Calculating Covariance Statistics | What is it?

Calculating Covariance Statistics

Calculating Covariance Statistics | Formula

A measure of the degree to which two variables move together. A positive value means that on average, they move in the same direction.

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Correlation Coefficient Formula Calculation | Definition

Correlation Coefficient Formula

Correlation Coefficient Formula Calculation

Correlation coefficient (r) is a measure of the degree of correlation between two quantities or variables, such as the rates of return on stocks and on bonds. A negative coefficient of correlation indicates an inverse or negative relationship, whereas a positive value indicates a direct or positive relationship. The range of values is from -1 to +1 inclusive. A zero (0) value indicates that no correlation exists. Correlation coefficients are useful in asset class identification and portfolio diversification.

Correlation Coefficient Graph

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Investment Correlation | Financial Correlation | Definition | What is an Investment Correlation?

Investment Correlation | Financial

Investment Correlation | Financial Correlation

(1) Correlation is a relationship between two quantities, such that when one changes, the other does. If the quantities simultaneously increase or decrease in value, a positive correlation exists. If one increases as the other decreases, a negative correlation exists. For example, the resale value of an automobile and its mileage tend to be negatively correlated; the more miles on a car's odometer, the less the car is worth. In contrast, auto insurance costs and accident incidents are positively correlated; the more accidents a driver experiences, the more costly the driver's auto insurance.

Correlation Graphs

(2) A measure (ranging in value from 1.00 to -1.00) of the association between a dependent variable (fund, portfolio) and one or more independent variables (index). Correlation is a measure, not necessarily of causality, but rather of the strength of a relationship. A correlation coefficient of 1.00 implies that the variables move perfectly in lockstep; a correlation coefficient of -1.00 implies that they move inversely in lockstep; and a coefficient of 0.00 implies that the variables as calibrated are uncorrelated.


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Capital Asset Pricing Model | CAPM | Definition | What is the Capital Asset Pricing Model?

Capital Asset Pricing Model

Capital Asset Pricing Model | Definition

Capital Asset Pricing Model. A system of equations that describes the way prices of individual assets are determined in efficient markets, that is, in markets where information is freely available and reflected instantaneously in asset prices. According to this model, prices are determined in such a way that risk premiums are proportional to systematic risk, measured by the beta coefficient, which cannot be eliminated by diversification.

CAPM provides an explicit expression of the expected returns for all assets. Basically, the model holds that if investors are risk averse, high-risk stocks must have higher expected returns than low-risk stocks. CAPM maintains that the expected return of a security or a portfolio is equal to the rate on a risk-free investment plus a risk premium.

The basic formula for CAPM is:

Re – Rf + b(Rm – Rf )

Where

Equals

Re

Expected/required rate of return

Rf

Risk-free rate of return

Rm

Market rate of return

image\ebx_725430706.gif

Beta (measure of systematic risk)

image\ebx_725430706.gif (Rm – Rf )

Risk premium


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Beta Finance | Beta Formula and Calculation | Definition | What is Beta in Finance?

Beta Finance

Beta Finance Calculation and Formula | Definition

Beta is a measure of the systematic, non-diversifiable risk of an investment. The beta coefficient of a security, fund, or portfolio represents its market sensitivity, relative to a given market index and time period. The S&P 500 is commonly used as a market index for such calculations.

Beta is a statistical estimate of the expected average change in an investment's rate of return that corresponds to a one percent change in the market over the time period selected.

A beta value of 0.0 indicates that the investment is risk-free or independent of the market. T-bills are often used as examples of risk-free investments. A value of 0.5 indicates that the security, fund, or portfolio is expected to be only half as risky or sensitive as the average for the market. A value of 1.0 indicates that the investment has the same risk or response as the market, as defined by a market index, such as the S&P 500 or the Russell 3000®. A value of 2.0 indicates that it is expected to be twice as risky or sensitive as the market.

In Russell Style Classification (RSC), beta is calculated as follows:

Formula for Beta

Where

Equals

image\ebx_725430706.gif

Beta

_
x

Benchmark return

_
y

Portfolio return

In Russell Performance Universes (RPU), beta is calculated as follows:

Formula for Beta

Where

Equals

image\ebx_725430706.gif

Beta

n

Number of observations

Rxi

Market excess return
(market proxy return minus risk-free proxy return)

Ryi

Portfolio's excess return
(portfolio return minus risk-free proxy return)


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Average Standard Deviation | Formula Calculation | Definition

Average Standard Deviation | Formula

Average Standard Deviation | Formula Calculation

The square root of the arithmetic mean of the square of the deviations from the average value for a set of observations.

In Russell Style Classification (RSC), average standard deviation is calculated as follows:

Formula for Average Standard Deviation

Where

Equals

s

Average standard deviation

__
R

Average return over T time periods

Rt

Return at time t

T

Total number of time periods


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Average Annual Rate of Return Calculation | Formula

Average Annual Rate of Return

Average Annual Rate of Return Calculation Formula

Arithmetic average of a portfolio's returns over a specific period of time or set of observations.

In Russell Style Classification (RSC), average rate of return is calculated as follows:

Formula for Average Rate of Return

Where

Equals

__
R


Average rate of return

Rt

Return at time t

T

Number of time points

In Russell Performance Universes (RPU), the formula for average rate of return is:

Formula for Average Rate of Return

Where

Equals

u

Average rate of return

Ri

i-th return

n

Number of observations


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Appraisal Ratio Calculation | Formula | What is it?

Appraisal Ratio Calculation

Appraisal Ratio Calculation | Formula

The alpha of a portfolio divided by the non-systematic risk of the portfolio. The ratio measures the abnormal return per unit of risk that in principle could be diversified away from holding a market index portfolio.

In Russell Style Classification (RSC), the appraisal ratio is calculated as follows:

Formula for Appraisal Ratio

Where

Equals

image\ebx_1232661717.gif p

Jensen alpha

image\ebx_438050777.gif (e p)

Standard error


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Annualized Standard Deviation Calculation | Formula

Annualized Standard Deviation Formula

Annualized Standard Deviation Calculation Formula

Standard deviation that has been calculated from periodic returns and then annualized. Annualized standard deviation or risk is based on a minimum of 12 observations (for example, 12 months or 12 quarters).

In Russell Performance Universes (RPU), annualized standard deviation is calculated as follows:

Formula for Annualized Standard Deviation

Where

Equals

image\ebx_-733617394.gif a

Annualized risk

n

Number of observations

Ri

i-th return

P

Periodicity (number of time periods)


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Calculate Annualized Rate of Return Formula | Definition

Calculate Annualized Rate of Return

Formula to Calculate Annualized Rate of Return

The rate of return over a given period expressed on an annual basis or as a return per year. Annualized rate of return is computed on a time-weighted basis.

(1) In Russell Performance Attribution (RPA), the geometric average investment return for a period greater than or equal to one year, expressed as a 12-month period.

(2) In Russell Performance Universes (RPU), annualized rate of return is calculated as follows:

Formula for Annualized Rate of Return

Where

Equals

Ra

Annualized rate of return

Rc

Cumulative rate of return

P

Periodicity (number of time periods in a year:
4 for quarterly data, 12 for monthly data)

N

Number of observations


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Alpha | Alternative Investment Portfolios | Hedge Funds

Alpha | Investment Portfolios

Alpha | Alternative Investment Portfolios

(1) A measure of a portfolio's return in excess of the market return, after both have been adjusted for risk. It is also a measure of the manager's contribution to performance due to security selection. A positive alpha indicates that the portfolio outperformed the market on a risk-adjusted basis, and a negative alpha indicates the portfolio did worse than the market.

In Russell Performance Universes (RPU), alpha is calculated as follows:

Formula for Alpha

Where

Equals

image\ebx_1232661717.gif

Alpha

Ryi

Portfolio excess return
(portfolio return minus risk free proxy return)

n

Number of observations

image\ebx_725430706.gif

Beta; sensitivity of a portfolio's rate of return to the market

Rxi

Market excess return
(market proxy return minus risk-free proxy)

(2) In the context of a mutual fund, alpha is the premium the fund would be expected to earn if the market rate of return were equal to the risk-free rate (e.g., T-bill rate) -- that is a premium of zero for the market rate of return. A positive alpha value indicates that the fund has earned on average a premium above that expected for the market at the same level of risk (variability) as the fund. A negative alpha indicates that the fund averaged less than that expected for the market at the fund's risk level.

(3) A measure of selection risk (also known as residual risk) of a mutual fund in relation to the market. A positive alpha is the extra return awarded to the investor for taking a risk, instead of accepting the market return. Because of this, alpha is sometimes used as a performance indicator of mutual funds.

For example, an alpha of 0.4 means the fund outperformed the market-based return estimate by 0.4%. An alpha of -0.6 means a fund's monthly return was 0.6% less than would have been predicted from the change in the market alone.

(4) Alpha is also known as the average differential return of a mutual fund. The average differential return is the difference between the average return on the fund and a point on the market line corresponding to the fund's beta coefficient, where the market line is determined by the average excess returns for the market and the market portfolio's beta.

(5) In the context of a Jensen index, alpha represents the performance of a portfolio that diverges from the portfolio's beta. In this context alpha can also be used as a measure of the portfolio manager's performance.

In Russell Style Classification (RSC), alpha is calculated as follows:

Formula for Alpha

Where

Equals

image\ebx_1232661717.gif

Alpha

_
x


Benchmark return

_
y


Portfolio return

image\ebx_725430706.gif

Beta


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What is an Actuary? | What are Actuaries? | Definition

What is an Actuary?

What is an Actuary? | Definition

A person who specializes in the application of mathematics, probability, statistics, and risk theory to financial problems involving future uncertainty. These uncertainties are usually associated with life insurance, property and casualty insurance, annuities, pension or other employee benefit plans, and investments. Actuaries also provide expert testimony in courts of law on the value of lost future earnings.

Professional certifications for actuaries include:

ASA

Associate of the Society of Actuaries

Canada, UK, USA

FIA

Fellow of the Institute of Actuaries

UK

FSA

Fellow of the Society of Actuaries

Canada, UK, USA


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Guide to Equity and Bond Universe | Definitions | What are types of Bond and Mortgage Universes?

Guide to Equity and Bond Universe

Guide to Equity and Bond Universe | Definitions


Market Oriented Accounts Universe

These managers do not evidence a consistent preference for the types of companies emphasized in Value or Growth portfolios. However, two distinct types of organizations fall into this category: (1) those that construct portfolios with growth and valuation characteristics similar to the broad market over a market cycle and (2) those willing to make meaningful bets in growth or value emphasis across time, but with no consistent preference. Market-Oriented managers typically are willing to consider companies representative of the broad market when seeking investment opportunities.

Portfolios may either be well diversified or take meaningful sector/factor bets relative to the market toward both growth and value over time. Average growth and valuation characteristics over time are near those of broad market indexes.

Currency: US dollars

Market Oriented Mutual Funds Universe

These managers do not evidence a strong preference for the types of companies emphasized in Value or Growth portfolios. Market-Oriented managers typically are willing to consider companies across the broad market when seeking investment opportunities. Two distinct types of organizations fall into this category: (1) those that construct portfolios with growth and valuation characteristics consistently similar to the broad market and (2) those willing to make meaningful bets in growth or value emphasis across time, but with no consistent preference. All returns are net of fees. Fund data, investment objectives, and style definitions are provided by Morningstar. Although data are gathered from reliable sources, accuracy and completeness cannot be guaranteed.

Portfolios may either be well diversified or take meaningful sector/factor bets relative to the market toward both growth and value over time. Average growth and valuation characteristics over time are near those of broad market indexes. The investment style of the fund must be Market-Oriented, or Blend. The funds must also have a minimum of four years of history and at least $10 million in net assets.

Currency: US dollars

Municipal Bond Accounts Universe

Portfolios invested primarily in municipal bonds and tax-advantaged instruments for taxable clients. Includes commingled funds, separate accounts, and mutual funds (gross of fees). Portfolios tend to represent fully discretionary, unconstrained assignments. Fund data supplied directly from individual managers and by Morningstar. Although data are gathered from reliable sources, accuracy and completeness cannot be guaranteed..

Currency: US dollars

Non-US Equity Mutual Funds Universe

These funds invest primarily in securities of companies outside the United States. All returns are net of fees. Fund data, investment objectives, and style definitions are provided by Morningstar. Although data are gathered from reliable sources, accuracy and completeness cannot be guaranteed.

Funds are selected using the following criteria:

  • The investment objective of the fund must be Foreign.

  • Funds must have a minimum of four years history and at least $10 million in net assets.

Currency: US dollar

Small Capitalization Accounts Universe

Manage

rs in this style focus on small capitalization stocks. These companies may be unseasoned and rapidly growing but sometimes simply are small businesses with long histories. Typical characteristics of small capitalization portfolios are below-market dividend yields, above-market betas, and high residual risk relative to broad market indexes.

Focus is on small capitalization companies. Other characteristics vary by manager, depending on whether they pursue a Growth, Market-Oriented, or Value philosophy when selecting small stocks.

Currency: US dollars

Non-US Equity Portfolios Universe

Limited to separate accounts and pooled funds. None are permitted to hold US equities, but all can use US dollar short-term investments. Accounts must be fully discretionary and equity-oriented. Returns must be total fund returns.

Currency: US dollars

For over 1,000 additional terms and definitions please see our Investment Glossary Guide.

Value Equity Accounts Universe

Managers in this group are referred to as "value investors". While differences exist in how managers in this style define "value," an issue's current market price is a critical variable. For example, some organizations focus on companies having low absolute or relative P/E ratios, while others stress issues with above-market dividend yields. Additional measures that are frequently used are price/book value and price/sales ratios. A stock whose price has declined because of adverse investor sentiment may also attract some of these managers. Historical growth and profitability characteristics frequently are well below market averages, and overall characteristics are in sharp contrast to those of Growth managers.

The focus is on buying securities at low valuations on an absolute basis or relative to the market and/or historical levels. Portfolios typically exhibit below-average price/book value ratios, below-average P/E ratios, and/or high dividend yields. Risk characteristics in terms of volatility and beta vary but frequently are below market averages.

Currency: US dollars


Value Equity Mutual Funds Universe

While differences exist in how managers in this style define "value," an issue's current market price generally is the critical variable. For example, some organizations focus on companies having low absolute or relative P/E ratios, while others stress issues with above-market dividend yields. Additional measures that may be used are price/book value and price/sales ratios. A stock whose price has declined because of adverse investor sentiment may also attract some of these managers. Historical growth and profitability characteristics frequently are well below market averages, and overall characteristics are in sharp contrast to those of Growth managers. All returns are net of fees. Fund data, investment objectives, and style definitions are provided by Morningstar. Although data are gathered from reliable sources, accuracy and completeness cannot be guaranteed.

Funds are selected using the following criteria:

  • The investment style of the fund must be Value

  • Funds must also have a minimum of four years of history and at least $10 million in net assets.

Currency: US dollars

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Long Term Universe | 1 Page Guide

Long Term Universe

Long Term Universes Guide

Long Term Fixed Income Universe

These funds invest primarily in securities with maturities over ten years. All returns are net of fees. Fund data, investment objectives, and style definitions are provided by Morningstar. Although data are gathered from reliable sources, accuracy and completeness cannot be guaranteed.

Funds are selected using the following criteria:

  • The investment objective of the fund must be Corporate-General, Corporate-High Quality, or Government General.

  • The average maturity of the fund must be greater than 10 years.

  • Funds must also have a minimum of four years history and at least $10 million in net assets.

Currency: US dollars

Long Term Bond Accounts Universe

Portfolios invested primarily in securities with maturities over 10 years or having no maturity restrictions and managed with an orientation toward remaining fully invested in longer term securities. Minimum duration is 4 years, and "neutral" duration is longer than that of the broad market (e.g., the Lehman Brothers Aggregate Bond Index). Includes separate accounts, pooled funds, and mutual funds (gross of fees) managed by investment advisors, banks, and insurance companies. Fund data supplied directly from individual managers and by Morningstar. Although data are gathered from reliable sources, accuracy and completeness cannot be guaranteed.

Currency: US dollars


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Fixed Income Universe Guide | 1 Page Summary Page

Fixed Income Universes

Fixed Income Universe Guide

Fixed Income Mutual Funds Universe

The funds normally have more than 75% of assets in fixed income issues. All returns are net of fees. Fund data, investment objectives, and style definitions are provided by Morningstar. Although data are gathered from reliable sources, accuracy and completeness cannot be guaranteed.

Funds are selected using the following criteria:

  • The investment objective of the fund must be Corporate-General, Corporate-High Quality, Government-General, Government-Treasury, or Government-Mortgage.
  • The average maturity of the fund must be greater than one year.
  • Funds must also have a minimum of four years of history and at least $10 million in net assets.
Currency: US dollars

Fixed Income Accounts Universe

A combination of the Fixed Income Pooled Accounts and Fixed Income Separate Accounts universes. Consists of investment advisor, bank, and insurance company portfolios. These are fixed income-oriented, fully discretionary, tax-free portfolios. Pooled accounts are included from investment advisors if the advisor is (1) organized as a trust company or (2) a registered investment company acting as an advisor to a bank. Mutual funds can be included if they are gross of fees.

Currency: US dollars

Fixed Income Pooled Accounts Universe

Consists of tax-free, fully discretionary, fixed income pooled accounts for banks, insurance companies, and investment advisors. Pooled accounts are included from investment advisors if the advisor is (1) organized as a trust company or (2) registered as an investment company acting as an advisor to a bank. Mutual funds can be included if they are gross of fees.

Currency: US dollars

Fixed Income Separate Accounts Universe

Consists of investment advisor, bank, and insurance company fixed income separate accounts. These are fixed income-oriented, tax-free, fully discretionary portfolios of bonds. Employee benefit accounts are preferred.

Currency: US dollars

Fixed Income Universe Overview

Frank Russell Company's fixed income universes are designed to illustrate representative manager performance within a specific portion of the fixed income markets. The criteria for including accounts is simply based on whether the account is managed in a discretionary manner against a benchmark that represents that portion of the market. Within the US fixed income market, Russell universes are predominantly based on either maturity or sector groupings. The maturity based universes are:

Universe

Maturity Range

STIF/Cash

0 to 1 years

Short Term

0 to 3 years

Short-Intermediate

1 to 3 years

Intermediate

1 to 10 years

Sector Rotation

1 to 30 years

Active Duration

1 to 30 years

Long Term

10 to 30 years

Within these universes that are grouped by maturity, there are three that deserve further comment. The two broad universes, Sector Rotation and Active Duration, differ in that the Sector Rotation universe includes accounts where the duration is managed within a range of one year around the duration of a broad index. The Active Duration universe includes accounts with allowable duration ranges that exceed a one-year range. The Long Term universe differs from the other universes in that it is a collection of accounts which all have a long maturity emphasis, but there is no single maturity focal point.

The remaining US fixed income universes are based on sector groupings and include the municipal, high yield, and mortgage universes. These universes are based on investment returns for specific sectors within the market. In the multi-currency fixed income area, universes are created based on different geographical and currency exposures. Russell currently has an unhedged global, an unhedged non-US, and a hedged non-US universe.



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Equity Universe | Types of Equity Universes | Definition | What is an equity universe?

Equity Universe

Equity Universe | Types of Equity Universes | Definition


Emerging Markets Debt Portfolios Universe

Includes discretionary separate accounts, commingled funds, and mutual funds (gross of fees) managed for US dollar-oriented investors. Portfolios are managed against an emerging market fixed income performance benchmark (measured in US dollars). Minimum account size is US$ 10 million. Typical regions invested in include Latin America, Eastern Europe and Africa.

Currency: US dollars

Caution: Investments in emerging markets involve exposure to economic structures that are generally less diverse and mature, as well as to political systems which can be expected to have less stability, than those of more developed countries.

Emerging Markets Equity Mutual Funds Universe

These funds are composed of equity-oriented portfolios with a globally diversified emerging market orientation. Regional and country fund portfolios are specifically excluded. All returns are net of fees. Fund data, investment objectives, and style definitions are provided by Morningstar. Although data are gathered from reliable sources, accuracy and completeness cannot be guaranteed.

Funds are selected using the following criteria:

  • The investment objective of the fund must be emerging markets.

  • Funds must have a minimum of at least $10 million in net assets.

Caution: Investments in emerging markets involve exposure to economic structures that are generally less diverse and mature, as well as to political systems which can be expected to have less stability, than those of more developed countries.

Emerging Markets Equity Portfolios Universe

Composed of fully discretionary, equity-oriented portfolios with a globally diversified emerging market orientation. Typical countries would include Argentina, Brazil, Chile, Mexico, Venezuela, Thailand, India, Korea, Taiwan, Indonesia, Philippines, Greece, Portugal, Turkey, and Jordan. Regional and country fund portfolios are specifically excluded. Includes portfolios managed for global investors. Returns included must be total fund returns.

Currency: Multiple currencies

Caution: Investments in emerging markets involve exposure to economic structures that are generally less diverse and mature, as well as to political systems which can be expected to have less stability, than those of more developed countries.

Emerging Markets Equity Portfolios Universe

Composed of fully discretionary, equity-oriented portfolios with a globally diversified emerging market orientation. Typical countries would include Argentina, Brazil, Chile, Mexico, Venezuela, Thailand, India, Korea, Taiwan, Indonesia, Philippines, Greece, Portugal, Turkey, and Jordan. Regional and country fund portfolios are specifically excluded. Includes portfolios managed for global investors. Returns included must be total fund returns.

Currency: Multiple currencies

Caution: Investments in emerging markets involve exposure to economic structures that are generally less diverse and mature, as well as to political systems which can be expected to have less stability, than those of more developed countries.

Emerging Markets Equity Portfolios Universe

Composed of fully discretionary, equity-oriented portfolios with a globally diversified emerging market orientation. Typical countries would include Argentina, Brazil, Chile, Mexico, Venezuela, Thailand, India, Korea, Taiwan, Indonesia, Philippines, Greece, Portugal, Turkey, and Jordan. Regional and country fund portfolios are specifically excluded. Includes portfolios managed for global investors. Returns included must be total fund returns.

Currency: Multiple currencies

Caution: Investments in emerging markets involve exposure to economic structures that are generally less diverse and mature, as well as to political systems which can be expected to have less stability, than those of more developed countries.

Equity Oriented Separate Accounts Universe

Consists of investment advisor, bank, and insurance company portfolios. These are equity-oriented, separately managed, fully discretionary, tax-free portfolios with a minimum size of $5 million. Employee benefit accounts are preferred. An equity-oriented portfolio has the discretion to go to 100% in common stocks; the account may have large cash balances at times, and bonds may be used when they are considered attractive alternatives to equities.

Equity Pooled Accounts Universe

Consists of tax-free, fully discretionary, equity pooled accounts for banks, insurance companies, and investment advisors. Portfolio size must be at least $5 million. Pooled accounts are included from investment advisors if the advisor is (1) organized as a trust company or (2) registered as an investment company acting as an advisor to a bank. Mutual funds can be included if they are gross of fees.


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Core Non-US Equity Portfolios Universe | Definition | What is it?

Core Non-US Equity Portfolios Universe

Core Non-US Equity Portfolios Universe | Definition

Limited to separate accounts and pooled funds available to institutional investors. None are permitted to hold US equities, but all can use US dollar short-term investments. Accounts must be fully discretionary, equity-oriented and have less than 5% exposure to emerging market countries. Returns included must be total fund returns. Fund data is supplied by Morningstar and directly from individual managers.

Currency: US dollars


For over 1,000 additional terms and definitions please see our Investment Glossary Guide.

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