The three steps in the portfolio management process are:

1. Planning: Determine client needs and circumstances, including the client’s return objectives, risk tolerance, constraints, and preferences. Create, and then periodically review and update, an investment policy statement (IPS) that spells out these needs and circumstances.

2. Execution: Construct the client portfolio by determining suitable allocations to various asset classes based on the IPS and on expectations about macroeconomic variables such as inflation, interest rates, and GDP growth (top-down analysis). Identify attractively priced securities within an asset class for client portfolios based on valuation estimates from security analysts (bottom-up analysis).

3. Feedback: Monitor and rebalance the portfolio to adjust asset class allocations and securities holdings in response to market performance. Measure and report performance relative to the performance benchmark specified in the IPS.

Mutual funds combine funds from many investors into a single portfolio that is invested in a specified class of securities or to match a specific index. Many varieties exist, including money market funds, bond funds, stock funds, and balanced (hybrid) funds. Open-ended shares can be bought or sold at the net asset value. Closed-ended funds have a fixed number of shares that trade at a price determined by the market.

Exchange-traded funds are similar to mutual funds, but investors can buy and sell ETF shares in the same way as shares of stock. Management fees are generally low, though trading ETFs results in brokerage costs.

Separately managed accounts are portfolios managed for individual investors who have substantial assets. In return for an annual fee based on assets, the investor receives personalized investment advice.

Hedge funds are available only to accredited investors and are exempt from most reporting requirements. Many different hedge fund strategies exist. A typical annual fee structure is 20% of excess performance plus 2% of assets under management.

Buyout funds involve taking a company private by buying all available shares, usually funded by issuing debt. The company is then restructured to increase cash flow. Investors typically exit the investment within three to five years.

Venture capital funds are similar to buyout funds, except that the companies purchased are in the start-up phase. Venture capital funds, like buyout funds, also provide advice and expertise to the start-ups.

Holding period return is used to measure an investment’s return over a specific period.

Arithmetic mean return is the simple average of a series of periodic returns.

Geometric mean return is a compound annual rate.

Money-weighted rate of return is the IRR calculated using periodic cash flows into and out of an account and is the discount rate that makes the present value of cash inflows equal to the present value of cash outflows.

Gross return is total return after deducting commissions on trades and other costs necessary to generate the returns, but before deducting fees for the management and administration of the investment account.

Net return is the return after management and administration fees have been deducted.

Pretax nominal return is the numerical percentage return of an investment, without considering the effects of taxes and inflation.

After-tax nominal return is the numerical return after the tax liability is deducted, without adjusting for inflation.

Real return is the increase in an investor’s purchasing power, roughly equal to nominal return minus inflation.

Leveraged return is the gain or loss on an investment as a percentage of an investor’s cash investment.

We can calculate the population variance, σ², when we know the return R_t for period t, the total number T of periods, and the mean μ of the population's distribution:

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In finance, we typically analyze only a sample of returns, so the sample variance applies instead:

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Covariance measures the extent to which two variables move together over time. Positive covariance means the variables (e.g., rates of return on two stocks) tend to move together. Negative covariance means that the two variables tend to move in opposite directions. Covariance of zero means there is no linear relationship between the two variables.

Correlation is a standardized measure of co-movement that is bounded by −1 and +1:

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As predicted by theory, asset classes with the greatest average returns have also had the highest risk.

Some of the major asset classes that investors consider when building a diversified portfolio include (ranked from most risk and return to least) small-capitalization stocks, large-capitalization stocks, long-term corporate bonds, long-term Treasury bonds, and Treasury bills.

In addition to risk and return, when analyzing investments, investors also take into consideration an investment’s liquidity, as well as non-normal characteristics such as skewness and kurtosis.

A risk-averse investor is one that dislikes risk. Given two investments that have equal expected returns, a risk-averse investor will choose the one with less risk. However, a risk-averse investor will hold risky assets if he feels that the extra return he expects to earn is adequate compensation for the additional risk. Assets in the financial markets are priced according to the preferences of risk-averse investors.

A risk-seeking (risk-loving) investor actually prefers more risk to less and, given investments with equal expected returns, will choose the more risky investment.

A risk-neutral investor has no preference regarding risk and would be indifferent between two investments with the same expected return but different standard deviation of return.

The standard deviation of returns for a portfolio of two risky assets is calculated as follows:

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For each level of expected portfolio return, the portfolio that has the least risk is known as a minimum-variance portfolio. Taken together, these portfolios form a line called the minimum-variance frontier.

On a risk versus return graph, the one risky portfolio that is farthest to the left (has the least risk) is known as the global minimum-variance portfolio.

Those portfolios that have the greatest expected return for each level of risk make up the efficient frontier. The efficient frontier coincides with the top portion of the minimum variance frontier. Risk-averse investors would only choose a portfolio that lies on the efficient frontier.

An indifference curve plots combinations of risk and expected return that an investor finds equally acceptable. Indifference curves generally slope upward because risk-averse investors will only take on more risk if they are compensated with greater expected returns. A more risk-averse investor will have steeper indifference curves.

Flatter indifference curves (less risk aversion) result in an optimal portfolio with higher risk and higher expected return. An investor who is less risk averse will optimally choose a portfolio with more invested in the risky asset portfolio and less invested in the risk-free asset.

Systematic (market) risk is due to factors, such as GDP growth and interest rate changes, that affect the values of all risky securities. Systematic risk cannot be reduced by diversification. Unsystematic (firm-specific) risk can be reduced by portfolio diversification.

Because one of the assumptions underlying the CAPM is that portfolio diversification to eliminate unsystematic risk is costless, investors cannot increase expected equilibrium portfolio returns by taking on unsystematic risk.

A return generating model is an equation that estimates the expected return of an investment, based on a security's exposure to one or more macroeconomic, fundamental, or statistical factors.


The simplest return generating model is the market model, which assumes the return on an asset is related to the return on the market portfolio in the following manner:

R_i = α_i + β_iR_m + e_i

Beta can be calculated using the following equation:

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where [Cov(R_i, R_m)] and ρ_i,m are the covariance and correlation between the asset and the market, and σ_i and σ_m are the standard deviations of asset returns and market returns.

The theoretical average beta of stocks in the market is 1. A beta of zero indicates that a security’s return is uncorrelated with the returns of the market.

The capital asset pricing model (CAPM) requires several assumptions:

• Investors are risk averse, utility maximizing, and rational.
• Markets are free of frictions like costs and taxes.
• All investors plan using the same time period.
• All investors have the same expectations of security returns.
• Investments are infinitely divisible.
• Prices are unaffected by an investor's trades.

The security market line (SML) is a graphical representation of the CAPM that plots expected return versus beta for any security.

The CAPM relates expected return to the market factor (beta) using the following formula:

E(R_i) − R_f = β_i[E(R_m) − R_f]

The CAPM and the SML indicate what a security’s equilibrium required rate of return should be based on the security’s exposure to market risk. An analyst can compare his expected rate of return on a security to the required rate of return indicated by the SML to determine whether the security is overvalued, undervalued, or properly valued.

The Sharpe ratio measures excess return per unit of total risk and is useful for comparing portfolios on a risk-adjusted basis. The M-squared measure provides the same portfolio rankings as the Sharpe ratio but is stated in percentage terms:

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The Treynor measure measures a portfolio’s excess return per unit of systematic risk. Jensen’s alpha is the difference between a portfolio’s return and the return of a portfolio on the SML that has the same beta:

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Jensen's alpha = α_P = R_P − [R_f + β_P(R_M − R_f)]

Many IPS include the following sections:

• Introduction—Describes the client.
• Statement of Purpose—The intentions of the IPS.
• Statement of Duties and Responsibilities—Of the client, the asset custodian, and the investment managers.
• Procedures—Related to keeping the IPS updated and responding to unforeseen events.
• Investment Objectives—The client’s investment needs, specified in terms of required return and risk tolerance.
• Investment Constraints—Factors that may hinder the ability to meet investment objectives; typically categorized as time horizon, taxes, liquidity, legal and regulatory, and unique needs.
• Investment Guidelines—For example, whether leverage, derivatives, or specific kinds of assets are allowed.
• Evaluation and Review—Related to feedback on investment results.
• Appendices—May specify the portfolio’s strategic asset allocation (policy portfolio) or the portfolio’s rebalancing policy.

Risk objectives are specifications for portfolio risk that are developed to embody a client’s risk tolerance. Risk objectives can be either absolute (e.g., no losses greater than 10% in any year) or relative (e.g., annual return will be within 2% of FTSE return).

Return objectives are typically based on an investor’s desire to meet a future financial goal, such as a particular level of income in retirement. Return objectives can be absolute (e.g., 9% annual return) or relative (e.g., outperform the S&P 500 by 2% per year).

The achievability of an investor’s return expectations may be hindered by the investor’s risk objectives.

Willingness to take financial risk is related to an investor’s psychological factors, such as personality type and level of financial knowledge.

Ability or capacity to take risk depends on financial factors, such as wealth relative to liabilities, income stability, and time horizon.

A client’s overall risk tolerance depends on both his ability to take risk and his willingness to take risk. A willingness greater than ability, or vice versa, is typically resolved by choosing the more conservative of the two and counseling the client.

Investment constraints include:

• Liquidity—The need to draw cash from the portfolio for anticipated or unexpected future spending needs. High liquidity needs often translate to a high portfolio allocation to bonds or cash.
• Time horizon—Often the period over which assets are accumulated and before withdrawals begin. Risky or illiquid investments may be inappropriate for an investor with a short time horizon.
• Tax considerations—Concerns the tax treatments of the investor’s various accounts, the relative tax treatment of capital gains and income, and the investor’s marginal tax bracket.
• Legal and regulatory—Constraints such as government restrictions on portfolio contents or laws against insider trading.
• Unique circumstances—Restrictions due to investor preferences (religious, ethical, etc.) or other factors not already considered.

Strategic asset allocation is a set of percentage allocations to various asset classes that is designed to meet the investor’s objectives. The strategic asset allocation is developed by combining the objectives and constraints in the IPS with the performance expectations of the various asset classes. The strategic asset allocation provides the basic structure of a portfolio.

Tactical asset allocation refers to an allocation that deviates from the baseline (strategic) allocation in order to profit from a forecast of shorter-term opportunities in specific asset classes.