What is the rate of return for a security when there is no risk-free rate (CAPM)?
"For starters, the risk-free rate has nothing to do with stocks.  It would be independent of anything.  It pays out the same return in all states of nature.  The definition of a risk-free asset is that regardless of how the universe turns out, including a meteor striking the Earth killing everyone but the recipient, then the payout would happen exactly as planned.  One could imagine a computer still being on, connected to a power supply and printing a check.  Most people use the 90-day t-bill as the risk-free rate.  A beta greater than one implies it is more volatile than the market, not that it moves more perfectly. The CAPM should not be used for this.  Cryptocurrencies should not be used with this model because they have valuation dynamics related to the new issue of coins.  In other words, they have non-market price movements as well as market price movements. In general, you should not use the CAPM because it doesn't work empirically.  It is famous, but it is also wrong.  A scientific hypothesis that is not supported by the data is a bad idea.  My strong recommendation is that you read ""The Intelligent Investor,"" by Benjamin Graham.  It was last published in 1972, and it is still being printed.  I believe Warren Buffett wrote the current forward for it.  Always go where the data supports you and never anywhere else, no matter how elegant. Finally, unless you are doing this like a trip to Vegas, for fun and willing to take the losses, I would avoid cryptocurrencies because you don't know what you are doing yet.  It is obvious from the posting.  I have multiple decades working in every type of financial institution and at every level, bottom to top.  I also have a doctorate, and I am an incredible researcher.  I am professionally qualified in three different disciplines. If you want to learn how to do this, start with the ""Intelligent Investor.""  Get a basic book on accounting and learn basic accounting.  Pick up economics textbooks at least through ""Intermediate"" for both microeconomics and macroeconomics.  Get William Bolstad's book ""Introduction to Bayesian Statistics.""  You will need them for reasons that go very far beyond this post.  Trust me; you want to master that book.  Find a statistician and ask them to teach it to you as a special topics course.  It will help you as both either a Marine officer or a Naval officer.  Then after that pick up a copy of ""Security Analysis.""  Either the 1943 copy (yes it is in print) by Benjamin Graham if you feel good about accounting, or the 1987 copy by Cottle under the Graham/Dodd imprimatur.  Then, if you are still interested in cryptocurrencies and they will be blasé by then, then pick up an economics textbook on money.  If I were you, I would learn about Yap money, commodity money, and prison money first, then you might understand why a cryptocurrency may not be an investment for you."
"A kid can lose everything he owns in a crap shoot and live. But a senior citizen might not afford medical treatment if interest rates turn and their bonds underperform. In modern portfolio theory, risk/""aggression"" is measured by beta and you get more return by increasing risk. Risk-adjusted return is measured by the Sharpe ratio and the efficient frontier shows how much return you get for each level of risk. For simplicity, we will assume that choosing beta is the only investment choice you make. You are buying a house tomorrow all cash, you should set aside that much in liquid assets today. (Return = who cares, Beta = 0) Your kids go to college in 5 years, so you invest funds now with a 5 year investment horizon to produce, with a reasonable level of certainty, the needed cash then. (Beta = low) You wish to leave money in your estate. Invest for the highest return with a horizon of your lifetime. (Return = maximum, Beta = who cares) In other words, you set risk based on how important your expenses are now or later. And your portfolio is a weighted average. On paper, let's say you have sold yourself into indentured servitude. In return you have received a paid-up-front annuity which pays dividends and increases annually. For someone in their twenties: This adds up to a present value of $1 million. When young, the value of lifetime remaining wages is high. It is also low risk, you will probably find a job eventually in any market condition. If your portfolio is significantly smaller than $1 million this means that the low risk of future wages pulls down your beta, and therefore: Youth invest aggressively with available funds because they compensate large, low-risk future earnings to meet their desired risk appetite." Are you geometrically linking the spot rates for each spot period over of the next year? I.e. are you looking at the spot strip, or just taking today's spot rate and annualizing it?  If you are looking at the spot strip, then a YTM for a bond maturing in one year should equal the return from investing in rolling one month spot rates for the next year - more or less. If this variance is large, then there is scope for arbitrage. Nobody is going to buy a stock without returns.  However, returns are dividends + capital gains.  So long as there is enough of the latter it doesn't matter if there is none of the former. Consider:  Berkshire Hathaway--Warren Buffet's company.  It has never paid dividends.  It just keeps going up because Warren Buffet makes the money grow.  I would expect the price to crash if it ever paid dividends--that would be an indication that Warren Buffet couldn't find anything good to do with the money and thus an indication that the growth was going to stop. Disclaimer: I don't work in the finance industry, and simply took a few classes in corporate finance and management during my undergrad.  It depends on what type of investing you're talking about. If you're talking about building a portfolio of securities, then CAPM is the basis for most valuation models. Generally, CAPM will have you discount based on your best available risk-free rate (usually t-bills or some other fixed income source with a reliable backer). Even after your valuation, the basic theory of risk management for an investment portfolio is still to maintain a diverse basket of poorly correlated products.  If you're talking about corporate finance where a firm is considering an investment such as a new project, then a determining a WACC and using it as a discount rate for your cash flow is a basic strategy.   This is a basic strategy, but there are better ones depending on the specifics of the investment. This is where evaluating exposures is important. To hedge counterparty risk, you might discount by the estimated probability of non-payment or buy trade insurance. To hedge currency risk, you might buy forwards, options, or look into a money market hedge. To hedge political risks like repatriation or changes in tax laws or regulation you might buy political risk insurance. To hedge exposure to a particular commodity price, you can trade futures. "A stock, at its most basic, is worth exactly what someone else will pay to buy it right now (or in the near future), just like anything else of value. However, what someone's willing to pay for it is typically based on what the person can get from it. There are a couple of ways to value a stock. The first way is on expected earnings per share, most of would normally (but not always) be paid in dividends. This is a metric that can be calculated based on the most recently reported earnings, and can be estimated based on news about the company or the industry its in (or those of suppliers, likely buyers, etc) to predict future earnings. Let's say the stock price is exactly $100 right now, and you buy one share. In one quarter, the company is expected to pay out $2 per share in dividends. That is a 2% ROI realized in 3 months. If you took that $2 and blew it on... coffee, maybe, or you stuffed it in your mattress, you'd realize a total gain of $8 in one year, or in ROI terms an annual rate of 8%. However, if you reinvested the money, you'd be making money on that money, and would have a little more. You can calculate the exact percentage using the ""future value"" formula. Conversely, if you wanted to know what you should pay, given this level of earnings per share, to realize a given rate of return, you can use the ""present value"" formula. If you wanted a 9% return on your money, you'd pay less for the stock than its current value, all other things being equal. Vice-versa if you were happy with a lesser rate of return. The current rate of return based on stock price and current earnings is what the market as a whole is willing to tolerate. This is how bonds are valued, based on a desired rate of return by the market, and it also works for stocks, with the caveat that the dividends, and what you'll get back at the ""end"", are no longer constant as they are with a bond. Now, in your case, the company doesn't pay dividends. Ever. It simply retains all the earnings it's ever made, reinvesting them into doing new things or more things. By the above method, the rate of return from dividends alone is zero, and so the future value of your investment is whatever you paid for it. People don't like it when the best case for their money is that it just sits there. However, there's another way to think of the stock's value, which is it's more core definition; a share of the company itself. If the company is profitable, and keeps all this profit, then a share of the company equals, in part, a share of that retained earnings. This is very simplistic, but if the company's assets are worth 1 billion dollars, and it has one hundred million shares of stock, each share of stock is worth $10, because that's the value of that fraction of the company as divided up among all outstanding shares. If the company then reports earnings of $100 million, the value of the company is now 1.1 billion, and its stock should go up to $11 per share, because that's the new value of one ten-millionth of the company's value. Your ROI on this stock is $1, in whatever time period the reporting happens (typically quarterly, giving this stock a roughly 4% APY). This is a totally valid way to value stocks and to shop for them; it's very similar to how commodities, for instance gold, are bought and sold. Gold never pays you dividends. Doesn't give you voting rights either. Its value at any given time is solely what someone else will pay to have it. That's just fine with a lot of people right now; gold's currently trading at around $1,700 an ounce, and it's been the biggest moneymaker in our economy since the bottom fell out of the housing market (if you'd bought gold in 2008, you would have more than doubled your money in 4 years; I challenge you to find anything else that's done nearly as well over the same time). In reality, a combination of both of these valuation methods are used to value stocks. If a stock pays dividends, then each person gets money now, but because there's less retained earnings and thus less change in the total asset value of the company, the actual share price doesn't move (much). If a stock doesn't pay dividends, then people only get money when they cash out the actual stock, but if the company is profitable (Apple, BH, etc) then one share should grow in value as the value of that small fraction of the company continues to grow. Both of these are sources of ROI, and both are seen in a company that will both retain some earnings and pay out dividends on the rest." "The key is to look at total return, that is dividend yields plus capital growth. Some stocks have yields of 5%-7%, and no growth. In that case, you get the dividends, and not a whole lot more. These are called dividend stocks. Other stocks pay no dividends. But if they can grow at 15%-20% a year or more, you're fine.These are called growth stocks. The safest way is to get a ""balanced"" combination of dividends and growth, say a yield of 3% growing at 8%-10% a year, for a total return of 11%-13%. meaning that you get the best of both worlds.These are called dividend growth stocks." No citation, but I once read the average holding period of a 30 yr treasury is 8 hours. A rise in the rate by just .1% will drop the value by just under 2% wiping out nearly a full year's gains. With 29 years to go the value of the 3% bond will be worth $981 if the rate were then 3.1% It's at 3.16% the bond would drop to exactly $970 after the year, i.e. you've gotten no return at all.  I view this as pretty high risk. "I recommend you take a look at this lecture (really, the whole series is enlightening), from Swenson. He identifies 3 sources of returns: diversification, timing and selection. He appears to discard timing and selection as impossible. A student kinda calls him out on this. Diversification reduces risk, not increase returns. It turns out they did time the market, by shorting .com's before the bubble, and real estate just before the downturn. In 1990, Yale started a ""Absolute Return"" unit and allocated like 15 percent to it, mostly by selling US equities, that specializes in these sorts of hedging moves. As for why you might employ managers for specific areas, consider that the expense ratio Wall Street charges you or me still represent a very nice salary when applied to the billions in Yale's portfolio. So they hire internally to reduce expenses, and I'm sure they're kept busy. They also need people to sell off assets to maintain ratios, and figuring out which ones to sell might take specialized knowledge. Finally, in some areas, you functionally cannot invest without management. For example, Yale has a substantial allocation in private equity, and by definition that doesn't trade on the open market. The other thing you should consider is that for all its diversification, Yale lost 25 percent of their portfolio in 2009. For a technique that's supposed to reduce volatility, they seem to have a large range of returns over the past five years." Your question is a complex one because knowledge of the investor's beliefs about the market is required.  For almost any quantitative portfolio, one must have a good estimate of the expected return vector and covariance matrix of the assets in question.  The expected return vector, in particular, is far from estimable.  No one agrees on it and there is no way to know who is right and who is wrong. In a world satisfying the conditions of the CAPM, you can bypass this problem because the main implication of the CAPM is that the market weights are optimal.  In that case the answer to your question is that you should determine the market weights of the various assets and use those along with saving in a risk-free account or borrowing, depending on your risk tolerance.  This portfolio has the added benefit that you don't need to rebalance much...the weights in your portfolio adjust at the same rate as the market weights. Any portfolio that has something besides this also includes some notion of expected return aside from CAPM fair pricing.  The question for you, then, is whether you have such a notion.  If you do, you can mix your information with the market weights to come up with a portfolio.  This is what the Black-Litterman method does, for example: get the expected return vector implied by market weights and the covariance matrix, mix with your expected return vector, then use mean-variance optimization to come up with your final weights. 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. The CCAPM attempts to link asset prices/equity risk premiums to the 'intertemporal substitution of consumption' instead of the normal beta. So essentially what it's trying to say is you prefer to smooth consumption, you hate volatile consumption patterns, therefore you demand higher returns in booms and will settle for lower returns in downturns. (It may sound counter-intuitive at first, but think in terms of marginal utilities, in booms your marginal utility is lower as you're already well off, therefore you demand more of an asset).   The CCAPM tries to link asset prices to real economic theory (consumption) whereas CAPM is derived from the assumption that investors only care about mean and variance of returns (no real link to the real side of the economy).   There are almost no real world applications for the CCAPM. Empirically it is almost a complete failure, complex extensions have only gotten it so far, see the 'equity premium puzzle' by Mehra and Prescott (1985). "I'm not familiar with the Dupire model; I'll have to take a look at (it sounds cool though).  I think that all arbitrage-free models are ""incomplete"" in the sense that they don't say, ""This is a price that doesn't imply any arbitrage opportunities *anywhere*,"" but instead say, ""This is a price that doesn't imply any arbitrage opportunities within a specific set of securities.""  What set you're using will vary from one model to another, and I'd say (although other people might reasonably disagree) that taking a volatility structure as given is as much no-arbitrage as taking a term structure as given.  As a side note, I'd say that what (theoretically) distinguishes an equilibrium model is that you're supposed to *know* the parameters, not guess at them or observe them from the real world.  By that definition, a really complete CAPM or Black-Scholes would explain how to derive the correct beta or volatility from fundamental analysis.  Also, I've upvoted you elsewhere for some really good comments you made about intrinsic value." It depends how much risk you're prepared to accept. The short-term risk-free rate of return at present is something in the vicinity of 0.1% (three month US treasuries are currently yielding 0.08%), so anything paying a higher rate on money that's accessible quickly will involve some degree of risk -- the higher the rate then the higher the risk. I think I may have gotten my reasoning backwards, since beta can be thought of as just the quantification of the relationship in prices but in itself isn't the actual reason behind them.  Risk free are things such as Treasury bonds/bills. You made 94$ on an investment of 554.80 *100 = 55480$ for an approx holding period of 1 year. So the % return is ~0.16%, which is not much better than the short term us treasury rate. The current 1 year treasury rate is 0.27%: http://ycharts.com/indicators/1_year_treasury_rate So yes, you have a risk free portfolio, so you make the risk free rate. Remember this is an European option, so you are stuck for 1 year. if you found the same mispricing in an American option, then you found an arbitrage.