A client hands you two mutual funds. Fund A returned 11% last year with a beta of 1.4. Fund B returned 9% with a beta of 0.7. The naive answer says Fund A won. The exam-correct answer requires risk-adjusted math, and on the Series 66 you have about 90 seconds to do it.
Money today is worth more than the same dollars tomorrow. You can invest today's dollar and earn a return. The discount rate captures that opportunity cost: it is the return you give up by waiting.
Two operations dominate every time-value-of-money (TVM) question on the exam. Discounting moves a future amount back to today's value. Compounding moves a present amount forward to a future date. The same arithmetic runs in both directions; only the sign of the exponent changes.
KEY: PV and the discount rate move in opposite directions. Raise the rate, the PV falls. Lower the rate, the PV rises.
Common mistakes
- Using arithmetic mean for multi-period performance. Arithmetic mean overstates compound returns and is forbidden in standardized performance reporting. Always use geometric mean for multi-year returns. The exam bait answer quotes the simple average; the correct answer is lower.
- Confusing beta and standard deviation. Beta measures systematic risk only, the market-driven component. Standard deviation measures total risk. Candidates pick "high beta" when the question asks about a single non-diversified holding (where total risk matters), or pick "high standard deviation" when comparing two diversified portfolios (where only beta matters).
- Misreading the NPV vs. IRR conflict. When NPV says accept Project A and IRR says accept Project B, candidates split the difference or pick IRR because percentages feel intuitive. NPV wins the tiebreaker because it measures actual dollars created. A 40% IRR on a $1,000 project loses to a 15% IRR on a $1,000,000 project.
Bottom line
- Time value of money: PV and FV move in opposite directions; a higher discount rate means a lower PV; NPV > 0 accept, IRR > required return accept
- On mutually exclusive projects where NPV and IRR conflict, NPV wins because it measures actual dollars created
- Standard deviation measures total risk (systematic + unsystematic); beta measures systematic risk only against the market (market beta = 1.0)
- Sharpe ratio uses standard deviation (total risk), Treynor uses beta (systematic risk), and Jensen's alpha is actual return minus CAPM-required return
Exam shortcut
"NPV > 0 = green light" mnemonic. Picture a traffic light at zero. Positive NPV is green (accept), zero is yellow (indifferent), negative is red (reject). Same logic works for IRR vs. hurdle rate. IRR above the hurdle is green. Sharpe vs. Treynor, total vs. team. Sharpe uses standard deviation (S for "single, standalone, total"). Treynor uses beta (T for "team member, one sleeve in a bigger portfolio").
The full lesson (about 3,306 words, 22 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- A1
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