate that would give you whiplash. This perspective aligns with the broker's opinion.  If the stocks are low, it means their perceived value is artificially low, and selling it would be a mistake because the market is perceiving those pieces of paper as being worth less than they actually are.  In this case, Bob wins by keeping the stocks, and selling bonds, because the stocks are perceived as undervalued, and thus are worth keeping until perceptions change. On the other hand, consider the assumption we carefully slid into the argument without any fanfare: the assumption that the actual value of the stock aligns with its historical value.  ""Past performance does not predict future results.""  Its entirely possible that the actual value of the stocks is actually much lower than the historical value, and that it was the perceived value that was artificially higher.  It may be continuing to do so... who knows how overvalued the perceived value actually was!  In this case, Bob wins by keeping the bonds.  In this case, the stocks may have ""underperformed"" to drive perceptions towards their actual value, and Bob has a great chance to get out from under this market. The reality is somewhere between them.  The actual values are moving, and the perceived values are moving, and the world mixes them up enough to make Scratchers lottery tickets look like a decent investment instrument.  So what can we do? Bob's broker has a smart idea, he's just not fully explaining it because it is unprofessional to do so.  Historically speaking, Bobs who lost a bunch of money in the stock market are poor judges of where the stock market is going next (arguably, you should be talking to the Joes who made a bunch of money. They might have more of a clue.).  Humans are emotional beings, and we have an emotional instinct to cut ties when things start to go south.  The market preys on emotional thinkers, happily giving them what they want in exchange for taking some of their money.  Bob's broker is quoting a well recognized phrase that is a polite way of saying ""you are being emotional in your judgement, and here is a phrasing to suggest you should temper that judgement."" Of course the broker may also not know what they're doing!  (I've seen arguments that they don't!)  Plenty of people listened to their brokers all the way to the great crash of 2008.  Brokers are human too, they just put their emotions in different places.  So now Bob has no clear voice to listen to.  Sounds like a trap! However, there is a solution.  Bob should think about more than just simple dollars.  Bob should think about the rest of his life, and where he would like the risk to appear.  If Bob draws from Fund #1 (liquidating stocks), then Bob has made a choice to realize any losses or gains early... specifically now.  He may win, he may lose.  However, no matter what, he will have a less volatile portfolio, and thus he can rely on it more in the long run. If Bob draws from Fund #2 (liquidating bonds) instead, then Bob has made a choice not to realize any losses or gains right away.  He may win, he may lose.  However, whether he wins or loses will not be clear, perhaps until retirement when he needs to draw on that money, and finds Fund #1 is still under-performing, so he has to work a few more years before retirement.  There is a magical assumption that the stock market will always continue rewarding risk takers, but no one has quite been able to prove it! Once Bob includes his life perspective in the mix, and doesn't look just at the cold hard dollars on the table, Bob can make a more educated decision.  Just to throw more options on the table, Bob might rationally choose to do any one of a number of other options which are not extremes, in order to find a happy medium that best fits Bob's life needs: * I intentionally chose to label Fund #1 as stocks and Fund #2 as bonds, even though this is a terribly crude assumption, because I feel those words have an emotional attachment associated to them which #1 and #2 simply do not.  Given that part of the argument is that emotions play a part, it seemed reasonable to dig into underlying emotional biases as part of my wording.  Feel free to replace words as you see fit to remove this bias if desired."