Alpha is a measure of the risk-adjusted value added by an investment strategy over its benchmark.

It is important to keep in mind that while an Alpha can be computed for any investment strategy using any benchmark, whether it is meaningful depends on how sensible the benchmark is for that strategy. For instance one would not expect stocks to represent a meaningful benchmark for bonds. Therefore the Alpha of a bond portfolio calculated with a stock benchmark will not yield useful insights into the behavior of that portfolio.

Beta is most often explained as a measure of how a security (or portfolio) moves in relation to a reference market index. It answers the question, "When markets go up or down, does the strategy typically go up or down more than the market or less than the market"? For instance if a stock moves up one percent while the S&P 500 index also moves up one percent, the beta of that stock is 1. If a portfolio loses two percent while the market index moves up one percent, that portfolio has a beta of minus two relative to the index. It is negative in this case because the portfolio moved in the opposite direction from the index.

Beta is also sometimes used as a broad reference to global capital markets. Most investors are familiar with what stocks and bonds are. These are securities issued by companies or governments, that respectively make up the 'equity markets' and the 'bond markets'. There are several other major parts of the global capital markets however, including the foreign exchange market, the physical and financial commodities markets (think of coffee, cocoa, grains etc.) where participants may trade futures, options or the actual commodity referenced in their contract, as well as markets for other assets such as land, timber and real estate for instance.

In this context, a 'beta' strategy simply refers to the concept of an investment strategy that tries to reflect the global combination of these various parts of capital markets. The investment objectives of beta strategies usually include remaining invested globally across key asset classes, not simply stocks or bonds, to benefit from the low cross-correlation of different asset classes over time. In concept, a global beta approach attempts to generate the returns of the growing world economy whose asset prices tend to rise over time, while smoothing the ups and downs through extensive diversification. In contrast, the stock of a company, an equity mutual fund, or a bond mutual fund, do not attempt to diversify across asset classes. The price of these securities moves partially under the influence of how global investors view the asset class they belong to (that is the 'beta' in a stock for instance), and partially because of fundamental factors that are unique to the company in case of a stock, or the group of underlying companies in the case of a mutual fund.

Exposure is defined in this glossary as the term generally used to describe the degree and direction an investment strategy is invested in its market of reference. The beta-adjusted exposure is a modified measure of exposure that is used for investment funds or portfolios. It is computed as a weighted average exposure of the securities in the portfolio, where the weights are each security's own beta. For instance a stock portfolio that is 50% in cash (cash has zero exposure to equities) and 50% invested in one stock with a beta of 0.3 has an exposure of 50% but a beta-adjusted exposure of 0.3 multiplied by 50%, or 15%.

Just as exposures are important to assess the risk and value added of a strategy, so are beta-adjusted exposures. A portfolio with an equity beta-adjusted exposure of 15% can be expected, all else being equal, to go up and down about 15 percent of the reference equity index. If the equity index moves up 20 percent, the portfolio can be expected to gain 3 percent as a result. This gain is commensurate with the equity risk assumed in the portfolio. A strategy that purports to manage risks by keeping its equity exposure to a maximum of 30 percent for instance, yet returns consistently the same profits as the equity index over a significantly long period of time, requires investigation to make sure one understands where returns come from and what risks are assumed to generate them. Conversely, investors who are keen to take equity risk for part of their portfolio should not allocate that portion of their assets to a strategy with low beta-adjusted equity exposures.

Because the beta of listed securities changes as market prices move, the beta-adjusted exposure of a portfolio is a function of time.

Diversification is one measure of investment risk. A highly diversified portfolio intuitively should involve less risk than a concentrated portfolio. Diversification however is a often misunderstood concept. A portfolio's risk is reduced if the underlying sources of investment risk are diverse. This does not mean that a portfolio with many investment holdings is necessarily diversified. For instance a portfolio with a large number of stock positions may in aggregate be little different from a risk perspective to a broad stock market index. While sources of returns may have been diversified through exposures to small caps, large caps etc., the sources of risk may not be well diversified. Conversely, an investment portfolio holding few securities may turn out to be more diversified than another portfolio with more securities if the sources of risk in the few securities are very different.

The correlation of a portfolio to various asset classes such as stocks or bonds, can be used to give a sense of diversification. A high correlation to a particular asset class indicates that risk sources in the portfolio are essentially those of the broad asset class.

Dollar cost averaging consists in investing money in a strategy or security in chunks over time instead of in a lump sum. This is often described as a way to minimize the chance of investing just before markets fall, although it is better thought of as an approach to maximize the chances of realizing an investment strategy's average long-term expected returns by spreading the starting point of each chunk of money across various market conditions.

All investment strategies are subject to doing better or worse in particular market conditions that may not simply be summarized by being a rising or falling market. Often, a range of conditions need to be present for meaningfully impacting near-term performance on the up or downside. Therefore it may not be obvious whether current market conditions are favorable or unfavorable to initiating an investment on a particular day. Spreading an investment over a number of months mechanically diversifies this 'starting risk', which will have the effect of bringing an investment's return closer to its long-term expected average value.

The drawdown of an investment strategy refers to the decline in value of the strategy relative to its historic peak value. For instance if an investment historically peaked at $1000 but is currently worth $900, its current drawdown is $100 out of $1000. This is normally referred to as a ten percent drawdown and denoted as -10%. When an investment reaches and exceeds its previous peak value, the drawdown is zero.

It is important to realize that all investment strategies with a bona fide mark-to-market are in a state of drawdown most of the time. This is because an account invested in that strategy -or in any stock or bond-, only reaches a new high once in a while. After a new peak value is reached, market prices will fluctuate down and up below that peak, until another peak is eventually reached.

The drawdown of any security or strategy is therefore a function of time that changes with every tick of the ticker tape. These charts immediately reveal the depth of drawdowns over time as well as the length of time required to recover, in other words how long it took before the strategy reached a new high and the drawdown reverted back to a zero value.

Drawdown history is a powerful indicator of an investment's behavior, although because it is a function of time it can be challenging to fully analyze. To simplify this analysis, institutional investors typically focus on a few defining characteristics of the drawdown history: The maximum drawdown, the period of time when this worst drawdown occurred, as well as the time it took to recover. In addition, a few other standard financial metrics such as the MAR ratio are designed to convey a quick understanding of the severity of the worst drawdown relative to a strategy's long-term expected returns.

When investing in bonds, one needs to pay attention to two major risks: Interest rates and credit quality. Bond prices move inversely with interest rates. The sensitivity of a bond's price to interest rates is called the “Modified Duration” risk, usually abridged to “duration” risk.

As for the second risk, a bond's credit quality is reflected by its credit rating and its “credit spread”. The “spread” refers to the difference in yield between that bond and a U.S. government bond of similar maturity which would by definition have no credit risk. For instance if a 30-year corporate bond yields 6% while the U.S. 30-year treasury bond yields 3.25% as it does today, the “spread” is 6% minus 3.25%, or 2.75%. That 2.75% is the risk premium the market is offering investors for holding the corporate bond instead of the treasury of same maturity.

As confidence in the broad economy rises and wanes, investors' confidence in the ability of corporations to repay their debt will change. For instance in times of economic stress investors may feel that small companies are more likely than larger corporates to face problems repaying their debt. The “spread” on small company bonds would widen as investors sell these bonds, while the spread on larger corporate debt would become smaller as investors buy their bonds, driving prices up and the corresponding yields down. The sensitivity of a bond's price to fluctuations in spread values is called the “spread duration”, mirroring the sensitivity of price to interest rates which is simply the “duration”.

Duration is conveniently measured in years. For instance if a bond has a duration of 10 years, it means that a 1 percent change in interest rates will move the bond's price by 10 percent. The price will fall 10 percent if rates suddenly rise by 1 percent. They will rise 10 percent if rates fall by 1 percent.

An efficient frontier is the set of investment portfolios that offer the highest expected returns for a given level of risk.

Exposure is the term generally used to describe the degree and direction an investment strategy is invested in the market. The 'market' for an equity strategy usually refers to the equity markets or an equity index such as the S&P 500. The 'exposures' of a bond strategy may refer to a bond index or a subset of the bond market that makes sense for the specific strategy. For instance a strategy that uses 100% of its capital to buy stocks has a 100% exposure to equities. If only 50% of the capital is used to buy stocks, and the other 50% is invested in bonds, the equity exposure is 50%.

One can think of exposures as a measure of risk. A strategy that invests 100% of its capital to buy large capitalization U.S. stocks and returns the same of less than the S&P 500 index is taking 100% of the risk of the index and not offering anything valuable in return. In contrast a strategy that uses 50% of its capital to buy large capitalization stocks, keeps 50% in cash, yet returns the same as the S&P 500 index, is a valuable strategy. Its equity exposure is 50%, meaning that it takes only half the risk of the S&P 500 index, but it manages to deliver the same profitability as the index.

The Information ratio is a measure of the risk-adjusted return of a security or portfolio. It is commonly used to assess the value added by an active money manager compared to a passive index. The higher the Information ratio, the better the manager. Top-flight money managers whose investment strategy is focused on a specific asset class for which a passive index is available typically achieve annualized Information ratios of about one-half.

A negative Information ratio means that over the time period considered, the index returned more than the portfolio. This would typically be the case when using an index such as the S&P 500 for instance, and computing the Information ratio over a time interval corresponding to an equity bull market. In a bull market, equity indices can return over twenty percent per annum, which a risk-controlled or otherwise diversified strategy is likely not designed to achieve. Therefore when interpreting Information ratios, it is important that the comparative index be chosen sensibly relative to the investment strategy that is being assessed, and that the time period over which it is computed not significantly bias the outcome in favor of or against the strategy. The Information ratio is an insightful metric when computed over a number a full bull and bear market cycles, each of which lasts about seven years.

Emotomy's Portfolio Analyzer uses the Vanguard Total Stock Market Index Fund (Ticker symbol: VTSMX) as a default market index when computing Information ratios. A custom index may also have been assigned by the Chief Investment Officer of your firm.

Leverage describes a situation where an investor borrows money to invest more than the capital available in an account. For instance an investor with $100 in available capital may wish to purchase $150 worth of securities. In that case the investor borrows $50, which is referred to as the leverage or loaned amount. Leverage is commonly expressed as a percentage or a ratio. In our example the leverage is 50% ($50 for $100 in capital), also sometimes referred to as '1.5 to 1'.

In the United States, the Federal Reserve has established a rule that limits the amount of money a brokerage firm can lend to most investors. This rule is known as Reg. T after the regulation number it corresponds to. Reg T limits leverage to 100% for most investors, which means that investors can purchase securities for an amount at most equal to twice the capital in their brokerage account. An investor with $100,000 in a brokerage account can purchase up to $200,000 of securities using that account. The extra $100,000 is a loan from the brokerage firm to the account holder, on which the customer pays a daily interest rate.

The use of leverage enhances returns and losses. If an investors with $100,000 in capital purchases a stock for the full $100,000 and that stock loses 10%, the loss is simply 10% and the account is now worth $90,000. But suppose the investor purchases that same stock with 50% leverage, that is by borrowing $50,000 from the brokerage firm holding the account. The stock loses 10% resulting in a loss of $15,000 on $150,000 invested. The account is now worth $85,000 (the original $100,000 minus the loss), if we neglect borrowing costs. The amount borrowed has not changed and is still equal to $50,000, so that the leverage in the account is now $50,000 on $85,000 in capital, or 59%, higher than the initial 50%. In this fashion, leverage in the account rises mechanically as losses accumulate. To ensure that they recover the money they loan investors, brokerage firms monitor the leverage in each customer account as security prices move. They will require that a customer add money to an account when leverage reaches certain limits. This is known as a margin call. Adding money to an account mechanically reduces leverage because the total value of the account rises while the amount borrowed remains the same. In our example should the brokerage firm have a 59% leverage limit for this particular customer, it might ask that the customer add for instance $10,000 to the account. The account capital would then equal $95,000 and the leverage would fall from 59% to $50,000 divided by $95,000 or 53%. If the customer does not add money as requested, the brokerage firm will sell some of the positions in the account to reduce the amount borrowed, which also reduces leverage.

The MAR ratio is one of the metrics used to intuitively summarize the severity of expected drawdowns. It is computed by dividing the annual returns since inception of a strategy by the maximum drawdown since inception. The S&P 500 index has returned 6% annually on average between 1998 and 2013, with a maximum peak-to-trough loss of 55%. Its MAR ratio is then 6 divided by 55, or 0.11. This means that the annual return is about 11 percent of the maximum drawdown.

As a technical point, readers will notice that the dimension of the MAR ratio is the inverse of time. Some may find it easier to think in terms of the inverse of the MAR ratio, which has dimension of time. For instance the inverse of the MAR ratio for the S&P 500 is 9, which means that it would take 9 years of average returns to recover from the maximum historical drawdown.

The 'Up-Market Capture ratio' and 'Down-Market Capture ratio', sometimes referred to as the Up (or Down) Capture ratios, are indicators of how much a strategy and a market index move in lockstep when the index is either up or down respectively. The Up-Capture ratio is the ratio of the strategy's compounded return in periods when the index had positive returns (hence the 'Up'), divided by the index return during these same periods. Therefore an Up-Capture ratio of 100 means that the strategy returned the same profits as the index when the index was up. An Up-Capture ratio of 120 means that the strategy returned 20 percent more than the index when the index was up, and a ratio of 85 means it returned only 85 percent of the index. A negative Up-Capture ratio indicates that on the whole the strategy lost money in periods when the index was positive. A higher Up-Capture ratio is more desirable than a lower one.

Conversely the Down-Capture ratio is the ratio of the strategy's compounded return in periods when the index had negative returns (hence the 'Down'), divided by the index return during these same periods. A Down-Capture ratio of 100 means that the strategy experienced the same loss as the index when the index was down. A Down-Capture ratio of 120 means that the strategy lost 20 percent more than the index when the index was down, and a ratio of 85 means it lost only 85 percent of the index losses, i.e. it did better than the index, when that index was down. A negative Down-Capture ratio indicates that on the whole the strategy made money in periods when the index was negative. A lower Down-Capture ratio is more desirable than a higher one.

Finally, the Capture ratio is defined as the Up-Market Capture ratio divided by the Down-Market Capture ratio. The higher this ratio, the better the ability of the strategy to capture the index's upside while limiting losses when the index is down.

It is important to keep in mind that while market capture ratios can be computed for any investment strategy using any benchmark, whether these ratios are meaningful depends on how sensible the benchmark is for that strategy. For instance one does not expect a bond strategy to reliably capture the upside of stocks. Therefore the market capture ratios of a bond-heavy portfolio calculated with a stock benchmark will not yield useful insights into the behavior of that portfolio.

The Omega ratio is a risk-return performance measure of an investment portfolio that measures the likelihood of achieving a threshold return target. The higher the Omega ratio, the greater the probability that the threshold return will be met or exceeded. Emotomy uses 0 percent as a default threshold return target.

Rebalancing is the act of buying and selling securities to bring an investment account in line with its target asset allocation.

Risk parity is an investment approach that allocates capital across assets based on the risk these assets represent.

Risk scores are indicators of risk versus return that range between 0 and 100 for each investment portfolio. A risk score represents the ranking of a specific portfolio relative to all other portfolios built by investors on this website. A low, medium or high risk score does not by itself indicate that a portfolio is more or less suitable than another. It is a measure of where the portfolio stands relative to all other available portfolios on the spectrum of lower risk for lower returns to higher risk for higher returns. This is different from the Sharpe ratio which measures a portfolio's excess returns per 'unit' of risk.

The risk score is best understood by visualizing a two-dimensional chart (example) showing risk on one axis and returns on the other. The risk score measures the distance of the portfolio from the origin of the chart. Longer distances correspond to portfolios taking more risk while aiming for higher returns. It is however possible that two portfolios the same distance away from the origin will have differing returns and risk. For instance a portfolio with 10% returns and 10% risk stands at a distance of 0.141 from the origin, the same as a portfolio with 14.1% return and zero risk, or another with zero returns and 14.1% risk. To fairly compare these portfolios, it is necessary to penalize those that sought higher risk but delivered lower annual returns. To do this, we modify the 'distance' by dividing it by the Sharpe ratio. This approach will increase the risk score of portfolios that took high risks but delivered low returns, and conversely will lower the risk score of portfolios that took the same risks but generated higher returns.

The scaling from 0 to 100 is arrived at by evaluating all building-block portfolios as well as all portfolios saved by users of this website to create an efficient frontier. A score of 100 is assigned to the portfolio on the efficient frontier with the highest risk score. The risk scores of all other portfolios are scaled relative to that benchmark.

The remaining question is what financial metric is used as a measure of 'risk'. We use a modified maximum drawdown for this purpose, which we define as the maximum of two numbers: (1) the portfolio's maximum historical drawdown, and (2) the loss the portfolio would experience should interest rates rise by 2 percent uniformly across the yield curve. This metric is designed so that the different durations of portfolios are incorporated in the resulting relative risk-return scores, even if the potential impact of duration is not reflected in the available historical track records which mostly correspond to periods of falling interest rates.

The Sharpe ratio is a financial metric that gives an indication of the risk-adjusted return of a security or investment strategy. It is computed by dividing excess returns, i.e. returns over a risk-free rate benchmark, by volatility. One can think of this ratio as measuring how many units of returns the strategy yields for each unit of risk. A high Sharpe ratio is therefore more desirable than a low ratio. A security with negative returns over a period of time will have a negative Sharpe ratio over that period, since the denominator of the ratio (the volatility) is always positive by definition.

In practice, few listed securities or strategies have Sharpe ratios in excess of 0.5 over long periods of time. For instance the Sharpe ratio of the S&P 500 Index over the sixteen-year period from 1998 through 2013 calculated using a risk-free rate of one percent, was 0.13. A Sharpe ratio close to 1 over a period of time longer than one equity market cycle, namely about five to seven years, is generally considered an excellent risk-return profile. Such high Sharpe ratios are characteristic of some of the world's top hedge fund managers. Sharpe ratios are calculated using a risk-free rate equal to 1 percent.

Short selling is the act of selling securities that are not currently owned by the seller, with the objective to repurchase them at a later date when their price has fallen. To effect this transaction, the short-seller borrows the securities from another person who owns them, sells them in the market at current prices, and returns them to the lender when they are eventually repurchased. Brokerage firms intermediate these transactions by finding a lender for each short-seller, tracking who owes what to whom (details can be complex), and taking a fee in the middle.

The Sortino ratio is a variation of the Sharpe ratio that also gives an indication of the risk-adjusted return of a security or investment strategy. It is computed by dividing excess returns, i.e. returns over a benchmark that is usually referred to as the Minimum Acceptable Return or MAR, by downside volatility instead of by total volatility as in the Sharpe ratio calculation. In measuring how many units of returns the strategy yields for each unit of risk, the Sortino ratio only counts as risk the downward motion of price to avoid penalizing the ratio with the volatility induced by upwards price movements. A high Sortino ratio is more desirable than a low ratio. Emotomy computes the Sortino ratio of its building-block strategies using a MAR equal to 0 percent.

'Stop-loss' is an expression that means what is sounds like. When markets temporarily become unfavorable to an investment strategy, that strategy starts losing money. Once losses reach a pre-determined stop-loss target, in other words reach the maximum level that the investor is willing to tolerate, the strategy liquidates all its investment positions and moves to cash. It is possible to apply stop loss targets to individual security positions or to an entire investment portfolio. Stop-loss targets are usually expressed in percentage terms, and are measured from the historical peak value of the investors' account.

For instance suppose an investor opens an account with $100,000 to invest in a strategy with a stop-loss set at 10 percent. For the first year, despite unavoidable ups and downs in value from day to day, the strategy never loses more than 10 percent and ends the year with a 15 percent return. At the start of the second year, the account is now worth $115,000. In the second year markets become less favorable and the strategy loses money until a 10 percent loss is reached. The account has lost $11,500 from its peak value of $115,000 and is now worth $103,500. Because the 10% stop-loss target has been reached, the strategy liquidates all positions and the account will be 100 percent in cash from that day onwards.

A stop loss is therefore a straightforward technique whose appeal is that it is easily understood. However, it does not guarantee that an investment strategy will not lose more than the stop-loss limit. The first reason is that markets can fall fairly quickly. By the time an investment strategy actually moves to cash, security prices might have fallen further below the stop loss limit, and the execution of sell orders in a falling market may also contribute to further losses. The second and more fundamental reason is that a stop-loss discipline is necessarily accompanied by a reinvestment discipline. After money is re-invested an investor can experience further losses if markets conditions once again become unfavorable before the account fully recovers its former peak value. Consequently the main objective of the reinvestment criteria is to identify a time period when market conditions for the strategy seem to have markedly improved, but that carries no guarantee of profitability over the near term.

Turnover is a measure of trading activity in a portfolio. It is usually given as a percentage that represents the total value of securities bought or sold over an annual period, whichever is less, divided by the average portfolio value in that period. For instance a 25 percent turnover for a $100 million portfolio indicates that the portfolio buys or sells at least $25 million worth of securities per year. Although turnover is usually disclosed by funds as a fixed number, it is a metric that can be computed daily for the past year. It can vary significantly for different investment strategies as well as for the same investment strategy when market conditions change. There is no 'right' or 'wrong' turnover figure, and a lower turnover is not necessarily better or worse than a higher one. Turnover is simply intended to convey a sense of how much trading is involved in executing a particular strategy. For investors who are tax sensitive, turnover is one indicator of whether a strategy may be suitable to their circumstances.

Volatility, also sometimes referred to as the standard deviation of returns, is one measure of risk amongst several others also mentioned in this glossary. It measures how far an investment's profitability typically swings above and below its long-term average. If an investment yields 10% over long periods, but with fluctuations mostly between 5% and 15%, these fluctuations of +/-5% are what volatility represents.

Between 1998 and 2013, the S&P 500 index has returned 6% annually on average, with a volatility of 21%. This means that statistically, one can think of this index as returning between 6% - 21% and 6% + 21% most of the time, or between -15% and +27%. 'Most of the time' in this context means about two-thirds of the annual periods between 1998 and 2013, since we are referring to annual returns.

Volatility is useful to quickly figure out what swing in returns one should expect from an investment. However because it measures the fluctuations about a mean, one must also know this mean to make sense of volatility. A 10% average return with 10% volatility will swing regularly between zero and +20%, whereas a 20% return with 10% volatility can be expected to yield returns that vary between +10% and +30%. The volatility number itself is not very meaningful without the mean that it is anchored to.

Trailing 12-Month Portfolio Yield is the calculated percentage of income distributions over the most recent 12 months. It is calculated by taking the weighted average of the yields of the underlying funds, based and their current composition in your portfolio. Changes in portfolio positions over time are not considered in this calculation.

The Z-Score of a function is a transformation of that function obtained by removing the average and dividing by the standard deviation. A Z-score of 0 means that the value of original function is the average. A Z-score can also be positive or negative, indicating whether the value of the function is above or below the average and by how many standard deviations.