How do annual risks translate into long-term risks?
"The short answer is the annualised volatility over twenty years should be pretty much the same as the annualised volatility over five years. For independent, identically distributed returns the volatility scales proportionally. So for any number of monthly returns T, setting the annualization factor m = 12 annualises the volatility.  It should be the same for all time scales.  However, note the discussion here: https://quant.stackexchange.com/a/7496/7178 Scaling volatility [like this] only is mathematically correct when the   underlying price model is driven by Geometric Brownian motion which   implies that prices are log normally distributed and returns are   normally distributed. Particularly the comment: ""its a well known fact that volatility is overestimated when scaled over long periods of time without a change of model to estimate such ""long-term"" volatility."" Now, a demonstration.  I have modelled 12,000 monthly returns with mean = 3% and standard deviation = 2, so the annualised volatility should be Sqrt(12) * 2 = 6.9282.   Calculating annualised volatility for return sequences of various lengths (3, 6, 12, 60 months etc.) reveals an inaccuracy for shorter sequences.  The five-year sequence average got closest to the theoretically expected figure (6.9282), and, as the commenter noted ""volatility is [slightly] overestimated when scaled over long periods of time"". Annualised volatility for varying return sequence lengths  Edit re. comment Reinvesting returns does not affect the volatility much.  For instance, comparing some data I have handy, the Dow Jones Industrial Average Capital Returns (CR) versus Net Returns (NR).  The return differences are somewhat smoothed, 0.1% each month, 0.25% every third month.  More erratic dividend reinvestment would increase the volatility."
I find the higher estimates a bit unbelievable. A big part of my job is liability valuation and small assumption changes can have a huge impact on results.  They may be right (future) dollar value wise but the proper way to think about this stuff is in present value terms.  This could actually be a really interesting study - you all just gave me a great idea for a potential masters thesis :) Since near-term at-the-money (ATM) options are generally the most liquid, the listed implied vol for a stock is usually pretty close to the nearest ATM volatility, but there's not a set convention that I'm aware of.  Also note that for most stocks, vol skew (the difference in vol between away-from-the-money and at-the-money options) is relatively small,  correct me if I'm wrong, IV is the markets assessment that the stock is about 70% likely (1 Standard Deviation) to move (in either direction) by that percent over the next year. Not exactly.  It's an annualized standard deviation of the anticipated movements over the time period of the option that it's implied from.  Implied vol for near-term options can be higher or lower than longer-term options, depending on if the market believes that there will be more uncertainty in the short-term.  Also, it's the bounds of the expected movement in that time period. so if a stock is at $100 with an implied vol of 30% for 1-year term options, then the market thinks that the stock will be somewhere between $70 and $130 after 1 year.  If you look at the implied vol for a 6-month term option, half of that vol is the range of expected movement in 6 months. "This article is written by an idiot!!  Risk ≠ failure, risk = possibility of failure  Reward (return) should be commensurate with risk and this is why long-shot propositions should be worthwhile. An example of this could be something like the following; an investment with a 95% chance of success should return about 5% on the investment (1 in 20 risk of loss, 1/20th return on investment for taking the risk) while a long-shot investment with a 5% chance of success should be paying a 2000% return (1 in 20 will succeed but they will pay 20 times the investment if they do).  An investment with a 0% chance of return (that you are suckered into due to ""opacity"") is not an investment, it is being robbed and it should be illegal. WTF is opacity? Lying?" I can think of a few simple and quick techniques for timing the market over the long term, and they can be used individually or in combination with each other. There are also some additional techniques to give early warning of possible turns in the market. The first is using a Moving Average (MA) as an indication of when to sell. Simply if the price closes below the MA it is time to sell. Obviously if the period you are looking at is long term you would probably use a weekly or even monthly chart and use a relatively large period MA such as a 50 week or 100 week moving average. The longer the period the more the MA will lag behind the price but the less false signals and whipsawing there will be. As we are looking long term (5 years +) I would use a weekly chart with a 100 week Exponential MA. The second technique is using a Rate Of Change (ROC) Indicator, which is a momentum indicator. The idea for timing the markets in the long term is to buy when the indicator crosses above the zero line and sell when it crosses below the zero line. For long term investing I would use a 13 week EMA of the 52 week ROC (the EMA smooths out the ROC indicator to reduce the chance of false signals). The beauty of these two indicators is they can be used effectively together. Below are examples of using these two indicators in combination on the S&P500 and the Australian S&P ASX200 over the past 20 years.  S&P500 1995 to 2015  ASX200 1995 to 2015 If I was investing in an ETF tracking one of these indexes I would use these two indicators together by using the MA as an early warning system and maybe tighten any stop losses I have so that if the market takes a sudden turn downward the majority of my profits would be protected. I would then use the ROC Indicator to sell out completely out of the ETF when it crosses below zero or to buy back in when the ROC moves back above zero. As you can see in both charts the two indicators would have kept you out of the market during the worst of the downfalls in 2000 and 2008 for the S&P500 and 2008 for the ASX200. If there is a false signal that gets you out of the market you can quite easily get back in if the indicator goes back above zero. Using these indicators you would have gotten into the market 3 times and out of it twice for the S&P500 over a 20 year period. For the ASX200 you would have gone in 6 times and out 5 times, also over a 20 year period. For individual shares I would use the ROC indicator over the main index the shares belong to, to give an indication of when to be buying individual stocks and when to tighten stop losses and stay on the sidelines. My philosophy is to buy rising stocks in a rising market and sell falling stocks in a falling market. So if the ROC indicator is above zero I would be looking to buy fundamentally healthy stocks that are up-trending and place a 20% trailing stop loss on them. If I get stopped out of one stock then I would look to replace it with another as long as the ROC is still above zero. If the ROC indicator crosses below zero I would tighten my trailing stop losses to 5% and not buy any new stocks once I get stopped out. Some additional indicators I would use for individual stock would be trend lines and using the MACD as a momentum indicator. These two indicators can give you further early warning that the stock may be about to reverse from its current trend, so you can tighten your stop loss even if the ROC is still above zero. Here is an example chart to explain:  GEM.AX 3 Year Weekly Chart Basically if the price closes below the trend line it may be time to close out the position or at the very least tighten up your trailing stop loss to 5%. If the price breaks below an established uptrend line it may well be the end of the uptrend. The definition of an uptrend is higher highs and higher lows. As GEM has broken below the uptrend line and has maid a lower low, all that is needed to confirm the uptrend is over is a lower high. But months before the price broke below the uptrend line, the MACD momentum indicator was showing bearish divergence between it and the price. In early September 2014 the price made a higher high but the MACD made a lower high. This is called a bearish divergence and is an early warning signal that the momentum in the uptrend is weakening and the trend could be reversing soon. Notice I said could and not would. In this situation I would reduce my trailing stop to 10% and keep a watchful eye on this stock over the coming months. There are many other indicators that could be used as signals or as early warnings, but I thought I would talk about some of my favourites and ones I use on a daily and weekly basis. If you were to employ any of these techniques into your investing or trading it may take a little while to learn about them properly and to implement them into your trading plan, but once you have done that you would only need to spend 1 to 2 hours per week managing your portfolio if trading long-term or about 1 hour per nigh (after market close) if trading more medium term. Stock index funds are likely, but not certainly, to be a good long-term investment.  In countries other than the USA, there have been 30+ year periods where stocks either underperformed compared to bonds, or even lost value in absolute terms.  This suggests that it may be an overgeneralization to assume that they always do well in the long term.  Furthermore, it may suggest that they are persistently overvalued for the risk, and perhaps due for a long-term correction.  (If everybody assumes they're safe, the equity risk premium is likely to be eaten up.) Putting all of your money into them would, for most people, be taking an unnecessary risk.  You should cover some other asset classes too.  If stocks do very well, a portfolio with some allocation to more stable assets will still do fairly well.  If they crash, a portfolio with less risky assets will have a better chance of being at least adequate. What is the importance or benefit of the assumption that high-risk is preferable for younger people/investors instead of older people? Law of averages most high risk investments [stocks for examples, including Mutual funds]. Take any stock market [some have data for nearly 100 years] on a 15 year or 30 years horizon, the year on year growth is around 15 to 18 percentage. Again depends on which country, market etc ... Equally important every stock market in the same 15 year of 30 year time, if you take specific 3 year window, it would have lost 50% or more value. As one cannot predict for future, someone who is 55 years, if he catches wrong cycle, he will lose 50%. A young person even if he catches the cycle and loses 50%, he can sit tight as it will on 30 years average wipe out that loss. These scenarios discuss the period to 2025. They assess the deep uncertainty that is paralysing decision-taking. They identify the roots of this as the failure of the social model on which the West has operated since the 1920s. Related and pending problems imply that this situation is not recoverable without major change: for example, pensions shortfalls are greater in real terms that entire expenditure on World War II, and health care and age support will treble that. Due to the prolonged recession, competition will impact complex industries earlier than expected.  Social responses which seek job protection, the maintenance of welfare and also support in old age will tear at the social fabric of the industrial world. There are ways to meet this, implying a major change in approach, and a characteristic way in which to fail to respond to it in time, creating a dangerous and unstable world. The need for such change will alter the social and commercial environment very considerably. The absence of such change will alter it even more.  The summary is available [here](http://www.chforum.org/scenario2012/paper-4-6.shtml) or at the foot of the link given in the header. The much richer paper is [here](http://www.chforum.org/scenario2012/paper-4-1.shtml).  These scenarios are the latest in a series in a project that dates back to 1995. Over a hundred people participated from every continent, over a six month period. The working documents are available on the web. "Some thoughts on your questions in order, Duration: You might want to look at the longest-dated option (often a ""LEAP""), for a couple reasons. One is that transaction costs (spread plus commission, especially spread) are killer on options, so a longer option means fewer transactions, since you don't have to keep rolling the option. Two is that any fundamentals-based views on stocks might tend to require 3-5 years to (relatively) reliably work out, so if you're a fundamental investor, a 3-6 month option isn't great. Over 3-6 months, momentum, short-term news, short squeezes, etc. can often dominate fundamentals in determining the price. One exception is if you just want to hedge a short-term event, such as a pending announcement on drug approval or something, and then you would buy the shortest option that still expires after the event; but options are usually super-expensive when they span an event like this. Strike: Strike price on a long option can be thought of as a tradeoff between the max loss and minimizing ""insurance costs."" That is, if you buy a deeply in-the-money put or call, the time value will be minimal and thus you aren't paying so much for ""insurance,"" but you may have 1/3 or 1/2 of the value of the underlying tied up in the option and subject to loss. If you buy a put or call ""at the money,"" then you might have only say 10% of the value of the underlying tied up in the option and subject to loss, but almost the whole 10% may be time value (insurance cost), so you are losing 10% if the underlying stock price stays flat. I think of the deep in-the-money options as similar to buying stocks on margin (but the ""implied"" interest costs may be less than consumer margin borrowing rates, and for long options you can't get a margin call). The at-the-money options are more like buying insurance, and it's expensive. The commissions and spreads add significant cost, on top of the natural time value cost of the option. The annual costs would generally exceed the long-run average return on a diversified stock fund, which is daunting. Undervalued/overvalued options, pt. 1: First thing is to be sure the options prices on a given underlying make sense at all; there are things that ""should"" hold, for example a synthetic long or short should match up to an actual long or short. These kinds of rules can break, for example on LinkedIn (LNKD) after its IPO, when shorting was not permitted, the synthetic long was quite a bit cheaper than a real long. Usually though this happens because the arbitrage is not practical. For example on LNKD, the shares to short weren't really available, so people doing synthetic shorts with options were driving up the price of the synthetic short and down the price of the synthetic long. If you did actually want to be long the stock, then the synthetic long was a great deal. However, a riskless arbitrage (buy synthetic long, short the stock) was not possible, and that's why the prices were messed up. Another basic relationship that should hold is put-call parity: http://en.wikipedia.org/wiki/Put%E2%80%93call_parity Undervalued/overvalued options, pt. 2: Assuming the relationship to the underlying is sane (synthetic positions equivalent to actual positions) then the valuation of the option could focus on volatility. That is, the time value of the option implies the stock will move a certain amount. If the time value is high and you think the stock won't move much, you might short the option, while if the time value is low and you think the stock will move a lot, you might buy the option. You can get implied volatility from your broker perhaps, or Morningstar.com for example has a bunch of data on option prices and the implied components of the price model. I don't know how useful this really is though. The spreads on options are so wide that making money on predicting volatility better than the market is pretty darn hard. That is, the spread probably exceeds the amount of the mispricing. The price of the underlying is more important to the value of an option than the assumed volatility. How many contracts: Each contract is 100 shares, so you just match that up. If you want to hedge 100 shares, buy one contract. To get the notional value of the underlying multiply by 100. So say you buy a call for $30, and the stock is trading at $100, then you have a call on 100 shares which are currently priced at $10,000 and the option will cost $30*100=3,000. You are leveraged about 3 to 1. (This points to an issue with options for individual investors, which is that one contract is a pretty large notional value relative to most portfolios.)" There's probably a risk committee and an investment committee where several high level executives analyze and discuss the investments they will do and which risk level to take.  Is all based on numbers and evidence, but in the end people decide how much risk to take.  Then there Risk Management I suppose supervises the risk and that they don't go over the threshold (measured by VAR or whatever) I use two measures to define investment risk: What's the longest period of time over which this investment has had negative returns? What's the worst-case fall in the value of this investment (peak to trough)? I find that the former works best for long-term investments, like retirement. As a concrete example, I have most of my retirement money in equity, since the Sensex has had zero returns over as long as a decade. Since my investment time-frame is longer, equity is risk-free, by this measure. For short-term investments, like money put aside to buy a car next year, the second measure works better. For this purpose, I might choose a debt fund that isn't the safest, and has had a worst-case 8% loss over the past decade. I can afford that loss, putting in more money from my pocket to buy the car, if needed. So, I might choose this fund for this purpose, taking a slight risk to earn higher return. In any case, how much money I need for a car can only be a rough guess, so having 8% less than originally planned may turn out to be enough. Or it may turn out that the entire amount originally planned for is insufficient, in which case a further 8% shortfall may not be a big deal. These two measures I've defined are simple to explain and understand, unlike academic stuff like beta, standard deviation, information ratio or other mumbo-jumbo. And they are simple to apply to a practical problem, as I've illustrated with the two examples above. On the other hand, if someone tells me that the standard deviation of a mutual fund is 15%, I'll have no idea what that means, or how to apply that to my financial situation. All this suffers from the problem of being limited to historical data, and the future may not be like the past. But that affects any risk statistic, and you can't do better unless you have a time machine. First, you need to understand how modern insurance companies operate. On the front end, they write contracts with customers, collecting up front premiums, and promising to pay out to cover future losses. Efficient premiums cover exactly what's paid out; if you charge too much customers leave for competition, and if you charge too little the company goes under, or at least loses money. Large armies of people are employed to accurately guess future risks, hopefully to the point of certainty you have in human mortality.  So over time, they will pay back those premiums. And there's a constant stream of new premiums coming in to replace money going out. So there's this effective pool of money they can use to buffer against large losses with; it's called float. And when the pool of money remains relatively constant, they can invest it longer term than the people who comprise the underlying risk. Large insurance companies like Berkshire Hathaway function in this manner; it's where Warren Buffet finds capital to invest while hiding from Wall St in Nebraska. The way these companies profit is by making sure the equation works:  Profits = Premiums - Payouts + Return on float Payouts could be just payments for insured risk. But they could also be for the whole life insurance you're running across from time to time. These contracts offer the insured the chance to invest their money with the people who invest the float. And as long as the return on float is greater than the return they're offering, it's still profitable for the company. Since this guarantees suboptimal returns for you, it's usually a good idea to buy term insurance (much cheaper) and invest the difference yourself. The obvious risk is that you might buy at a time when the market is particularly high.  Of course, you won't know that is the case until afterwards. A common way to reduce that risk is dollar cost averaging, where you buy gradually over a period of time. I don't think you can always assume a 12-month time horizon.  Sometimes, the analyst's comments might provide some color on what kind of a time horizon they're thinking of, but it might be quite vague. That's not true - insurance companies can manage that risk and look to Re-insure that risk with very large pools of risk capital through reinsurance.   Government agencies traditionally have not looked to buy insurance but are now starting to insure such catastrophic risks.  I believe the NFIP has some sort of excess risk cover such that if losses are greater than $500 million, then it triggers a payout from large private insurers. "Forecasts of stock market direction are not reliable, so you shouldn't be putting much weight on them.  Long term, you can expect to do better in stocks, but obtaining this better expected return has the danger of ""buying in"" to the market at a particularly bad moment, leading to a substantially lower return.  So mitigate that risk while moving in a big piece of cash by ""dollar cost averaging"".  An example would be to divide your cash hoard (conceptually) into say six pieces, and invest each piece in the index fund two months apart.  After a year you will have invested the whole sum at about the average of the index for the year."