implementation of risk managed momentum strategy
The paragraph before on page 115 states: Scaling corresponds to having a weight in the long and   short legs that is different from one and varies over time,   but the strategy is still self-financing. Meaning that the long and short positions are no longer equal due to weighting one side more highly than the other. The weighting of one side (either long or short) is the number between 0.2 and 2 that you mention.
"There are two umbrellas in investing: active management and passive management. Passive management is based on the idea ""you can't beat the market."" Passive investors believe in the efficient markets hypothesis: ""the market interprets all information about an asset, so price is equal to underlying value"". Another idea in this field is that there's a minimum risk associated with any given return. You can't increase your expected return without assuming more risk. To see it graphically:   As expected return goes up, so does risk. If we stat with a portfolio of 100 bonds, then remove 30 bonds and add 30 stocks, we'll have a portfolio that's 70% bonds/30% stocks. Turns out that this makes expected return increase and lower risk because of diversification. Markowitz showed that you could reduce the overall portfolio risk by adding a riskier, but uncorrelated, asset! Basically, if your entire portfolio is US stocks, then you'll lose money whenever US stocks fall. But, if you have half US stocks, quarter US bonds, and quarter European stocks, then even if the US market tanks, half your portfolio will be unaffected (theoretically). Adding different types of uncorrelated assets can reduce risk and increase returns.  Let's tie this all together. We should get a variety of stocks to reduce our risk, and we can't beat the market by security selection. Ideally, we ought to buy nearly every stock in the market so that  So what's our solution? Why, the exchange traded fund (ETF) of course! An ETF is basically a bunch of stocks that trade as a single ticker symbol. For example, consider the SPDR S&P 500 (SPY). You can purchase a unit of ""SPY"" and it will move up/down proportional to the S&P 500. This gives us diversification among stocks, to prevent any significant downside while limiting our upside. How do we diversify across asset classes? Luckily, we can purchase ETF's for almost anything: Gold ETF's (commodities), US bond ETF's (domestic bonds), International stock ETFs, Intl. bonds ETFs, etc. So, we can buy ETF's to give us exposure to various asset classes, thus diversifying among asset classes and within each asset class. Determining what % of our portfolio to put in any given asset class is known as asset allocation and some people say up to 90% of portfolio returns can be determined by asset allocation.  That pretty much sums up passive management. The idea is to buy ETFs across asset classes and just leave them. You can readjust your portfolio holdings periodically, but otherwise there is no rapid trading. Now the other umbrella is active management. The unifying idea is that you can generate superior returns by stock selection. Active investors reject the idea of efficient markets.  A classic and time proven strategy is value investing. After the collapse of 07/08, bank stocks greatly fell, but all the other stocks fell with them. Some stocks worth $100 were selling for $50. Value investors quickly snapped up these stocks because they had a margin of safety. Even if the stock didn't go back to 100, it could go up to $80 or $90 eventually, and investors profit. The main ideas in value investing are: have a big margin of safety, look at a company's fundamentals (earnings, book value, etc), and see if it promises adequate return. Coke has tremendous earnings and it's a great company, but it's so large that you're never going to make 20% profits on it annually, because it just can't grow that fast. Another field of active investing is technical analysis. As opposed to the ""fundamental analysis"" of value investing, technical analysis involves looking at charts for patterns, and looking at stock history to determine future paths. Things like resistance points and trend lines also play a role. Technical analysts believe that stocks are just ticker symbols and that you can use guidelines to predict where they're headed.  Another type of active investing is day trading. This basically involves buying and selling stocks every hour or every minute or just at a rapid pace. Day traders don't hold onto investments for very long, and are always trying to predict the market in the short term and take advantage of it. Many individual investors are also day traders.  The other question is, how do you choose a strategy? The short answer is: pick whatever works for you. The long answer is: Day trading and technical analysis is a lot of luck. If there are consistent systems for trading , then people are keeping them secret, because there is no book that you can read and become a consistent trader. High frequency trading (HFT) is an area where people basically mint money, but it s more technology and less actual investing, and would not be categorized as day trading.  Benjamin Graham once said: In the short run, the market is a voting machine but in the long run it is a weighing machine. Value investing will work because there's evidence for it throughout history, but you need a certain temperament for it and most people don't have that. Furthermore, it takes a lot of time to adequately study stocks, and people with day jobs can't devote that kind of time. So there you have it. This is my opinion and by no means definitive, but I hope you have a starting point to continue your study. I included the theory in the beginning because there are too many monkeys on CNBC and the news who just don't understand fundamental economics and finance, and there's no sense in applying a theory until you can understand why it works and when it doesn't." "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?" "...or neither. Even if the overall benefit of X transport system is positive, if there isn't enough concentrated economic need, willingness to pay, and high risk long term investors, it won't generate enough momentum to go forward. This is especially true if sufficient ""I've got mine"" options exist." The issue is the time frame. With a one year investment horizon the only way for a fund manager to be confident that they are not going to lose their shirt is to invest your money in ultra conservative low volatility investments. Otherwise a year like 2008 in the US stock market would break them. Note if you are willing to expand your payback time period to multiple years then you are essentially looking at an annuity and it's market loss rider. Of course those contacts are always structured such that the insurance company is extremely confident that they will be able to make more in the market than they are promising to pay back (multiple decade time horizons). "Investing is always a matter of balancing risk vs reward, with the two being fairly strongly linked.  Risk-free assets generally keep up with inflation, if that; these days advice is that even in retirement you're going to want something with better eturns for at least part of your portfolio. A ""whole market"" strategy is a reasonable idea, but not well defined. You need to decide wheher/how to weight stocks vs bonds, for example, and short/long term. And you may want international or REIT in the mix; again the question is how much. Again, the tradeoff is trying to decide how much volatility and risk you are comfortable with and picking a mix which comes in somewhere around that point -- and noting which assets tend to move out of synch with each other (stock/bond is the classic example) to help tune that. The recommendation for higher risk/return when you have a longer horizon before you need the money comes from being able to tolerate more volatility early on when you have less at risk and more time to let the market recover. That lets you take a more aggressive position and, on average, ger higher returns. Over time, you generally want to dial that back (in the direction of lower-risk if not risk free) so a late blip doesn't cause you to lose too much of what you've already gained... but see above re ""risk free"". That's the theoretical answer. The practical answer is that running various strategies against both historical data and statistical simulations of what the market might do in the future suggests some specific distributions among the categories I've mentioned do seem to work better than others. (The mix I use -- which is basically a whole-market with weighting factors for the categories mentioned above -- was the result of starting with a general mix appropriate to my risk tolerance based on historical data, then checking it by running about 100 monte-carlo simulations of the market for the next 50 years.)" What you may be looking for are multi-manager ETFs; these invest in a basket of diversified funds to get the best out of all of the funds. The problem with multi-manager funds is, of course, that you pay fees twice; once to the fund itself and once to each of the funds in the fund. The low fees on ETFs mean that it is not very profitable to actively maintain one so there are not many around (Googling returns very few). Noting that historic success doesn't guarantee future success and that fees are being applied to fees these funds only really benefit from diversification of manager performance risk. partial source of information and an example of a (non-outperforming) Multi-manager ETF: http://www.etfstrategy.co.uk/advisorshares-sets-date-for-multi-manager-etf-with-charitable-twist-give-53126/ I think your premise is slightly flawed. Every investment can add or reduce risk, depending on how it's used. If your ordering above is intended to represent the probability you will lose your principal, then it's roughly right, with caveats. If you buy a long-term government bond and interest rates increase while you're holding it, its value will decrease on the secondary markets. If you need/want to sell it before maturity, you may not recover your principal, and if you hold it, you will probably be subject to erosion of value due to inflation (inflation and interest rates are correlated). Over the short-term, the stock market can be very volatile, and you can suffer large paper losses. But over the long-term (decades), the stock market has beaten inflation. But this is true in aggregate, so, if you want to decrease equity risk, you need to invest in a very diversified portfolio (index mutual funds) and hold the portfolio for a long time. With a strategy like this, the stock market is not that risky over time. Derivatives, if used for their original purpose, can actually reduce volatility (and therefore risk) by reducing both the upside and downside of your other investments. For example, if you sell covered calls on your equity investments, you get an income stream as long as the underlying equities have a value that stays below the strike price. The cost to you is that you are forced to sell the equity at the strike price if its value increases above that. The person on the other side of that transaction loses the price of the call if the equity price doesn't go up, but gets a benefit if it does. In the commodity markets, Southwest Airlines used derivatives (options to buy at a fixed price in the future) on fuel to hedge against increases in fuel prices for years. This way, they added predictability to their cost structure and were able to beat the competition when fuel prices rose. Even had fuel prices dropped to zero, their exposure was limited to the pre-negotiated price of the fuel, which they'd already planned for. On the other hand, if you start doing things like selling uncovered calls, you expose yourself to potentially infinite losses, since there are no caps on how high the price of a stock can go. So it's not possible to say that derivatives as a class of investment are risky per se, because they can be used to reduce risk. I would take hedge funds, as a class, out of your list. You can't generally invest in those unless you have quite a lot of money, and they use strategies that vary widely, many of which are quite risky. "Yes, and the math that tells you when is called the Kelly Criterion. The Kelly Criterion is on its face about how much you should bet on a positive-sum game. Imagine you have a game where you flip a coin, and if heads you are given 3 times your bet, and if tails you lose your bet.  Naively you'd think ""great, I should play, and bet every dollar I have!"" -- after all, it has a 50% average return on investment.  You get back on average 1.5$ for every dollar you bet, so every dollar you don't bet is a 0.5$ loss. But if you do this and you play every day for 10 years, you'll almost always end up bankrupt.  Funny that. On the other hand, if you bet nothing, you are losing out on a great investment.  So under certain assumptions, you neither want to bet everything, nor do you want to bet nothing (assuming you can repeat the bet almost indefinitely). The question then becomes, what percentage of your bankroll should you bet? Kelly Criterion answers this question.  The typical Kelly Criterion case is where we are making a bet with positive returns, not an insurance against loss; but with a bit of mathematical trickery, we can use it to determine how much you should spend on insuring against loss. An ""easy"" way to undertand the Kelly Criterion is that you want to maximize the logarithm of your worth in a given period.  Such a maximization results in the largest long-term value in some sense. Let us give it a try in an insurance case. Suppose you have a 1 million dollar asset.  It has a 1% chance per year of being destroyed by some random event (flood, fire, taxes, pitchforks). You can buy insurance against this for 2% of its value per year.  It even covers pitchforks. On its face this looks like a bad deal.  Your expected loss is only 1%, but the cost to hide the loss is 2%? If this is your only asset, then the loss makes your net worth 0.  The log of zero is negative infinity.  Under Kelly, any insurance (no matter how inefficient) is worth it.  This is a bit of an extreme case, and we'll cover why it doesn't apply even when it seems like it does elsewhere. Now suppose you have 1 million dollars in other assets.  In the insured case, we always end the year with 1.98 million dollars, regardless of if the disaster happens.  In the non-insured case, 99% of the time we have 2 million dollars, and 1% of the time we have 1 million dollars. We want to maximize the expected log value of our worth.  We have log(2 million - 20,000) (the insured case) vs 1% * log(1 million) + 99% * log(2 million). Or 13.7953 vs 14.49.  The Kelly Criterion says insurance is worth it; note that you could ""afford"" to replace your home, but because it makes up so much of your net worth, Kelly says the ""hit it too painful"" and you should just pay for insurance. Now suppose you are worth 1 billion.  We have log(1 billion - 20k) on the insured side, and 1%*log(999 million) + 99% * log(1 billion) on the uninsured side. The logs of each side are 21.42 vs 20.72.  (Note that the base of the logarithm doesn't matter; so long as you use the same base on each side). According to Kelly, we have found a case where insurance isn't worth it. The Kelly Criterion roughly tells you ""if I took this bet every (period of time), would I be on average richer after (many repeats of this bet) than if I didn't take this bet?""  When the answer is ""no"", it implies self-insurance is more efficient than using external insurance.  The answer is going to be sensitive to the profit margin of the insurance product you are buying, and the size of the asset relative to your total wealth. Now, the Kelly Criterion can easily be misapplied.  Being worth financially zero in current assets can easily ignore non-financial assets (like your ability to work, or friends, or whatever).  And it presumes repeat to infinity, and people tend not to live that long. But it is a good starting spot. Note that the option of bankruptcy can easily make insurance not ""worth it"" for people far poorer; this is one of the reasons why banks insist you have insurance on your proprety. You can use Kelly to calculate how much insurance you should purchase at a given profit margin for the insurance company given your net worth and the risk involved.  This can be used in Finance to work out how much you should hedge your bets in an investment as well; in effect, it quantifies how having money makes it easier to make money." I don't know of any books, but there are a lot of good white papers on the subject if you take the time to look for them. For example, Moody's has a white paper on their LGD model (LossCalc) that explains their calibration methodology.   Searching for academic papers on the subject is really the only way to go, because credit risk is a field that really is just being explored. Really only since 2006 have banks started to actively try to use a risk rating model that incorporates PD and LGD. This is because of data insufficiency - banks just didn't keep active and centralized loan level data that is required to calibrate the models.  tl;dr: Use the internet - it is your friend. "Your interpretation is *reasonable*, yes. But I think the author -- here, at least -- has an alternative interpretation that applies just as frequently.  In a large and/or public company, especially one that is not in a strong growth period, there is an *incredible* incentive to not get blamed -- and therefore, fired or undesirably transferred -- if something goes wrong.   The CYA approach may lead to a better decision by seeking best practices, or it may not. A given situation may be better served by some variation on best practicies. But the author is right in that CYA is top-of-mind in decision-making for many.  If something fails, but the decision-maker has done sufficient CYA -- ""We followed best practices but we hit a perfect storm of headwinds..."" -- then failure doesn't matter." Quick and dirty paper but pretty interesting.. I'm not in Portfolio Management but I probably would have ended up at the modal number as well.   I don't know the subject deeply enough to answer my own question, but is the bias always toward underestimation of variance? Or is that a complex of the way the problem was set up?   Another question I have for those in investment management; Would this impact asset allocation? Thanks for the answer/comments! The time-based method was something we mooted and something I almost went with. But just to wrap this up, the method we settled on was this: Every time there is an entry or exit into the fund, we divvy out any unrealised market profits/losses according to each person's profit share (based on % of the asset purchased at buy-in) JUST BEFORE the entry/exit. These realised profits are then locked in for those particpants, and then the unrealised profits/loss counter starts at zero, we do a fresh recalculation of shareholding after the entry/exit, and then we start again. Hope this helps anyone with the same issue! the strategy is tested all the way to 97. how is the continuous series backadjusted? the emini is rolledover and Ratio back adjusted to the 2nd nearest contract, 9 days prior to expiration. since it is an intraday trade, the discrepancy to the real thing should be next to irrelevant. but comparing it to the spx could make it interesting.  what would be a good format to present the results ? jpeg? pdf ? "Rebalancing has been studied empirically quite a bit, but not particularly carefully and actually turns out to be very hard to study well.  The main problem is that you don't know until afterward if your target weights were optimal so a bad rebalancing program might give better performance if it strayed closer to optimal weights even if it didn't do an efficient job of keeping near the target weights. In your particular case either method might be preferred depending on a number of things: You can see why there isn't a generally correct answer to your question and the results of empirical studies might very wildly depending on the mix of assets and risk tolerance.  Still if your portfolio is not too complicated you can estimate the costs of the two methods without too much trouble and figure out if it is worthwhile to you. EDIT In Response to Comment Below: Your example gets at what makes rebalancing so hard empirically but also generally pretty easy in practice.  If you were to target 75% Equity (25% bonds?) and look at returns only for 30 years the ""best"" rebalancing method would be to never rebalance and just let 75% equity go to near 100% as equity has better long term returns.  This happens when you look only at returns as the final number and don't take into account the change in risk in your portfolio. In practice, most people that are still adding (or subtracting in retirement) to a retirement portfolio are adding (removing) a significant amount compared to the total amount in their portfolio.  In the case you discribe, it is cheaper (massively cheaper in the presence of load fees) just to use new capital to trade toward your target, keeping your risk profile.  New money should be large enough to keep you near enough your target.  If you just estimate the trading costs/fees in both cases I think you'll see just how large the difference is between the two methods this will dwarf any small differences in return over the long run even if you can't trade back all the way to your target." well well, good question, worth a discussion, the more filters you add to your strategy (volatility in this case), the lower its predictive power. i mean, one could further filter it by day of the week, whether prices are above or below a 200 day moving average...etc.