Portfolio Math You Must Know for the Series 66

The Series 66 is unique among NASAA exams because it tests both state securities law and investment concepts. The math portion covers topics you would expect in a finance course: risk measures, return calculations, bond math, and valuation ratios. Candidates who have a strong grasp of the law but weak quantitative skills find themselves frustrated by these questions.

This post covers the portfolio math formulas that appear most frequently on the Series 66, with worked examples and the logic behind each calculation.

Return Calculations

Total Return

Total return measures the complete gain or loss on an investment, including both price appreciation and income received.

Formula: Total return = (Ending value minus beginning value plus income) divided by beginning value

Example: An investor buys a stock for $40, receives $2 in dividends during the year, and sells it for $45. Total return = ($45 minus $40 plus $2) divided by $40 = $7 divided by $40 = 17.5 percent.

Holding Period Return vs. Annualized Return

Holding period return measures the return over the actual holding period, regardless of length. Annualized return adjusts the holding period return to a one-year equivalent, allowing comparison across investments held for different periods.

For the Series 66, you may see questions asking for the annualized return of a holding period that is not exactly one year. A common approach is to multiply the holding period return by the fraction (12 divided by the number of months held).

Risk Measures

Standard Deviation

Standard deviation measures the dispersion of returns around the average return. A higher standard deviation means more volatility. The Series 66 does not typically ask you to calculate standard deviation from raw data, but you must understand what it represents and how to use it in comparisons.

A portfolio with a standard deviation of 15 percent is more volatile than one with a standard deviation of 8 percent. When two portfolios have the same expected return, the one with lower standard deviation is preferred by a risk-averse investor.

Beta

Beta measures a security's sensitivity to market movements relative to a benchmark (typically the S&P 500, which has a beta of 1.0).

• Beta greater than 1: The security is more volatile than the market. A beta of 1.5 means the security tends to move 1.5 times as much as the market.
• Beta equal to 1: The security moves with the market.
• Beta less than 1: The security is less volatile than the market. Utility stocks and bonds often have betas below 1.
• Beta of 0: No correlation with market movements. Cash has a beta of approximately 0.
• Negative beta: The security tends to move opposite to the market. Gold and some inverse ETFs can have negative betas.

Portfolio beta: The beta of a portfolio is the weighted average of the betas of its component securities.

Example: A portfolio holds 60 percent in a stock with beta 1.2 and 40 percent in a bond fund with beta 0.3. Portfolio beta = (0.60 times 1.2) plus (0.40 times 0.3) = 0.72 plus 0.12 = 0.84.

Sharpe Ratio

The Sharpe ratio measures risk-adjusted return: how much return an investor earns per unit of total risk (standard deviation).

Formula: Sharpe ratio = (Portfolio return minus risk-free rate) divided by standard deviation

A higher Sharpe ratio is better. It means the investor is earning more return for each unit of risk taken.

Example: Portfolio A returns 10 percent with a standard deviation of 12 percent. The risk-free rate is 3 percent. Sharpe ratio = (10 minus 3) divided by 12 = 7 divided by 12 = 0.58.

Portfolio B returns 9 percent with a standard deviation of 8 percent. Sharpe ratio = (9 minus 3) divided by 8 = 6 divided by 8 = 0.75.

Portfolio B has a lower absolute return but a higher risk-adjusted return. For a risk-averse investor, Portfolio B is the better choice.

Bond Math

Current Yield

Formula: Current yield = Annual interest payment divided by current market price

Example: A bond pays $80 in annual interest and trades at $950. Current yield = $80 divided by $950 = 8.42 percent.

Yield to Maturity (Approximate)

The exact YTM requires a financial calculator or bond table. The approximate YTM formula gives a reasonable estimate:

Formula: Approximate YTM = (Annual interest plus discount divided by years remaining) divided by average of par and price

Or, for a premium bond: (Annual interest minus premium divided by years remaining) divided by average of par and price.

Example: A bond has a $1,000 par value, a $90 annual coupon, trades at $920, and has 10 years to maturity.

Discount = $1,000 minus $920 = $80. Annual discount accretion = $80 divided by 10 = $8.

Approximate YTM = ($90 plus $8) divided by (($1,000 plus $920) divided by 2) = $98 divided by $960 = 10.2 percent.

Duration

Duration measures how sensitive a bond's price is to interest rate changes. A bond with a duration of 5 years will decline approximately 5 percent in price for every 1 percent increase in interest rates (and rise approximately 5 percent for every 1 percent decrease).

Longer maturity bonds have higher duration. Lower coupon bonds have higher duration. Duration decreases as the bond approaches maturity.

The Series 66 tests duration conceptually. Know that duration is a measure of interest rate sensitivity, and that investors who expect rates to rise prefer lower-duration bonds to minimize price declines.

Valuation Ratios

Price-to-Earnings Ratio (P/E)

Formula: P/E = Market price per share divided by earnings per share

A P/E of 20 means investors are paying $20 for each dollar of current earnings. Higher P/E stocks are priced for higher future growth. The exam may ask you to determine whether a stock is overvalued or undervalued relative to its sector P/E or the market P/E.

Dividend Yield

Formula: Dividend yield = Annual dividend per share divided by market price per share

Example: A stock pays $2 in annual dividends and trades at $50. Dividend yield = $2 divided by $50 = 4 percent.

Earnings Per Share (EPS)

Formula: EPS = (Net income minus preferred dividends) divided by weighted average common shares outstanding

Diluted EPS accounts for the potential conversion of options, warrants, and convertible securities into common shares.

Correlation and Diversification

Correlation measures how two securities move in relation to each other. Correlation ranges from plus 1 (perfect positive correlation) to minus 1 (perfect negative correlation).

Adding securities with low or negative correlation to a portfolio reduces overall portfolio volatility (standard deviation) without necessarily reducing expected return. This is the mathematical basis of diversification.

The efficient frontier is the set of portfolios that offer the highest expected return for each level of risk. The Series 66 tests the concept that rational investors should hold portfolios on the efficient frontier, not below it.

The capital market line (CML) extends the efficient frontier by incorporating a risk-free asset. The optimal portfolio for any investor is the point on the CML that matches their risk tolerance.

Practice these calculations until the process feels mechanical. The Series 66 is not a heavy math exam, but the quantitative questions it does include are straightforward if you know the formulas and understand the logic.