Portfolio Optimization using statistical signifiance?
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What you are looking for is called the Sharpe ratio:\n \nSharpe ratio = (return - risk free rate) / risk\n\nIt is explained best here:\nhttp://www.moneychimp.com/articles/risk/sharpe_ratio.htm
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Type this in google\n\n   "linear programming.pdf"\n\n  U will get your answer on the very first page, with sites like these\n\n    http://www.stats.ox.ac.uk/~yu/
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Gaussian distribution
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It's actually D.  A isn't correct because we aren't given the covariance between the two securities.  The portfolio risk is not the simple weighted average of the individual risks. \n\nThe formula is\n\nsquare root of the sum of the weights multiplied with the covariances.\n\nIf the securities are negatively correlated, the total risk can be less than either of the individual securities.  If they're positively correlated, the portfolio risk goes up.
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Learn stochastic calculus and maths modelization first. It's your only way to making consistent profit on the FX. Charts are a great way to "learn" except they have no PREDICTIVE value whatsoever... sounds familiar? ;)
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performance is variable, learning is stable
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symetric designs, ratios from diagram to real material
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An academic study found that the assumption that currency prices follow a random walk is a better predictor than any of the most used models based on macroeconomic data.  Later studies (by my PhD Thesis advisor) show that there is some predictability in prices if you have information on order flow.\n\nBottom line -- unless you are a major investment bank with information on your customer's FX demand, you are better off flipping a coin to predict direction than using some model to project where prices are going.
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/n/r\n\nyou prolly need the correct type of returns.
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Yes, the mathematical definition of risk is exactly that: larger variability is the return. However, the variation is symmetrical around the mean. The probabilty of having a larger return than the mean is just as big as the probability of having a smaller return than the mean.
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OK, let's put some numbers on the problem.  We have an asset with monthly volatility of about 10% and a near-zero expected return in the long run. How likely is it that its price will increase by 70% in five months?  If I am doing my math correctly, this would be a 3.17 standard deviation event, meaning that the likelihood of that happening is about 0.08%. \n\nIf you built an ARMA model, you could probably get a higher likelihood estimate though...  I'd run one out of curiosity, but I don't have eViews handy...
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most statistics follow a pattern, whether it be linear, quadratic, or whatever. Once you have enough data to establish a pattern, you can accurately predict the remainder of the line.\n\nFor instance, you have a line that looks to be half a parabola. Once it starts going back up, you can be pretty certain of where it's going to be.
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Risk Management is NOT about getting constant (i.e. low volatiliy) returns.\nRisk Management is NOT about getting risk with complete certainty.\n\nAs Mark Twain said: predicting is difficult, but it is more difficult to predict the future.\n\nRisk Management is about getting rich enough with as much uncertainty as you feel confortable with. \n\nThe first step towards risk management for pension funds is knowing the explicit or implied fund's liabilities:\nis it a defined benefit fund? then it's quite easy to determine the liabilities. \n\nIs it defined contribution? Then still the fund has, on behalf of the benefitial owners, liabilities to deal with, although they are not explicit and thus are more difficult to be sought after.\n\nYou should pursue two different (and at most times contrarian) objectives:\nfirst, maximize the expected surplus of the fund, AFTER the liabilities have been paid.\n\nSecond, minimize the VARIANCE of the difference between the liabilities and the assets plus the future contributions to the plan.\nThat is, you should, on hand \nmaximize e=(X-B)'E\nwhere X is the Asset Portfolio, B is the portfolio representing the future flows for the fund (i.e. contributions and withdrawals), E is a vector of expected returns for each asset or flow;\nand on the other hand\nminimize V=VAR{(X-B)'E}\n[Note: if X and B are deterministic and E is multinormal, then V= (X-B)'S(X-B) where S ithe covariance matrix for E]\n\nIt should be more than obvius that both function are ,generally speaking, not optimal in the same place. Thus, you need a PREFERENCE FUNCTION.\nIt's usual to have U=e-lV where l is the risk-aversion coefficient.\nDepending on how you model your assets and your flows, the function can turn out to be analytically treatable, or you might end up using some kind of simulation\n\nyou can look for more information at\nAIMR (American Insitute for Market Research)
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National Association of Securities Dealer Automated Quotation.
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Learn About:\n\nStandard Deviation\nAsset Price Forecasting\n& Risk Mngt.\n\nIt will help you when you talk to professional money managers.
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Tracking error is the standard deviation of the portfolio of differences:\nLet X be your portfolio; let B be the chosen benchmark.\nThen d=X-B is the portfolio of differences (which adds to zero)\nthen TE=std(d) is the tracking error. If you have a covariance matrix S for your assets, then \nTE=((X-B)'S(X-B))^(1/2).\n\nTracking error "interpretation" is the uncertainty of the excess returns (that is, of the return of the portfolio vs the benchmark's)
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In his book "Contrarian Investment Strategies: The Next Generation," David Dreman does a good job of explaining his rationale for a low P/E stock selection strategy.  On average, over long periods of time, low P/E stocks have outperformed high P/E stocks.  There has been much debate over why this is, but I'd summarize Mr. Dreman's theory of why this works as the following.  Analysts tend to be systematically too optimistic when forecasting companies' future growth rates.  Therefore, they are willing to pay a high multiple of current earnings for these stocks.  When it turns out they were wrong, the market strongly penalizes the prices of these high P/E stocks.  There appears to be an asymmetric payoff  between high P/E and low P/E stocks.  When high P/E stocks report a positive earnings surprise, they don't go up as much as they decline when they report a negative surprise.  The opposite is, on average, true of low P/E stocks.  It is this effect that may explain why value portfolios often outperform growth portfolios.  Turning to academia, a recent paper in the journal Review of Quantitative Finance and Accounting concludes, "Value portfolios outperform because of systematic errors in forecasting earnings growth rates."