Series 65 Portfolio Theory: CAPM, Sharpe Ratio, and the Math You Actually Need

The Series 65 is not a math-heavy exam, but it does test a specific set of quantitative concepts from portfolio theory. These concepts account for roughly 30% of the Client Investment Recommendations & Strategies section, which itself makes up 30% of the exam. Understanding these ideas — and the key formulas — is worth real points.

This post covers the portfolio theory material that actually shows up on the exam.

Modern Portfolio Theory

Modern Portfolio Theory (MPT), developed by Harry Markowitz, holds that investors can construct portfolios that maximize expected return for a given level of risk by combining assets that do not move perfectly in sync with each other.

The key insight is diversification: by combining assets with low or negative correlation, the portfolio's overall volatility can be lower than any individual asset's volatility. The exam tests whether you understand why diversification works — it is because of low or negative correlation, not because you simply own many securities.

The Efficient Frontier is the set of portfolios that offer the highest expected return for each level of risk. Portfolios on the efficient frontier are considered "efficient." Portfolios below the frontier are suboptimal — you could get more return for the same risk, or the same return for less risk.

Systematic vs. Unsystematic Risk

All risk falls into two buckets:

Systematic risk (market risk) affects the entire market and cannot be eliminated through diversification. Examples include interest rate risk, inflation risk, and broad economic recessions. Beta measures systematic risk.

Unsystematic risk (specific risk or company risk) is unique to a specific company or industry. Examples include business risk, regulatory risk, and key-person risk. Unsystematic risk CAN be reduced through diversification. A well-diversified portfolio of approximately 20–30 stocks eliminates most unsystematic risk.

Capital Asset Pricing Model (CAPM)

CAPM describes the relationship between risk and expected return for a security. The formula:

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

The term (Market Return − Risk-Free Rate) is called the market risk premium — it is the extra return the market offers above the risk-free rate to compensate for bearing market risk.

Beta measures how a security moves relative to the market:

• Beta = 1: The security moves in line with the market
• Beta > 1: More volatile than the market (amplified moves)
• Beta < 1: Less volatile than the market
• Beta < 0: Moves opposite the market (rare; some inverse ETFs)

Example: The risk-free rate is 3%, the market return is 9%, and a stock has a beta of 1.5. The expected return is 3% + 1.5 × (9% − 3%) = 3% + 9% = 12%.

Alpha

Alpha represents the excess return above what CAPM would predict. A positive alpha means the portfolio manager added value beyond what the risk level would justify. A negative alpha means the portfolio underperformed relative to its risk.

Alpha and beta together assess a portfolio manager's skill (alpha) and the systematic risk taken to achieve it (beta).

Standard Deviation

Standard deviation measures the total variability of returns around the average return. It captures both systematic and unsystematic risk and is used as the risk measure in the Sharpe Ratio.

The exam tests this rule of thumb for normal distributions:

• 1 standard deviation above and below the mean captures approximately 68% of outcomes
• 2 standard deviations captures approximately 95% of outcomes

The Sharpe Ratio

The Sharpe Ratio measures risk-adjusted return — specifically, how much excess return you earn per unit of total risk (standard deviation):

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

The risk-free rate used is typically the 90-day Treasury bill rate. A higher Sharpe Ratio is better — it means more return per unit of risk.

Example: A portfolio returns 12%, the risk-free rate is 3%, and the portfolio's standard deviation is 15%. Sharpe Ratio = (12% − 3%) / 15% = 0.60.

Time-Weighted vs. Money-Weighted Return

The exam distinguishes these two return calculation methods:

Time-weighted return measures the portfolio manager's performance independent of client cash flows. It chains together the returns for each sub-period. This is the standard measure used to evaluate manager skill because it removes the effect of client deposits and withdrawals.

Money-weighted return (internal rate of return) accounts for the timing and size of client cash flows. It reflects the investor's actual experience — if a large deposit came in right before a down period, that hurts the money-weighted return even if the manager's skill was fine.

When evaluating a portfolio manager's performance, use time-weighted return. When evaluating how the investor actually did, use money-weighted return.

Efficient Market Hypothesis

The Efficient Market Hypothesis (EMH) states that asset prices fully reflect all available information. It has three forms:

Weak form: Prices reflect all historical price and volume data. Therefore, technical analysis (charting) cannot consistently outperform the market.

Semi-strong form: Prices reflect all publicly available information — including historical prices, financial statements, earnings reports, and economic data. Therefore, fundamental analysis (analyzing financials) also cannot consistently outperform.

Strong form: Prices reflect all information, including private and insider information. No one can consistently outperform. Most academics and regulators reject the strong form because insider trading laws exist precisely because insider information is not fully reflected in prices.

Asset Allocation Strategies

Strategic asset allocation sets target weights for asset classes (e.g., 60% equity / 40% fixed income) and periodically rebalances back to those targets. It is long-term and does not attempt to time the market.

Tactical asset allocation actively shifts weights based on short-term market views. It is a form of active management and incurs higher transaction costs.

Dollar-cost averaging is the practice of investing a fixed dollar amount at regular intervals regardless of price. When prices are low, more shares are purchased; when prices are high, fewer shares are purchased. The result is that the average cost per share is always lower than the average price per share over the period. This is a mathematical certainty, not a prediction.

These concepts represent the core of what the Series 65 tests in portfolio theory. Understand the formulas, practice the calculations, and make sure you can explain the logic — the exam will test your understanding, not just your ability to recall a number.