Portfolio Management

Modern Portfolio Theory (MPT)

Modern Portfolio Theory, developed by Harry Markowitz in 1952, is one of the most important frameworks in investment management. MPT fundamentally changed how investors think about building portfolios by demonstrating that risk and return must be evaluated at the portfolio level, not just at the individual security level. Before Markowitz, investors evaluated each investment in isolation. MPT showed that the interaction between securities—specifically, how their returns move relative to each other—matters enormously.

The central insight of MPT is that diversification can reduce portfolio risk without necessarily sacrificing expected return. By combining assets whose returns do not move in perfect lockstep, an investor can achieve a more favorable risk-return tradeoff than holding any single asset alone. This is sometimes called the "only free lunch in finance."

Key Assumptions of MPT

MPT rests on several assumptions about investor behavior and markets:

• Investors are rational and risk-averse: Given two portfolios with the same expected return, investors will choose the one with lower risk. They require higher expected returns to accept higher risk.
• Markets are efficient: All investors have access to the same information, and securities are fairly priced.
• Returns are normally distributed: Investment returns follow a bell curve, which allows risk to be fully captured by standard deviation.
• Investors focus on a single-period investment horizon: All investment decisions are based on expected return and risk over one time period.
• There are no taxes or transaction costs: Investors can buy and sell freely without friction (relaxed in practice).

The Efficient Frontier

The efficient frontier is a curve on a graph plotting expected return (y-axis) against risk measured by standard deviation (x-axis). Every point on the efficient frontier represents a portfolio that offers the highest expected return for its level of risk. Portfolios below the efficient frontier are "inefficient" because they offer less return for the same level of risk, or more risk for the same return.

No rational investor would choose a portfolio below the efficient frontier. The goal of portfolio optimization is to move a portfolio as close to the efficient frontier as possible. The shape of the frontier curves upward and to the left because diversification allows portfolios to achieve better risk-return tradeoffs than individual securities alone.

Correlation and Covariance

The degree to which two assets' returns move together is measured by correlation and covariance. These concepts are the engine that drives diversification benefits.

Correlation coefficient (r) ranges from -1.0 to +1.0:

• +1.0 (perfect positive correlation): The two assets always move in the same direction by proportional amounts. No diversification benefit exists.
• 0 (zero correlation): The assets' returns are completely independent of each other. Significant diversification benefit.
• -1.0 (perfect negative correlation): The assets always move in opposite directions. Maximum diversification benefit—risk can theoretically be eliminated entirely.

Covariance measures the directional relationship between two asset returns in absolute terms. Unlike correlation, covariance is not bounded between -1 and +1, making it harder to interpret. Correlation is essentially a standardized version of covariance. The formula is: Correlation = Covariance / (Standard Deviation of A x Standard Deviation of B).

Systematic vs. Unsystematic Risk

Total portfolio risk can be divided into two distinct components: systematic risk (also called market risk, non-diversifiable risk, or undiversifiable risk) and unsystematic risk (also called company-specific risk, business risk, diversifiable risk, or unique risk). Understanding this distinction is critical for portfolio management and for the Series 65 exam.

Systematic Risk

Systematic risk affects the entire market or broad segments of the market. It cannot be eliminated through diversification. Examples include:

• Market risk: The risk that the overall market declines, pulling down most stocks regardless of their individual fundamentals.
• Interest rate risk: Changes in interest rates affect virtually all securities—bond prices fall when rates rise, and equities are impacted through discount rate changes.
• Inflation risk (purchasing power risk): Rising inflation erodes the real value of future cash flows from all investments.
• Exchange rate risk: For internationally diversified portfolios, currency fluctuations create risk across all foreign holdings.
• Political/regulatory risk: Government actions (tax changes, trade policy, regulation) can impact entire markets.

Unsystematic Risk

Unsystematic risk is specific to a single company, industry, or sector. It can be reduced or eliminated through diversification. Examples include:

• Business risk: Risk related to a specific company's operations (e.g., a product recall, management failure, competitive pressure).
• Financial risk: Risk arising from a company's capital structure and use of debt (leverage).
• Industry risk: Risk specific to a particular industry (e.g., regulatory changes affecting only pharmaceutical companies).

Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model, developed by William Sharpe, John Lintner, and Jan Mossin in the 1960s, builds on MPT to establish a relationship between the expected return of an investment and its systematic risk (beta). CAPM is arguably the most tested formula on the Series 65 exam.

The CAPM Formula

The CAPM formula calculates the expected return (also called the required return) of an asset:

Expected Return = Risk-Free Rate + Beta x (Market Return - Risk-Free Rate)

Or equivalently: E(R) = Rf + β x (Rm - Rf)

Where:

• E(R) = Expected (required) return of the asset
• Rf = Risk-free rate of return (typically the 91-day T-bill rate)
• β (Beta) = Measure of the asset's systematic risk relative to the market
• Rm = Expected return of the overall market
• (Rm - Rf) = Market risk premium (the extra return investors demand for taking market risk instead of investing in risk-free assets)

Alpha and Beta

Beta (β) measures a security's sensitivity to market movements—its systematic risk. Beta is the cornerstone of CAPM:

• β = 1.0: The security moves in line with the market. If the market goes up 10%, the security is expected to go up 10%.
• β > 1.0: The security is more volatile than the market (aggressive). A beta of 1.5 means if the market moves 10%, the security is expected to move 15% in the same direction.
• β < 1.0: The security is less volatile than the market (defensive). A beta of 0.5 means if the market moves 10%, the security is expected to move 5%.
• β = 0: The security has no correlation to the market (e.g., risk-free assets like T-bills).
• β < 0: The security moves inversely to the market (rare; some inverse ETFs have negative betas).

Alpha (α) represents the excess return of an investment relative to what CAPM predicts. It measures the value added (or subtracted) by the portfolio manager:

• Positive alpha: The manager outperformed the CAPM-predicted return (added value through skill or security selection).
• Zero alpha: The manager performed exactly as predicted by CAPM.
• Negative alpha: The manager underperformed the CAPM-predicted return.

Alpha is calculated as: α = Actual Return - Expected Return (from CAPM)

Risk-Adjusted Performance Measures

Simply comparing raw returns is inadequate for evaluating portfolio performance because it ignores risk. A portfolio that returned 15% might sound impressive, but if it took enormous risk to achieve that return, it may not have performed well on a risk-adjusted basis. The Series 65 exam tests four key risk-adjusted performance measures.

Standard Deviation

Standard deviation measures the total variability of returns around the average (mean) return. It captures both systematic and unsystematic risk. A higher standard deviation means returns are more spread out (more volatile), while a lower standard deviation means returns are more consistent.

In a normal distribution, approximately 68% of returns fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. For example, if a portfolio has a mean return of 10% with a standard deviation of 5%, then in roughly 68% of periods, the return will be between 5% and 15%.

Sharpe Ratio

The Sharpe ratio, developed by William Sharpe, measures the excess return per unit of total risk (standard deviation). It answers the question: "How much additional return am I earning for each unit of total risk I take?"

Sharpe Ratio = (Portfolio Return - Risk-Free Rate) / Standard Deviation of Portfolio

A higher Sharpe ratio indicates better risk-adjusted performance. It is most appropriate for evaluating a portfolio that represents the investor's entire investment, because it uses total risk (standard deviation) rather than just systematic risk.

Treynor Ratio

The Treynor ratio, developed by Jack Treynor, measures excess return per unit of systematic risk (beta). Unlike the Sharpe ratio, it only considers non-diversifiable risk.

Treynor Ratio = (Portfolio Return - Risk-Free Rate) / Beta of Portfolio

The Treynor ratio is most appropriate for evaluating a portfolio that is part of a larger, diversified portfolio. Since unsystematic risk can be diversified away in the larger portfolio, only systematic risk (beta) is relevant.

Jensen's Alpha (Jensen's Measure)

Jensen's alpha measures the absolute difference between the portfolio's actual return and the return predicted by CAPM given the portfolio's beta. It answers: "Did the manager add or destroy value?"

Jensen's Alpha = Actual Return - [Risk-Free Rate + Beta x (Market Return - Risk-Free Rate)]

A positive Jensen's alpha means the manager beat the CAPM-predicted return. A negative alpha means the manager underperformed.

R-Squared (Coefficient of Determination)

R-squared (R²) measures the percentage of a portfolio's return movements that can be explained by the movements of its benchmark index. R-squared ranges from 0% to 100%:

• R² = 100%: All of the portfolio's movements are perfectly explained by the benchmark. The portfolio tracks its benchmark exactly.
• R² = 85% or higher: Generally considered a high correlation to the benchmark. Beta is a reliable measure of the portfolio's risk.
• R² below 70%: The benchmark is a poor fit for the portfolio. Beta may not be meaningful, and the Sharpe ratio (which uses total risk) would be a more appropriate performance measure.

Asset Allocation Strategies

Asset allocation is the process of dividing a portfolio among different asset classes such as stocks, bonds, cash equivalents, real estate, and alternative investments. Research consistently shows that asset allocation is the primary determinant of portfolio returns—more important than individual security selection or market timing. The landmark Brinson, Hood, and Beebower (1986) study found that asset allocation explained over 90% of the variability in portfolio returns over time.

Strategic Asset Allocation

Strategic asset allocation establishes a long-term target mix of asset classes based on the investor's risk tolerance, time horizon, and financial goals. This is the "baseline" or "policy" allocation. The investor selects target weights (e.g., 60% stocks, 30% bonds, 10% cash) and periodically rebalances back to these targets as market movements cause drift.

Strategic allocation is a passive, long-term approach. It assumes that the target weights represent the optimal mix for the investor's circumstances and that markets are generally efficient over the long run. Changes to the strategic allocation occur only when the investor's circumstances change significantly (e.g., approaching retirement, major life event).

Tactical Asset Allocation

Tactical asset allocation involves making short-term deviations from the strategic allocation to capitalize on perceived market opportunities or inefficiencies. For example, if an adviser believes that stocks are temporarily undervalued, they might temporarily increase the equity allocation from 60% to 70% and reduce bonds accordingly.

Tactical allocation is an active, short-term overlay on the strategic allocation. It requires the adviser to make market timing judgments. The tactical deviations are typically bounded by preset limits (e.g., no more than plus or minus 10% from the strategic target). When the perceived opportunity passes, the portfolio returns to its strategic weights.

Dynamic Asset Allocation

Dynamic asset allocation adjusts the portfolio mix in response to changing market conditions on an ongoing basis. Unlike tactical allocation (which makes temporary deviations), dynamic allocation involves continuous adjustment. A common form is portfolio insurance, where the equity allocation is reduced as the market declines and increased as the market rises, based on a formula.

Dynamic allocation is most often used by institutional investors and relies on quantitative models or rules-based systems. It is more reactive than tactical allocation and adjusts continuously rather than making discrete timing bets.

Rebalancing and Dollar-Cost Averaging

Portfolio Rebalancing

Rebalancing is the process of restoring a portfolio to its target asset allocation. Over time, different asset classes produce different returns, causing the portfolio's actual allocation to drift from its target. For example, after a strong stock market rally, a 60/40 stock/bond portfolio might become 70/30. Rebalancing sells the outperformers and buys the underperformers to restore the original 60/40 mix.

There are two primary rebalancing methods:

• Calendar rebalancing: Rebalance at fixed intervals (quarterly, semi-annually, annually). Simple and systematic, but may rebalance when unnecessary or miss large drifts between scheduled dates.
• Threshold (percentage-of-portfolio) rebalancing: Rebalance whenever an asset class deviates from its target by a preset amount (e.g., plus or minus 5%). More responsive to market movements but requires continuous monitoring.

Rebalancing has a contrarian nature: it systematically sells assets that have risen in value and buys those that have fallen. This disciplined approach helps maintain the investor's desired risk level and may enhance returns by capitalizing on mean reversion.

Dollar-Cost Averaging (DCA)

Dollar-cost averaging is an investment strategy in which an investor invests a fixed dollar amount at regular intervals regardless of the market price. When prices are low, the fixed amount buys more shares. When prices are high, it buys fewer shares. Over time, this results in an average cost per share that is lower than the average price per share.

Diversification Across Asset Classes

Diversification is the practice of spreading investments across different asset classes, sectors, geographies, and investment styles to reduce overall portfolio risk. While diversification cannot eliminate systematic risk, it can effectively eliminate unsystematic risk. Academic research suggests that a portfolio of 20-30 different stocks across various sectors eliminates most unsystematic risk, though diversification across asset classes (stocks, bonds, real estate, commodities) provides additional benefits.

Asset Class Diversification

Different asset classes respond differently to economic conditions:

• Equities: Tend to perform well during economic growth but are vulnerable to recessions and market downturns.
• Fixed income (bonds): Often provide stability and income; government bonds may rise when equities fall (flight to quality).
• Real estate: Offers inflation protection and income, with low correlation to stocks and bonds.
• Commodities: Historically low correlation to stocks and bonds; may hedge against inflation.
• Cash equivalents: Provide safety and liquidity but offer minimal real returns.
• International investments: Provide geographic diversification, though global market correlations have increased over time.

The key to effective diversification is combining assets with low or negative correlations. A portfolio of 10 stocks from the same industry provides far less diversification than a portfolio of 10 stocks from 10 different industries, even though both hold 10 positions.