Study guide
This chapter maps to Section I of the official NASAA Series 66 outline, which is weighted at 8 percent, or about 8 of your 100 scored questions. Unlike the Series 65, the Series 66 version of this section is narrow: it covers only analytical methods, meaning time value of money, descriptive statistics, risk-adjusted performance measures, and financial ratio and valuation calculations. Master a small set of formulas and definitions and this section becomes some of the easiest points on the exam.
The Time Value of Money: FV, NPV, and IRR
The time value of money is the idea that a dollar today is worth more than a dollar tomorrow, because today's dollar can be invested and earn a return. Future value (FV) is what a sum grows to at a given rate: $10,000 compounding at 8 percent for one year becomes $10,800, and compounding means each period's earnings themselves earn a return in later periods. Present value runs the calculation in reverse, discounting a future cash flow back to today at a required rate of return. Net present value (NPV) applies discounting to an entire investment: add up the present values of all expected future cash flows, then subtract the initial cost. If NPV is positive, the investment is expected to earn more than the discount rate used, so it clears the investor's hurdle; if NPV is negative, it falls short. Suppose Maria can buy an investment for $9,500 that she calculates has a present value of $10,000 using her 7 percent required return. The NPV is positive $500, so the purchase makes sense at her required rate. Internal rate of return (IRR) is the discount rate that makes NPV exactly zero, in other words the compound annual return the investment's cash flows actually imply. IRR works best for investments with defined cash flows and a defined maturity, which is why a bond's yield to maturity is simply the IRR of its coupon payments and principal repayment. Know the relationships: if an investment's IRR exceeds the required return, its NPV is positive, and vice versa.
Descriptive Statistics: Central Tendency, Dispersion, and Correlation
The exam tests a handful of statistical vocabulary words. The mean is the simple average of a data set. The median is the middle value when the data are ranked, and it is the better measure when a few extreme values distort the average; one billionaire moving into a small town skews the mean income but barely moves the median. The mode is the value that appears most often, and the range is simply the highest value minus the lowest. Standard deviation measures how widely an investment's returns are dispersed around their average, so it is the exam's standard measure of total risk, or volatility. A fund averaging 8 percent with a standard deviation of 4 percent has been far steadier than one averaging 8 percent with a standard deviation of 20 percent. If returns are normally distributed, roughly two thirds of outcomes fall within one standard deviation of the mean and about 95 percent fall within two. Correlation measures how two assets move relative to each other on a scale from +1.0 to -1.0. A correlation of +1.0 means the assets move in lockstep, 0 means their movements are unrelated, and -1.0 means they move exactly opposite each other. Diversification works best when portfolio holdings have low or negative correlation, because one asset's decline is offset by another's stability or gain. Combining two assets that are perfectly positively correlated provides essentially no risk-reduction benefit.
Risk-Adjusted Measures: Beta, Alpha, and the Sharpe Ratio
Raw return tells you little without knowing how much risk was taken to earn it, so the outline lists three risk-adjusted measures. Beta measures an investment's volatility relative to the overall market, which by definition has a beta of 1.0. A stock with a beta of 1.2 is expected to move about 20 percent more than the market in either direction: if the market rises 10 percent, the stock should rise roughly 12 percent. Beta captures only systematic risk, the market-wide risk that diversification cannot eliminate. A beta below 1.0 means less volatile than the market, and a negative beta means the asset tends to move opposite the market. Alpha measures the return earned above or below what was expected given the investment's beta. Positive alpha is the classic evidence of manager skill: if a portfolio's risk level predicted a 9 percent return and it actually earned 11 percent, the manager generated an alpha of +2. Index funds, which merely track the market, are expected to produce zero alpha before fees. The Sharpe ratio measures reward per unit of total risk: subtract the risk-free rate (typically the Treasury bill yield) from the portfolio's return, then divide by the portfolio's standard deviation. A higher Sharpe ratio means more excess return for each unit of volatility taken. Because the Sharpe ratio uses standard deviation rather than beta, it evaluates total risk and is meaningful even for portfolios that are not fully diversified.
Financial Ratios and Valuation Multiples
The outline names three balance-sheet ratios and two valuation multiples, and the exam expects you to both interpret and calculate them. The current ratio is current assets divided by current liabilities and measures short-term liquidity, the company's ability to pay bills coming due within a year. The quick ratio, also called the acid-test ratio, is stricter: it excludes inventory from current assets because inventory may be slow to convert to cash. A company with $500,000 of current assets, including $200,000 of inventory, and $250,000 of current liabilities has a current ratio of 2.0 but a quick ratio of only 1.2. The debt-to-equity ratio compares a company's long-term debt to its shareholders' equity and measures financial leverage; a highly leveraged company carries more fixed interest obligations and therefore more risk in a downturn or a rising-rate environment. The price-to-earnings (P/E) ratio is the market price per share divided by earnings per share. Growth companies typically command high P/E ratios because investors pay up for expected earnings expansion, while value investors hunt for low P/E stocks they believe the market has underpriced. A stock trading at $60 with earnings of $3 per share has a P/E of 20. The price-to-book (P/B) ratio divides market price by book value per share, where book value is total assets minus total liabilities, the accounting net worth. P/B is a favorite screen of value investors and is especially common when analyzing banks and other financial firms whose assets are largely financial.
Key terms
- Future value
- — The amount a sum of money will grow to at a stated compound rate of return over a stated period.
- Net present value (NPV)
- — The present value of an investment's expected cash flows, discounted at the required return, minus its cost.
- Internal rate of return (IRR)
- — The discount rate that makes an investment's net present value equal zero; a bond's yield to maturity is its IRR.
- Mean
- — The arithmetic average of a data set, which can be distorted by extreme outliers.
- Median
- — The middle value of a ranked data set, preferred over the mean when outliers skew the data.
- Standard deviation
- — A measure of how widely returns vary around their average; the exam's measure of total risk or volatility.
- Correlation
- — A measure from +1.0 to -1.0 of how closely two assets move together; low or negative correlation improves diversification.
- Beta
- — A measure of an investment's volatility relative to the overall market, which has a beta of 1.0.
- Alpha
- — The return earned above or below what an investment's risk level predicted, often read as manager skill.
- Sharpe ratio
- — Excess return over the risk-free rate divided by standard deviation; reward earned per unit of total risk.
- Quick ratio
- — Current assets excluding inventory divided by current liabilities; a strict test of short-term liquidity.
- Price-to-earnings ratio
- — Market price per share divided by earnings per share; high for growth stocks, low for value candidates.
Exam tips
- Link IRR and NPV: if IRR is greater than the required return, NPV is positive. If a question says NPV equals zero, the IRR equals the discount rate being used.
- When a question mentions a data set with one extreme outlier, the answer usually involves the median, not the mean.
- Match the risk measure to the risk type: beta and alpha deal with market (systematic) risk, while standard deviation and the Sharpe ratio deal with total risk. Sharpe uses the risk-free rate in the numerator; alpha compares actual return to the return predicted for the investment's beta.
- The quick (acid-test) ratio excludes inventory; a question giving you inventory data and asking for the stricter liquidity measure wants you to subtract it.
- Yield to maturity is the IRR of a bond; this cross-topic equivalence is a favorite way to test whether you understand both terms rather than just memorizing them.