Certified Financial Planner (CFP) Investment Planning Syllabus

Write the intrinsic value formulas for a call and a put option at expiration.

Call: $\max(S - K,\ 0)$. Put: $\max(K - S,\ 0)$, where $S$ is the underlying price and $K$ is the strike price.

Distinguish a futures contract from a forward contract.

Futures are standardized, exchange-traded, and marked-to-market daily with a clearinghouse counterparty. Forwards are customized, traded over-the-counter (OTC), settled at maturity, and carry counterparty risk.

Define systematic (market) risk versus unsystematic (diversifiable) risk.

Systematic risk affects the whole market and cannot be diversified away (e.g., interest rates, recessions); it is measured by beta. Unsystematic risk is firm/industry-specific and can be eliminated through diversification.

What does the standard deviation of returns measure, and how does it relate to variance?

Standard deviation measures total (absolute) volatility/dispersion of returns around the mean. It is the square root of variance: $\sigma = \sqrt{\sigma^{2}}$.

Define beta and state its formula in terms of covariance.

Beta measures a security's systematic risk relative to the market. $$\beta_i = \frac{\text{Cov}(R_i, R_m)}{\sigma_m^{2}}$$ A beta of 1 moves with the market; >1 is more volatile, <1 less.

What does the coefficient of determination ($R^{2}$) tell an investor about a portfolio relative to its benchmark?

$R^{2}$ measures the percentage of a portfolio's movement explained by movements in the benchmark/market. A high $R^{2}$ (near 1) means beta and alpha are reliable measures; a low $R^{2}$ makes them less meaningful.

Give the formula for the holding period return (HPR) of an investment.

$$\text{HPR} = \frac{(P_1 - P_0) + \text{Income}}{P_0}$$ where $P_0$ is the beginning price, $P_1$ the ending price, and Income is dividends/interest received.

Distinguish the arithmetic mean return from the geometric mean return.

Arithmetic mean is the simple average of periodic returns (good for estimating expected single-period return). Geometric mean is the compound average reflecting actual cumulative growth: $$R_g = \left[\prod_{t=1}^{n}(1+R_t)\right]^{1/n} - 1$$

Write the formula for the internal rate of return (IRR) condition.

IRR is the rate $r$ that sets net present value to zero: $$\sum_{t=0}^{n} \frac{CF_t}{(1+r)^{t}} = 0$$

Distinguish nominal return from real return and give the exact Fisher relationship.

Real return adjusts nominal return for inflation. $$1 + r_{real} = \frac{1 + r_{nominal}}{1 + i}$$ where $i$ is the inflation rate.

What does Modern Portfolio Theory (MPT) say about combining assets that are not perfectly correlated?

Combining assets with correlation less than $+1$ reduces portfolio risk (standard deviation) below the weighted average of the individual risks, without necessarily sacrificing return — the basis of diversification.

State the two-asset portfolio variance formula.

$$\sigma_p^{2} = w_1^{2}\sigma_1^{2} + w_2^{2}\sigma_2^{2} + 2 w_1 w_2 \rho_{1,2}\sigma_1\sigma_2$$ where $w$ are weights, $\sigma$ standard deviations, and $\rho_{1,2}$ the correlation coefficient.

Define the efficient frontier.

The efficient frontier is the set of optimal portfolios offering the highest expected return for each level of risk (or the lowest risk for a given return). Rational investors choose portfolios on this frontier.

What is the range of the correlation coefficient and what does each extreme imply for diversification?

Correlation ranges from $-1$ to $+1$. At $+1$ assets move identically (no diversification benefit); at $-1$ they move perfectly opposite (maximum diversification, risk can be eliminated); at $0$ they are uncorrelated.

State the Capital Asset Pricing Model (CAPM) equation.

$$E(R_i) = R_f + \beta_i \left[E(R_m) - R_f\right]$$ where $R_f$ is the risk-free rate, $\beta_i$ the security's beta, and $E(R_m) - R_f$ the market risk premium.

What is the difference between the Capital Market Line (CML) and the Security Market Line (SML) in terms of the risk measure on the x-axis?

The CML plots expected return against total risk (standard deviation, $\sigma$) and applies only to efficient portfolios. The SML plots expected return against systematic risk (beta, $\beta$) and applies to any individual security or portfolio.

What does Arbitrage Pricing Theory (APT) add beyond the single-factor CAPM?

APT is a multi-factor model: expected return is a linear function of several systematic risk factors (e.g., inflation, GDP, interest rates), each with its own beta, rather than the single market factor used in CAPM.

Define strategic asset allocation versus tactical asset allocation.

Strategic asset allocation sets long-term target weights based on the investor's goals and risk tolerance. Tactical asset allocation makes short-term deviations from those targets to exploit perceived market opportunities.

Describe how calendar (periodic) rebalancing differs from percentage-of-portfolio (tolerance-band) rebalancing.

Calendar rebalancing returns the portfolio to target weights at fixed intervals (e.g., quarterly). Percentage-of-portfolio rebalancing triggers only when an asset class drifts beyond a set tolerance band (e.g., $\pm 5\%$) from its target.

What is the disciplined 'buy low, sell high' effect produced by rebalancing?

Rebalancing forces selling asset classes that have appreciated (overweight) and buying those that have declined (underweight), systematically realizing gains and maintaining the target risk profile.

What are the primary required components of an Investment Policy Statement (IPS)?

Return objectives, risk tolerance, and the constraints commonly summarized as Time horizon, Liquidity needs, Taxes, Legal/regulatory factors, and Unique circumstances (the 'RR-TTLLU' framework).

In an IPS, what is the difference between an investor's ability and willingness to take risk?

Ability to take risk is objective — based on time horizon, wealth, liquidity needs, and income stability. Willingness is subjective — the investor's psychological comfort with volatility. The lower of the two generally governs.

What is the central premise of the Efficient Market Hypothesis (EMH) that argues for passive management?

EMH holds that security prices fully reflect available information, so consistently beating the market through active selection or timing is very difficult after costs — favoring low-cost passive index strategies.

Name the three forms of the Efficient Market Hypothesis and the information each incorporates.

Weak form: all past price/volume data (technical analysis cannot add value). Semi-strong form: all public information (fundamental analysis cannot add value). Strong form: all public and private (insider) information.

State the Sharpe ratio formula and what it measures.

$$\text{Sharpe} = \frac{R_p - R_f}{\sigma_p}$$ It measures excess return per unit of total risk (standard deviation); higher is better. Used to rank portfolios regardless of diversification.

State the Treynor ratio formula and how it differs from the Sharpe ratio.

$$\text{Treynor} = \frac{R_p - R_f}{\beta_p}$$ It measures excess return per unit of systematic risk (beta), appropriate for well-diversified portfolios, whereas Sharpe uses total risk ($\sigma$).

Define Jensen's alpha and interpret a positive value.

$$\alpha = R_p - \left[R_f + \beta_p(R_m - R_f)\right]$$ Alpha is return earned above what CAPM predicts for the portfolio's beta. A positive alpha indicates the manager added value (outperformed risk-adjusted expectations).

When is the Sharpe ratio preferred over the Treynor ratio for performance evaluation?

Use Sharpe (total risk) when the portfolio is not fully diversified or is the investor's entire holding; use Treynor (systematic risk) when the portfolio is well-diversified or one of several components.

Contrast the goals of fundamental analysis and technical analysis.

Fundamental analysis estimates a security's intrinsic value from financials, economy, and industry to find mispricing. Technical analysis studies past price and volume patterns/charts to forecast future price movements, ignoring intrinsic value.

In technical analysis, define support and resistance levels.

Support is a price level where buying interest tends to halt declines (a floor). Resistance is a price level where selling pressure tends to halt advances (a ceiling). Breaking through either signals a potential trend continuation.

Describe a bond laddering strategy and its main benefit.

Laddering buys bonds with staggered, sequential maturities so portions mature regularly. Benefits: reinvestment of proceeds at prevailing rates, reduced interest-rate timing risk, and steady liquidity.

Compare a bullet bond strategy with a barbell bond strategy.

A bullet concentrates maturities around a single target date. A barbell combines short-term and long-term bonds with little in the middle, giving high liquidity at the short end and higher yield/duration at the long end.

What is bond immunization and what does it protect against?

Immunization matches a portfolio's duration to the investor's time horizon so that price risk and reinvestment risk offset, locking in a target return regardless of interest-rate changes — protecting the funding of a future liability.

What is asset location (as opposed to asset allocation), and what is its general rule?

Asset location decides which account type holds each asset to minimize taxes. General rule: place tax-inefficient assets (taxable bonds, REITs, high-turnover funds) in tax-deferred/tax-exempt accounts, and tax-efficient assets (index equities, qualified dividends) in taxable accounts.

Explain tax-loss harvesting and the wash-sale rule constraint.

Tax-loss harvesting sells securities at a loss to offset capital gains (and up to \$3{,}000 of ordinary income annually). The wash-sale rule disallows the loss if a substantially identical security is bought within 30 days before or after the sale.

Compare the federal tax treatment of qualified dividends and long-term capital gains with that of ordinary income and short-term gains.

Qualified dividends and long-term capital gains (assets held more than one year) are taxed at preferential rates (0%/15%/20%). Short-term gains and ordinary income are taxed at higher ordinary marginal rates.

How do you compare a municipal bond's tax-exempt yield to a taxable bond using the taxable-equivalent yield?

$$\text{TEY} = \frac{\text{Tax-Exempt Yield}}{1 - \text{Marginal Tax Rate}}$$ It converts a muni's yield to the pre-tax yield a taxable bond would need to match it.

Define the behavioral bias of overconfidence and its typical effect on investing behavior.

Overconfidence is overestimating one's knowledge, predictive ability, or control. It typically leads to excessive trading, under-diversification, and underestimation of risk.

Define loss aversion and the related disposition effect.

Loss aversion (from prospect theory) means losses feel roughly twice as painful as equivalent gains feel good. The disposition effect is the resulting tendency to sell winners too early and hold losers too long to avoid realizing a loss.

Define anchoring and mental accounting as behavioral biases.

Anchoring: over-relying on an initial reference point (e.g., purchase price) when making decisions. Mental accounting: treating money differently based on arbitrary categories (e.g., 'play money' vs. savings) rather than viewing wealth holistically.

Define herding and recency (availability) bias in investor behavior.

Herding: following the crowd's actions rather than independent analysis, fueling bubbles and crashes. Recency/availability bias: overweighting recent or easily recalled events when judging probabilities, leading to chasing recent performance.