Modern Portfolio Theory & Construction

Rebalancing at fixed time intervals.

Example: The portfolio returns to target weights every January and July.

Calendar Rebalancing describes rebalancing at fixed time intervals; the portfolio rule concerns how exposures interact inside a portfolio rather than how one holding performs in isolation. CorrelationA statistic ranging from minus one to plus one that describes how two return series move together., position size, horizon and rebalancing determine the combined result.

The portfolio returns to target weights every January and July.

Assess Calendar Rebalancing with portfolio-level data: weights, correlations, volatilityThe degree and frequency of price or return fluctuations., drawdownA decline from a previous portfolio or asset-value peak., liquidityThe ease and speed with which an investment can be converted into cash without a major price concession. and contribution to risk, not a list of securities alone; a portfolio can contain many securities and still depend on one economic risk.

A model linking expected return to the risk-free rate, market riskThe possibility of loss because broad market prices or rates move against an investment. premium, and an asset's beta.

Example: A higher-beta share receives a higher required return under CAPM.

Capital Asset Pricing Model is a model linking expected return to the risk-free rate, market risk premium, and an asset's beta; the portfolio rule concerns how exposures interact inside a portfolio rather than how one holding performs in isolation. Correlation, position size, horizon and rebalancing determine the combined result.

A higher-beta share receives a higher required return under CAPM.

Assess Capital Asset Pricing Model with portfolio-level data: weights, correlations, volatility, drawdown, liquidity and contribution to risk, not a list of securities alone; rebalancing rules matter because market movement changes exposure continuously.

A portfolio structure using a diversified low-cost core plus smaller active or specialised holdings.

Example: An index fundA fund designed to track the holdings and performance of a stated market index. forms 80% of the portfolio while sector funds make up the satellites.

Core-Satellite Strategy is a portfolio structure using a diversified low-cost core plus smaller active or specialised holdings. The effect of the portfolio rule appears at portfolio level: adding an asset can change expected return, volatility, liquidity or drawdown even when the asset looks unchanged on its own.

An index fund forms 80% of the portfolio while sector funds make up the satellites.

Assess Core-Satellite Strategy with portfolio-level data: weights, correlations, volatility, drawdown, liquidity and contribution to risk, not a list of securities alone.

The reduction in overall portfolio risk achieved by combining assets that do not move identically.

Example: Adding bonds reduces volatility when bonds and shares respond differently to shocks.

DiversificationSpreading investments across assets, issuers, sectors, or markets to reduce dependence on one exposure. Benefit is the reduction in overall portfolio risk achieved by combining assets that do not move identically; the portfolio rule concerns how exposures interact inside a portfolio rather than how one holding performs in isolation. Correlation, position size, horizon and rebalancing determine the combined result.

Adding bonds reduces volatility when bonds and shares respond differently to shocks. For Diversification Benefit, price changes, contributions and withdrawals can move the portfolio away from the intended structure.

For Diversification Benefit, map every holding to its economic exposure, calculate the resulting weights and concentrations, and test how the portfolio behaves when the largest risks fall together; diversification can weaken during a crisis when correlations rise.

The movement of portfolio weights away from their targets because assets earn different returns.

Example: Strong share gains cause the equity allocation to drift from 50% to 61%.

Drift is the movement of portfolio weights away from their targets because assets earn different returns; the portfolio rule translates an investorA person or organisation that commits capital with the expectation of a financial return.'s objectives and constraints into weights, limits or decision rules across assets.

Strong share gains cause the equity allocation to drift from 50% to 61%. For Drift, price changes, contributions and withdrawals can move the portfolio away from the intended structure.

For Drift, map every holding to its economic exposure, calculate the resulting weights and concentrations, and test how the portfolio behaves when the largest risks fall together; rebalancing rules matter because market movement changes exposure continuously.

An approach that changes asset weights as markets, valuations, or investor circumstances change.

Example: Equity exposure falls automatically as portfolio volatility rises.

Dynamic Asset AllocationThe percentage of a portfolio invested across asset classes such as cash, bonds, shares, and property. is an approach that changes asset weights as markets, valuations, or investor circumstances change; a portfolio's experience of the portfolio rule depends on both the chosen holdings and how their returns move together under normal and stressed conditions.

Equity exposure falls automatically as portfolio volatility rises.

The useful question for Dynamic Asset Allocation is whether the structure can fund the investor's goals through both ordinary markets and plausible stress scenarios.

The set of portfolios offering the highest expected return for each level of risk under stated assumptions.

Example: An inefficient portfolio can be replaced by one with higher expected return at the same volatility.

Efficient Frontier is the set of portfolios offering the highest expected return for each level of risk under stated assumptions; the portfolio rule concerns how exposures interact inside a portfolio rather than how one holding performs in isolation. Correlation, position size, horizon and rebalancing determine the combined result.

An inefficient portfolio can be replaced by one with higher expected return at the same volatility. For Efficient Frontier, price changes, contributions and withdrawals can move the portfolio away from the intended structure.

Document the objective, target ranges, rebalancing rule, liquidity reserve and maximum acceptable loss associated with Efficient Frontier; review them after material life or market changes. A portfolio can contain many securities and still depend on one economic risk.

Assigning the same portfolio weight to each holding.

Example: A ten-stock portfolio places 10% in each company.

Equal Weighting describes assigning the same portfolio weight to each holding; the outcome from the rule depends on index construction: eligible universe, weighting method, rebalance dates, turnover, costs and treatment of distributions.

A ten-stock portfolio places 10% in each company.

For Equal Weighting, read the methodology, eligible universe, weighting and rebalance rules; compare live performance with the stated benchmarkA reference index or rate used to evaluate a fund's performance. after fees and trading costs. Rules remove discretion but do not remove investmentAn asset or commitment of money made with the expectation of future income, growth, or both. risk; Also compare Price Weighting, defined here as weighting index constituents according to their share prices.

The extra return investors require or expect from equities over a lower-risk reference.

Example: A higher equity risk premium lowers the present valueThe current worth of money expected in the future after applying a discount rate. of risky company cash flows.

Equity Risk Premium is the extra return investors require or expect from equities over a lower-risk reference; a portfolio's experience of the portfolio rule depends on both the chosen holdings and how their returns move together under normal and stressed conditions.

A higher equity risk premium lowers the present value of risky company cash flows. The stated numbers make the construction visible, but they should be tested under losses, liquidity pressure and changing correlations.

For Equity Risk Premium, map every holding to its economic exposure, calculate the resulting weights and concentrations, and test how the portfolio behaves when the largest risks fall together; modelled efficiency is sensitive to assumptions and estimation error.

The probability-weighted average of possible future returns or an estimate of future return.

Example: A 50% chance of 20% and 50% chance of 0% gives a 10% expected return.

Expected Return is the probability-weighted average of possible future returns or an estimate of future return. The effect of the portfolio rule appears at portfolio level: adding an asset can change expected return, volatility, liquidity or drawdown even when the asset looks unchanged on its own.

A 50% chance of 20% and 50% chance of 0% gives a 10% expected return.

Assess Expected Return with portfolio-level data: weights, correlations, volatility, drawdown, liquidity and contribution to risk, not a list of securities alone; modelled efficiency is sensitive to assumptions and estimation error.

Weighting companies using measures such as sales, cash flow, dividends, or book valueThe accounting value of shareholders' equity..

Example: A fundamentally weighted index gives more weight to firms with larger revenues.

Fundamental Weighting describes weighting companies using measures such as sales, cash flow, dividends, or book value; the rule describes a systematic exposure, but implementation determines whether an investor receives the theoretical return after fees and trading frictions.

A fundamentally weighted index gives more weight to firms with larger revenues.

Evaluate Fundamental Weighting through holdings and exposures rather than the product name; measure concentrationThe degree to which a portfolio depends on a small number of holdings, sectors, or issuers., turnover, tracking differenceThe actual return difference between an index-tracking fund and its benchmark over a period. and performance across full cycles. Back-tested performance can be sensitive to data mining and implementation assumptions.

The single portfolio with the lowest varianceThe average squared deviation of returns from their mean. on the entire feasible set.

Example: The global minimum-variance point sits at the far-left edge of the efficient frontier.

Global Minimum-Variance Portfolio is the single portfolio with the lowest variance on the entire feasible set; the portfolio rule concerns how exposures interact inside a portfolio rather than how one holding performs in isolation. Correlation, position size, horizon and rebalancing determine the combined result.

The global minimum-variance point sits at the far-left edge of the efficient frontier.

The useful question for Global Minimum-Variance Portfolio is whether the structure can fund the investor's goals through both ordinary markets and plausible stress scenarios; a portfolio can contain many securities and still depend on one economic risk.

Weighting securities according to their market values.

Example: The largest listed company receives the highest weight in a market-cap index.

Market-Capitalisation Weighting describes weighting securities according to their market values; the outcome from the rule depends on index construction: eligible universe, weighting method, rebalance dates, turnover, costs and treatment of distributions.

For example, the largest listed company receives the highest weight in a market-cap index.

Before investing through Market-Capitalisation Weighting, identify the economic reason the exposure should earn a return and the conditions under which it is likely to fail; back-tested performance can be sensitive to data mining and implementation assumptions.

The expected return of the broad market above the risk-free rate.

Example: If expected market return is 15% and the risk-free rate is 10%, the premium is 5%.

Market Risk Premium is the expected return of the broad market above the risk-free rate; the portfolio rule translates an investor's objectives and constraints into weights, limits or decision rules across assets.

If expected market return is 15% and the risk-free rate is 10%, the premium is 5%.

For Market Risk Premium, map every holding to its economic exposure, calculate the resulting weights and concentrations, and test how the portfolio behaves when the largest risks fall together.

A method that selects portfolio weights using expected returns, variances, and correlations.

Example: The optimiser favours assets with attractive expected returns and diversification benefits.

Mean-Variance Optimisation is a method that selects portfolio weights using expected returns, variances, and correlations; the portfolio rule concerns how exposures interact inside a portfolio rather than how one holding performs in isolation. Correlation, position size, horizon and rebalancing determine the combined result.

The optimiser favours assets with attractive expected returns and diversification benefits.

The useful question for Mean-Variance Optimisation is whether the structure can fund the investor's goals through both ordinary markets and plausible stress scenarios.

The portfolio with the lowest expected variance among the available combinations.

Example: Optimisation identifies the asset weights that minimise volatility.

Minimum-Variance Portfolio is the portfolio with the lowest expected variance among the available combinations; the effect of the portfolio rule appears at portfolio level: adding an asset can change expected return, volatility, liquidity or drawdown even when the asset looks unchanged on its own.

For example, optimisation identifies the asset weights that minimise volatility. For Minimum-Variance Portfolio, price changes, contributions and withdrawals can move the portfolio away from the intended structure.

The useful question for Minimum-Variance Portfolio is whether the structure can fund the investor's goals through both ordinary markets and plausible stress scenarios; rebalancing rules matter because market movement changes exposure continuously.

A framework for combining assets based on expected return, risk, and correlation.

Example: The framework shows why a diversified portfolio can be less risky than its individual holdings.

Modern Portfolio Theory is a framework for combining assets based on expected return, risk, and correlation; the portfolio rule concerns how exposures interact inside a portfolio rather than how one holding performs in isolation. Correlation, position size, horizon and rebalancing determine the combined result.

The framework shows why a diversified portfolio can be less risky than its individual holdings. The stated numbers make the construction visible, but they should be tested under losses, liquidity pressure and changing correlations.

For Modern Portfolio Theory, map every holding to its economic exposure, calculate the resulting weights and concentrations, and test how the portfolio behaves when the largest risks fall together.

The complete collection of investments owned by an investor or managed under one mandate.

Example: A portfolio may contain shares, bonds, cash, propertyLand and buildings held for use, rent, development, or capital appreciation., and private investments.

Portfolio is the complete collection of investments owned by an investor or managed under one mandate. The effect of the portfolio rule appears at portfolio level: adding an asset can change expected return, volatility, liquidity or drawdown even when the asset looks unchanged on its own.

A portfolio may contain shares, bonds, cash, property, and private investments.

Document the objective, target ranges, rebalancing rule, liquidity reserve and maximum acceptable loss associated with Portfolio; review them after material life or market changes.

The process of selecting and combining investments to meet return, risk, liquidity, and time-horizon objectives.

Example: An adviser builds a portfolio around the investor's retirement date and loss tolerance.

Portfolio Construction is the process of selecting and combining investments to meet return, risk, liquidity, and time-horizon objectives; the portfolio rule concerns how exposures interact inside a portfolio rather than how one holding performs in isolation. Correlation, position size, horizon and rebalancing determine the combined result.

An adviser builds a portfolio around the investor's retirement date and loss tolerance.

Assess Portfolio Construction with portfolio-level data: weights, correlations, volatility, drawdown, liquidity and contribution to risk, not a list of securities alone; rebalancing rules matter because market movement changes exposure continuously.

Weighting index constituents according to their share prices.

Example: A ₦200 share influences a price-weighted index more than a ₦20 share.

Price Weighting describes weighting index constituents according to their share prices; the outcome from the rule depends on index construction: eligible universe, weighting method, rebalance dates, turnover, costs and treatment of distributions.

A ₦200 share influences a price-weighted index more than a ₦20 share.

For Price Weighting, read the methodology, eligible universe, weighting and rebalance rules; compare live performance with the stated benchmark after fees and trading costs. A factor can underperform for many years even if its long-run rationale remains intact.

Restoring a portfolio toward its target weights by buying or selling assets.

Example: After equities rise to 70% of a 60% target, the investor sells some shares and buys bonds.

Rebalancing describes restoring a portfolio toward its target weights by buying or selling assets; the effect of the portfolio rule appears at portfolio level: adding an asset can change expected return, volatility, liquidity or drawdown even when the asset looks unchanged on its own.

For example, after equities rise to 70% of a 60% target, the investor sells some shares and buys bonds.

Document the objective, target ranges, rebalancing rule, liquidity reserve and maximum acceptable loss associated with Rebalancing; review them after material life or market changes.

The minimum expected return an investor demands for the time and risk involved.

Example: A project is rejected because its expected 12% return is below the 16% required return.

Required Return is the minimum expected return an investor demands for the time and risk involved; the portfolio rule concerns how exposures interact inside a portfolio rather than how one holding performs in isolation. Correlation, position size, horizon and rebalancing determine the combined result.

A project is rejected because its expected 12% return is below the 16% required return. For Required Return, price changes, contributions and withdrawals can move the portfolio away from the intended structure.

Document the objective, target ranges, rebalancing rule, liquidity reserve and maximum acceptable loss associated with Required Return; review them after material life or market changes. Diversification can weaken during a crisis when correlations rise.

The return assumed to be available from an investment with negligible default riskThe risk that an issuer does not pay interest or principal when due. over a matching period.

Example: Analysts often use a short-term government yield as a practical risk-free proxy.

Risk-Free Rate is the return assumed to be available from an investment with negligible default risk over a matching period; a portfolio's experience of the portfolio rule depends on both the chosen holdings and how their returns move together under normal and stressed conditions.

Analysts often use a short-term government yield as a practical risk-free proxy. The stated numbers make the construction visible, but they should be tested under losses, liquidity pressure and changing correlations.

For Risk-Free Rate, map every holding to its economic exposure, calculate the resulting weights and concentrations, and test how the portfolio behaves when the largest risks fall together; a portfolio can contain many securities and still depend on one economic risk.

An approach that allocates assets so each contributes a similar amount of portfolio risk.

Example: Because bonds are less volatile, a risk-parity portfolio may hold more bonds than shares.

Risk Parity is an approach that allocates assets so each contributes a similar amount of portfolio risk; a portfolio's experience of the portfolio rule depends on both the chosen holdings and how their returns move together under normal and stressed conditions.

Because bonds are less volatile, a risk-parity portfolio may hold more bonds than shares.

For Risk Parity, map every holding to its economic exposure, calculate the resulting weights and concentrations, and test how the portfolio behaves when the largest risks fall together; diversification can weaken during a crisis when correlations rise.

A line showing the CAPM relationship between expected return and beta.

Example: A securityA tradable financial claim or ownership interest, such as a share, bond, or fund unit. above the line appears to offer more return than its beta implies.

Security Market Line is a line showing the CAPM relationship between expected return and beta; the portfolio rule translates an investor's objectives and constraints into weights, limits or decision rules across assets.

For example, a security above the line appears to offer more return than its beta implies. For Security Market Line, price changes, contributions and withdrawals can move the portfolio away from the intended structure.

Assess Security Market Line with portfolio-level data: weights, correlations, volatility, drawdown, liquidity and contribution to risk, not a list of securities alone; diversification can weaken during a crisis when correlations rise.

A long-term target mix of asset classes based on an investor's objectives and constraints.

Example: A pension plan targets 50% bonds, 35% equities, 10% property, and 5% cash.

Strategic Asset Allocation is a long-term target mix of asset classes based on an investor's objectives and constraints; the portfolio rule concerns how exposures interact inside a portfolio rather than how one holding performs in isolation. Correlation, position size, horizon and rebalancing determine the combined result.

For example, a pension plan targets 50% bonds, 35% equities, 10% property, and 5% cash. The stated numbers make the construction visible, but they should be tested under losses, liquidity pressure and changing correlations.

Document the objective, target ranges, rebalancing rule, liquidity reserve and maximum acceptable loss associated with Strategic Asset Allocation; review them after material life or market changes. Diversification can weaken during a crisis when correlations rise.

A temporary deviation from long-term asset weights to exploit perceived opportunities or manage risk.

Example: The manager raises cash and reduces equities during unusually expensive market conditions.

Tactical Asset Allocation is a temporary deviation from long-term asset weights to exploit perceived opportunities or manage risk; a portfolio's experience of the portfolio rule depends on both the chosen holdings and how their returns move together under normal and stressed conditions.

The manager raises cash and reduces equities during unusually expensive market conditions. The stated numbers make the construction visible, but they should be tested under losses, liquidity pressure and changing correlations.

Document the objective, target ranges, rebalancing rule, liquidity reserve and maximum acceptable loss associated with Tactical Asset Allocation; review them after material life or market changes. Modelled efficiency is sensitive to assumptions and estimation error.

Rebalancing when an asset weight moves beyond a specified band.

Example: A 60% equity target triggers action whenever the weight moves below 55% or above 65%.

Threshold Rebalancing describes rebalancing when an asset weight moves beyond a specified band; a portfolio's experience of the portfolio rule depends on both the chosen holdings and how their returns move together under normal and stressed conditions.

A 60% equity target triggers action whenever the weight moves below 55% or above 65%.

Document the objective, target ranges, rebalancing rule, liquidity reserve and maximum acceptable loss associated with Threshold Rebalancing; review them after material life or market changes. A portfolio can contain many securities and still depend on one economic risk.