Is there a return-on-investment vs risk graph anywhere?
"There may well be several such graphs, I expect googling will turn them up; but the definition of risk is actually quite important here. My definition of risk might not be quite the same as yours, so the relative risk factors would be different. For example: in general, stocks are more risky than bonds.  But owning common shares in a blue-chip company might well be less risky than owning bonds from a company teetering on the edge of bankruptcy, and no single risk number can really capture that. Another example: while I can put all my money in short-term deposits, and it is pretty ""safe"", if it grows at 1% so that my investment portfolio cannot fund my retirement, then I have a risk that I will run out of money before I shuffle off this mortal coil.  How to capture that ""risk"" in a single number? So you will need to better define your parameters before you can prepare a visual aid. Good Luck" "Yes, there is a very good Return vs Risk graph put out at riskgrades.com.  Look at it soon, because it will be unavailable after 6-30-11.  The RA (return analysis) graph is what I think you are looking for. The first graph shown is an ""Average Return"", which I was told was for a 3 year period.  Three period returns of 3, 6 and 12 months, are also available.  You can specify the ticker symbols of funds or stocks you want a display of.  For funds, the return includes price and distributions (total return), but only price movement for stocks - per site webmaster. I've used the graphs for a few years, since Forbes identified it as a ""Best of the Web"" site.  Initially, I found numerous problems with some of the data and was able to work with the webmaster to correct them.  Lately though, they have NOT been correcting problems that I bring to their attention.  For example, try the symbols MUTHX, EDITX, AWSHX and you'll see that the Risk Grades on the graphs are seriously in error, and compress the graph results and cause overwriting and poor readability. If anyone knows of a similar product, I'd like to know about it.  Thanks,  George"
"Answering this question is weird, because it is not really precise in what you mean. Do you want all stocks in the US? Do you want a selection of stocks according to parameters?  Do you just want a cool looking graph? However, your possible misuse of the word derivative piqued my interest. Your reference to  gold and silver seems to indicate that you do not know what a derivative actually is. Or what it would do in a portfolio.  The straightforward way to ""see"" an efficient frontier is to do the following. For a set of stocks (in this case six ""randomly"" selected ones):      library(quantmod)  library(fPortfolio)  library(PerformanceAnalytics)     getSymbols(c(""STZ"", ""RAI"", ""AMZN"", ""MSFT"", ""TWX"", ""RHT""), from = ""2012-06-01"", to = ""2017-06-01"")     returns &lt;- NULL  tickerlist &lt;- c(""STZ"", ""RAI"", ""AMZN"", ""MSFT"", ""TWX"", ""RHT"")  for (ticker in tickerlist){   returns &lt;- cbind(returns, monthlyReturn(Ad(eval(as.symbol(ticker)))))  }  colnames(returns) &lt;- tickerlist  returns &lt;- as.timeSeries(returns)    frontier &lt;- portfolioFrontier(returns)  png(""frontier.png"", width = 800, height = 600)  plot(frontier, which = ""all"")  dev.off()    minvariancePortfolio(returns, constraints = ""LongOnly"")    Portfolio Weights:    STZ    RAI   AMZN   MSFT    TWX    RHT   0.1140 0.3912 0.0000 0.1421 0.1476 0.2051     Covariance Risk Budgets:    STZ    RAI   AMZN   MSFT    TWX    RHT   0.1140 0.3912 0.0000 0.1421 0.1476 0.2051     Target Returns and Risks:   mean    Cov   CVaR    VaR   0.0232 0.0354 0.0455 0.0360    https://imgur.com/QIxDdEI  The minimum variance portfolio of these six assets has a mean return is 0.0232 and variance is 0.0360. AMZN does not get any weight in the portfolio.  It kind of means that the other assets span it and it does not provide any additional diversification benefit.   Let us add two ETFs that track gold and silver to the mix, and see how little difference it makes:    getSymbols(c(""GLD"", ""SLV""), from = ""2012-06-01"", to = ""2017-06-01"")    returns &lt;- NULL  tickerlist &lt;- c(""STZ"", ""RAI"", ""AMZN"", ""MSFT"", ""TWX"", ""RHT"", ""GLD"", ""SLV"")  for (ticker in tickerlist){   returns &lt;- cbind(returns, monthlyReturn(Ad(eval(as.symbol(ticker)))))  }  colnames(returns) &lt;- tickerlist  returns &lt;- as.timeSeries(returns)   frontier &lt;- portfolioFrontier(returns)    png(""weights.png"", width = 800, height = 600)  weightsPlot(frontier)  dev.off()    # Optimal weights  out &lt;- minvariancePortfolio(returns, constraints = ""LongOnly"")  wghts &lt;- getWeights(out)  portret1 &lt;- returns%*%wghts  portret1 &lt;- cbind(monthprc, portret1)[,3]  colnames(portret1) &lt;- ""Optimal portfolio""    # Equal weights  wghts &lt;- rep(1/8, 8)  portret2 &lt;- returns%*%wghts  portret2 &lt;- cbind(monthprc, portret2)[,3]  colnames(portret2) &lt;- ""Equal weights portfolio""   png(""performance_both.png"", width = 800, height = 600)  par(mfrow=c(2,2))  chart.CumReturns(portret1, ylim = c(0, 2))  chart.CumReturns(portret2, ylim = c(0, 2))  chart.Drawdown(portret1, main = ""Drawdown"", ylim = c(-0.06, 0))  chart.Drawdown(portret2, main = ""Drawdown"", ylim = c(-0.06, 0))  dev.off()   https://imgur.com/sBHGz7s   Adding gold changes the minimum variance mean return to 0.0116 and the variance stays about the same 0.0332. You can see how the weights change at different return and variance profiles in the picture.  The takeaway is that adding gold decreases the return but does not do a lot for the risk of the portfolio.  You also notice that silver does not get included in the minimum variance efficient portfolio (and neither does AMZN).  https://imgur.com/rXPbXau  We can also compare the optimal weights to an equally weighted portfolio and see that the latter would have performed better but had much  larger drawdowns. Which is because it has a higher volatility, which might be undesirable.  ---  Everything below here is false, but illustrative.  So what about the derivative part? Let us assume you bought an out of the money call option with a strike of 50 on MSFT at the beginning of the  time series and held it to the end.  We need to decide on the the annualized cost-of-carry rate, the annualized rate of interest, the time to maturity is measured in years, the annualized  volatility of the underlying security is proxied by the historical volatility.   library(fOptions)   monthprc &lt;- Ad(MSFT)[endpoints(MSFT, ""months"")]  T &lt;- length(monthprc) # 60 months, 5 years  vol &lt;- sd(returns$MSFT)*sqrt(12) # annualized volatility    optprc &lt;- matrix(NA, 60, 1)  for (t in 1:60) {   s &lt;- as.numeric(monthprc[t])   optval &lt;- GBSOption(TypeFlag = ""c"", S = s, X = 50, Time = (T - t) / 12, r = 0.001, b = 0.001, sigma = vol)   optprc[t] &lt;- optval@price  }    monthprc &lt;- cbind(monthprc, optprc)  colnames(monthprc) &lt;- c(""MSFT"", ""MSFTCall50"")    MSFTCall50rets &lt;- monthlyReturn(monthprc[,2])  colnames(MSFTCall50rets) &lt;- ""MSFTCall50rets""    returns &lt;- merge(returns, MSFTCall50rets)    wghts &lt;- rep(1/9, 9)    portret3 &lt;- returns%*%wghts  portret3 &lt;- cbind(monthprc, portret3)[,3]  colnames(portret3) &lt;- ""Equal weights derivative portfolio""    png(""performance_deriv.png"", width = 800, height = 600)  par(mfrow=c(2,2))  chart.CumReturns(portret2, ylim = c(0, 4.5))  chart.CumReturns(portret3, ylim = c(0, 4.5))  chart.Drawdown(portret2, main = ""Drawdown"", ylim = c(-0.09, 0))  chart.Drawdown(portret3, main = ""Drawdown"", ylim = c(-0.09, 0))  dev.off()  https://imgur.com/SZ1xrYx   Even though we have a massively profitable instrument in the derivative. The portfolio analysis does not include it  because of the high volatility. However, if we just use equal weighting and essentially take a massive position in  the out of the money call (which would not be possible in real life), we get huge drawdowns and volatility, but  the returns are almost two fold. But nobody will sell you a five year call.  Others can correct any mistakes or misunderstandings in the above. It hopefully gives a starting point.  Read more at:   https://en.wikipedia.org/wiki/Modern_portfolio_theory https://en.wikipedia.org/wiki/Option_(finance)  The imgur album:  https://imgur.com/a/LoBEY" "You could use any of various financial APIs (e.g., Yahoo finance) to get prices of some reference stock and bond index funds.  That would be a reasonable approximation to market performance over a given time span. As for inflation data, just googling ""monthly inflation data"" gave me two pages with numbers that seem to agree and go back to 1914.  If you want to double-check their numbers you could go to the source at the BLS. As for whether any existing analysis exists, I'm not sure exactly what you mean.  I don't think you need to do much analysis to show that stock returns are different over different time periods." Other answers here explain very well the intent of your question. However, a word should be said about why people make different choices at all. So to directly answer your question, yes there is a theory but it does not say inaction is worse/better and instead explains why different people make different choices and how this information can be used to construct optimal portfolios for a specific individual. And that theory is called the Risk Aversion Theory. You can visit the following URLs to discover more about this theory: From a mathematical expected-value standpoint, there is no difference between gambling (e.g. buying a lottery ticket) and investing (e.g. buying a share of stock).  The former probably has negative expected value while the latter probably has positive expected value, but that is not a distinction to include in a definition (else every company that gives a bad quarterly earnings report suddenly changes categories). However, investment professionals have a vested interest in claiming there is a difference; that justifies them charging fees to steer you into the right investment.  Consequently, hair-splitting ideas like the motive behind a purchase are introduced.  The classification of an item to be purchased should not depend on the mental state of its purchaser. Depending on the situation, it may be right to engage in negative EV behavior.  For example, if you have $1000 and need $2000 by next week or else you can't have an operation and you will die (and you can't find anyone to give you a loan).  Your optimal strategy is to gamble your $1000, at the best odds you can get, with a possible outcome of $2000.  So even if you only have a 1/3 chance of winning and getting that operation, it's still the right bet if you can't find a better one. The short answer is that you would want to use the net inflow or net outflow, aka profit or loss.   In my experience, you've got a couple different uses for IRR and that may be driving the confusion.  Pretty much the same formula, but just coming at it from different angles.   Thinking about a stock or mutual fund investment, you could project a scenario with an up-front investment (net outflow) in the first period and then positive returns (dividends, then final sale proceeds, each a net inflow) in subsequent periods.  This is a model that more closely follows some of the logic you laid out. Thinking about a business project or investment, you tend to see more complicated and less smooth cashflows.  For example, you may have a large up-front capital expenditure in the first period, then have net profit (revenue less ongoing maintenance expense), then another large capital outlay, and so on.   In both cases you would want to base your analysis on the net inflow or net outflow in each period.  It just depends on the complexity of the cashflows trend as to whether you see a straightforward example (initial payment, then ongoing net inflows), or a less straightforward example with both inflows and outflows.   One other thing to note - you would only want to include those costs that are applicable to the project.  So you would not want to include the cost of overhead that would exist even if you did not undertake the project. "Mint.com does this quite well. The graph views of your budgets, investments, debts, and other aspects of your financial life can be shown in gestalt, or on a per-account basis (at least, it does for me). See the investment ""how it works"" page for more information.  ""Find out whether you're beating the market–or it's beating you. Compare your portfolio to market benchmarks, and instantly see your asset allocation across all your investment accounts: 401k, mutual funds, brokerage accounts, even IRAs.""" "not sure if I will help or just spread more gibberish but maybe the first concept I'd look at is risk tolerance.  Risk tolerance is discerning your ability to risk losing money to get better results.  So you know the saying ""the higher the risk the higher the reward""?  The way most people are going to operate is somewhere on the midpoint of behavior - not doing the riskiest thing, but not doing the very most cautious thing either.  So given that concept, some investments will be more appealing given different economic scenarios.  Typically stocks are going to reward your investment a little more aggressively than a treasury bond if the economy is humming along.  This drives prices of treasuries lower, stock yields higher.  In a crappy economy, people want to move their money into conservative investments like a treasury bond. Bond prices rise while stock prices dip.    If you google 'correlations between the market prices of stocks and the market prices of Treasury bonds' you will find plenty of helpful and hopefully not too convoluted articles a la http://finance.zacks.com/correlation-treasuries-stocks-10871.html Don't get freaked out by graphs, the graphs are just a way to put into a picture that correlation." The Investopedia article you linked to is a good start. Its key takeaway is that you should always consider risk-adjusted return when evaluating your portfolio. In general, investors seeking a higher level of return must face a higher likelihood of taking a loss (risk). Different types of stocks (large vs small; international vs US; different industry sectors) have different levels of historical risk and return. Not to mention stocks vs bonds or other financial instruments... So, it's key to make an apples-to-apples comparison against an appropriate benchmark. A benchmark will tell you how your portfolio is doing versus a comparable portfolio. An index, such as the S&P 500, is often used, because it tells you how your portfolio is doing compared against simply passively investing in a diversified basket of securities. First, I would start with analyzing your portfolio to understand its asset allocation. You can use a tool like the Morningstar X-Ray to do this. You may be happy with the asset allocation, or this tool may inform you to adjust your portfolio to meet your long-term goals. The next step will be to choose a benchmark. Given that you are investing primarily in non-US securities, you may want to pick a globally diversified index such as the Dow Jones Global Index. Depending on the region and stock characteristics you are investing in, you may want to pick a more specialized index, such as the ones listed here in this WSJ list. With your benchmark set, you can then see how your portfolio's returns compare to the index over time. IRR and ROI are helpful metrics in general, especially for corporate finance, but the comparison-based approach gives you a better picture of your portfolio's performance. You can still calculate your personal IRR, and make sure to include factors such as tax treatment and investment expenses that may not be fully reflected by just looking at benchmarks. Also, you can calculate the metrics listed in the Investopedia article, such as the Sharpe ratio, to give you another view on the risk-adjusted return. https://www.hussmanfunds.com/wmc/wmc171009m.png  &gt;The following charts will provide a sense of where the U.S. equity market currently stands. The first chart shows our margin-adjusted CAPE, which as noted above has a correlation of about -0.89 with actual subsequent market returns across U.S. market cycles since the 1920’s.  https://www.hussmanfunds.com/wmc/wmc171009.htm  It will turn, downside potential is historic. It has been hinted at in some other answers, but I want to say it explicitly: Volatility is not risk. Volatility is how much an investment goes up and down, risk is the chance that you will lose money. For example, stocks have relatively high volatility, but the risk that you will lose money over a 40 year period is virtually zero (in particular if you invest in index funds). Bonds, on the other hand, have basically no volatility (their cash flow is totally predictable if you trust the future of your government), but there is a significant risk that they will perform worse than stocks over a longer period. So, volatility equals risk only if you are day trading. A 401(k) is literally the opposite of that. For further reading: Never confuse risk and volatility Also, investing is not gambling. Gambling is bad because the odds are stacked against you. You need more than average luck to actually win and the longer you play, the more you will lose. Investing means buying productive capital that will produce further value. The odds are in your favor. Even if you do a moderately bad job at investing, the longer you stay, the more you will win. "they said the expected returns from the stock market are around 7-9%(ish).  (emphasis added) The key word in your quote is expected.  On average ""the market"" gains in the 7-9% range (more if you reinvest dividends), but there's a great deal of risk too, meaning that in any given year the market could be down 20% or be  up 30%. Your student loan, on the other hand, is risk free.  You are guaranteed to pay (lose) 4% a year in interest.  You can't directly compare the expected return of a risk-free asset with the expected return of a risky asset.  You can compare the risks of two assets with equal expected returns, and the expected returns of assets with equal risks, but you can't directly compare returns of assets with different risks.  So in two years, you might be better off if you had invested the money versus paying the loan, or you might be much worse off.  In ten years, your chances of coming out ahead are better, but still not guaranteed. What's confusing is I've heard that if you're investing, you should be investing in both stocks and bonds (since I'm young I wouldn't want to put much in bonds, though). So how would that factor in?  Bonds have lower risk (uncertainty) than stocks, but lower expected returns.  If you invest in both, your overall risk is lower, since sometimes (not always) the gain in stocks are offset by losses in bonds).  So there is value in diversifying, since you can get better expected returns from a diversified portfolio than from a single asset with a comparable amount of risk.  However, there it no risk-free asset that will have a better return than what you're paying in student loan interest." Problem with deciding investments in a company is that you have multiple potential options, each with their projected returns, but each also has some hard-to-estimate risks. A further problem is that these opportunities arrive one-by-one, so you usually cannot compare project A vs. project B to decide which one is better. The internal rate of return is a rule-of-thumb like way to make these decisions. The company board may set an IRR target of e.g. 15%, and each executive will compare their projects against that target. They'll execute only the projects that are projected to give a good return, but some of these projects will end up failing. Thus the real average profit will not be equal to IRR. Important thing is that this target number gives ways to compare projects, and also for the board to control the investments. If the company has a good track record of being successful at projects, the board might set an IRR target of 10% and expect to get e.g. 8% return on their investment. However, if the company has a much larger risk of projects failing, they might demand a predicted IRR of 20% to account for the risk. Ultimately if the IRR target is set too high, the company will find no projects it considers profitable to invest in. In practice if this happens, the company owners are better off taking out the cash as dividends and investing it elsewhere. "Not to state the obvious, but whenever an investment is being made, the ""nuts and bolts"" is your return on investment.  Analyzing the rate of return on an investment is the primary factor in any decision.  Ideally, once the actual mechanics of investment and side ""benefits"" are factored out, the goal is to be able to analyze the pure financial return. Usually the biggest problem faced in analyzing various investments is comparing the Present Value of an investment to a series of payments that may be made or received in the future.  When considering the purchase of a large equity, for example, you might be looking at what series of payments are required to purchase the asset.  You can also reverse this and ask, ""What amount of money is equivalent to this series of payments?"" Ultimately, the Present Value of an Annuity is the way to make these comparisons equal.   Fundamentally, the Present Value of an annuity is an amount of money that should, in theory, be equivalent to a series of payments.  There is, for example, technically no difference between $1064.94 today and $100 a month for a year, at an interest rate of 1% per month.  Grant you, most people would be happier with the money now, but that is what interest does - it compensates you for waiting on your money.   You can fire up a spreadsheet and calculate the Present Value as long as you have the monthly payment, interest rate, and number of periods.  Alternatively, you can calculate any one of those missing four variables - and the key is usually to understand what that rate would be in order to compare the investments. Finally, the taxable implication is really just an adjustment to the rate of return. Imagine the following three scenarios: (Obviously the rates are fictional - the goal is to show they are the same). Scenarios 1 & 2 are really just two sides of the same coin.  Using the Future Value formula in Excel = FV(0.5%, 12, -100), you get $1233.56.  In scenario 1, you would have $1233.56 in your bank account.  In scenario 2, your bank would have $1233.56 from you, and you would have $100 less debt per month.  They are equivalent transactions.   Scenario 3 is really just a variation on scenario 2, localized to the United States.  Because the interest is tax deductible, however, the rate of 6% isn't really accurate.  Assuming you had a 25% tax bracket, you'd actually be getting back one quarter of your interest.  Put another way, 7.5% mortgage interest costs you as much as 6% credit card debt. This is how you compare apples and organges - just turn everything into an annuity or a lump sum, using Present Value calculations.   Finally, quick rule of thumb - if you owe taxes in both Canada and the US, your Canadian taxes are probably higher than your American ones.  As such, any tax incentives will be concomitantly higher.  If you only can only use Canadian tax incentives, then look to those incentives, other things being equal." "The professional financial advisors do have tools which will take a general description of a portfolio and run monte-carlo simulations based on the stock market's historical behavior. After about 100 simulation passes they can give a statistical statement about the probable returns, the risk involved in that strategy, and their confidence in these numbers.  Note that they do not just use the historical data or individual stocks. There's no way to guarantee that the same historical accidents would have occurred that made one company more successful than another, or that they will again. ""Past performance is no guarantee of future results""... but general trends and patterns can be roughly modelled. Which makes that a good fit for those of us buying index funds, less good for those who want to play at a greater level of detail in the hope of doing better. But that's sorta the point; to beat market rate of return with the same kind of statistical confidence takes a lot more work." Modern portfolio theory has a strong theoretical background and its conclusions on the risk/return trade-off have a lot of good supporting evidence.  However, the conclusions it draws need to be used very carefully when thinking about retirement investing.  If you were really just trying to just pick the one investment that you would guess would make you the most money in the future then yes, given no other information, the riskiest asset would be the best one.   However, for most people the goal retirement investing is to be as sure as possible to retire comfortably.  If you were to just invest in a single, very risky asset you may have the highest expected return, but the risk involved would mean there might be a good chance you money may not be there when you need it. Instead, a broad diversified basket of riskier and safer assets leaning more toward the riskier investments when younger and the safer assets when you get closer to retirement tends to be a better fit with most people's retirement goals.  This tends to give (on average) more return when you are young and can better deal with the risk, but dials back the risk later in life when your investment portfolio is a majority of your wealth and you can least afford any major swings.  This combines the lessons of MPT (diversity, risk/return trade-off) in a clearer way with common goals of retirement. Caveat:  Your retirement goals and risk-tolerance may be very different from other peoples'.  It is often good to talk to (fee-only) financial planner.