CFA Level 1 - Quantitative Methods & Ethical Standards Flashcards

Question 1

Future Value ($FV$) Formula for an Ordinary Annuity

Accepted Answer

$FV = PMT \	imes \left[ \frac{(1 + r)^n - 1}{r} \ight]$

Where $PMT$ is the periodic annuity cash flow, $r$ is the discount rate per period, and $n$ is the total number of periods.

Question 2

Present Value ($PV$) Formula for a Perpetuity

Accepted Answer

$PV = \frac{PMT}{r}$

Where $PMT$ is the fixed periodic cash payment received indefinitely and $r$ is the periodic required rate of return.

Question 3

Net Present Value ($NPV$) Formula and Decision Rule

Accepted Answer

$NPV = \sum_{t=0}^{n} \frac{CF_t}{(1 + r)^t}$

**Decision Rule:** Accept projects with $NPV > 0$. If selecting among mutually exclusive projects, choose the one with the highest positive $NPV$.

Question 4

Internal Rate of Return ($IRR$) Definition and Rule

Accepted Answer

The discount rate $r$ that forces the net present value ($NPV$) of all cash flows to equal zero:

$\sum_{t=0}^{n} \frac{CF_t}{(1 + IRR)^t} = 0$

**Decision Rule:** Accept independent projects if $IRR > \	ext{Required Rate of Return}$.

Question 5

Money-Weighted vs. Time-Weighted Rate of Return

Accepted Answer

**Money-Weighted Return (MWR):** The internal rate of return ($IRR$) of a portfolio; highly sensitive to the timing and size of cash inflows/outflows.

**Time-Weighted Return (TWR):** Measures compound growth rate over sub-periods regardless of cash flow timing. Preferred metric for evaluating portfolio manager performance.

Question 6

Population Covariance and Correlation Coefficient Formula

Accepted Answer

**Covariance:** $Cov(X,Y) = \frac{\sum (X_i - \mu_X)(Y_i - \mu_Y)}{N}$

**Correlation:** $\ho_{X,Y} = \frac{Cov(X,Y)}{\sigma_X \cdot \sigma_Y}$

Correlation is bounded between $-1$ and $+1$.

Question 7

Bayes' Formula

Accepted Answer

$P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}$

Calculates the updated conditional probability of Event $A$ given that new event/information $B$ has occurred.

Question 8

Standard Normal Distribution ($Z$-score) Formula

Accepted Answer

$Z = \frac{X - \mu}{\sigma}$

Measures the standard distance (number of standard deviations $\sigma$) that a random observation $X$ deviates from the population mean $\mu$.

Question 9

Central Limit Theorem (CLT)

Accepted Answer

For any population with mean $\mu$ and standard deviation $\sigma$, as sample size $n$ becomes large ($n \ge 30$), the sampling distribution of the sample mean $\bar{X}$ approaches a normal distribution with mean $\mu$ and variance $\frac{\sigma^2}{n}$.

Question 10

Standard Error of the Sample Mean

Accepted Answer

$SE = \frac{s}{\sqrt{n}}$

Where $s$ is the sample standard deviation and $n$ is the sample size. Quantifies the dispersion/variability of the sample mean estimator around the true population mean.

Question 11

$t$-Statistic vs. $Z$-Statistic Selection Criteria

Accepted Answer

Use **$Z$-test** when population variance $\sigma^2$ is **known** (or large sample $n \ge 30$ with CLT).

Use **$t$-test** when population variance $\sigma^2$ is **unknown** and estimated via sample variance $s^2$:
$t = \frac{\bar{X} - \mu_0}{s / \sqrt{n}}$ with $n - 1$ degrees of freedom.

Question 12

Type I Error vs. Type II Error

Accepted Answer

**Type I Error ($\alpha$):** Rejecting a true null hypothesis $H_0$ (False Positive). The significance level equals $\alpha$.

**Type II Error ($\beta$):** Failing to reject a false null hypothesis $H_0$ (False Negative).

**Power of a Test:** $1 - \beta$ (probability of correctly rejecting $H_0$ when it is false).

Question 13

Two-Asset Portfolio Variance Formula

Accepted Answer

$\sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 \sigma_1 \sigma_2 \ho_{1,2}$

Where $w_i$ are portfolio weights, $\sigma_i^2$ are asset variances, and $\ho_{1,2}$ is the correlation coefficient between returns of Asset 1 and Asset 2.

Question 14

Standard I(B) - Independence and Objectivity

Accepted Answer

Members and candidates must exercise reasonable care and judgment to achieve and maintain independence and objectivity in their professional activities.

*Key Rule:* Must not offer, solicit, or accept any gift, benefit, or consideration that compromises independence. Gifts from clients are acceptable if disclosed in writing prior to acceptance, but gifts from third parties seeking influence are prohibited.

Question 15

Standard II(A) - Material Nonpublic Information & Mosaic Theory

Accepted Answer

**Rule:** Members/candidates possessing material nonpublic information must not act or cause others to act on it.

**Mosaic Theory Exception:** Financial analysts may reach investment conclusions and trade based on a combination of public information and nonmaterial nonpublic information without violating this standard.

Question 16

Standard III(A) - Loyalty, Prudence, and Care

Accepted Answer

Members and candidates have a duty of loyalty to clients, must act with reasonable care, and exercise prudent judgment.

*Key Application:* Client interests must always take precedence over employer or personal interests. Brokerage commissions generated from client accounts ('soft dollars') belong to the client and must be used to benefit the client.

Question 17

Standard III(B) - Fair Dealing Execution Principles

Accepted Answer

Members must deal fairly and objectively with all clients when providing investment analysis or taking investment action.

*Best Practices:* Distribute recommendations concurrently to all clients; allocate oversubscribed IPO/secondary trade executions on a pro-rata basis based on order size; treat fee-paying family accounts identically to non-family client accounts.

Question 18

Standard V(A) - Diligence and Reasonable Basis

Accepted Answer

Members and candidates must exercise diligence, independence, and thoroughness in analyzing investments and issuing recommendations.

*Requirement:* Must establish a reasonable and adequate basis for any investment recommendation or action, supported by appropriate research and investigation.

Question 19

Standard VI(B) - Priority of Transactions

Accepted Answer

Investment transactions for clients and employers must take priority over investment transactions in which a Member or Candidate is the beneficial owner.

*Rule:* Personal trading ('front-running') ahead of client or firm orders violates this standard. Personal transactions must occur only after clients and employers have had adequate opportunity to act.

Question 20

Ethics Scenario: Disclosure of Referral Fees (Standard VI(C))

Accepted Answer

**Requirement:** Members and candidates must disclose to their employer, clients, and prospective clients any compensation, consideration, or benefit received from or paid to others for recommending products or services.

**Example Violation:** Receiving an undisclosed commission from a third-party money manager for client referrals, even if the manager achieves superior returns.

CFA Level 1 - Quantitative Methods & Ethical Standards

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