Investment Management Certificate (IMC) Unit 2 — Investment Risk, Return and Portfolio Theory Syllabus

Why is a portfolio below the efficient frontier considered inefficient?

Because another portfolio exists that offers either a higher expected return for the same risk or the same return for lower risk. Rational investors will never hold dominated (inefficient) portfolios.

What is the minimum variance portfolio?

The portfolio of risky assets with the lowest possible standard deviation. It sits at the left-most tip of the efficient frontier; portfolios below it on the curve are inefficient.

How does the introduction of a risk-free asset change the efficient frontier?

It allows investors to combine the risk-free asset with the optimal risky portfolio, creating a straight line (the Capital Market Line) that dominates the curved efficient frontier of risky assets alone.

Define the Capital Market Line (CML) and give its equation.

The CML plots expected return against total risk (standard deviation) for efficient portfolios combining the risk-free asset and the market portfolio. $$E(R_{P}) = R_{f} + \frac{E(R_{M}) - R_{f}}{\sigma_{M}}\,\sigma_{P}$$

What does the slope of the Capital Market Line represent?

The market price of risk (Sharpe ratio of the market portfolio): $\frac{E(R_{M}) - R_{f}}{\sigma_{M}}$, the extra expected return per unit of total risk taken.

What is the tangency (market) portfolio in CML/CAPM theory?

The portfolio of risky assets where a line from the risk-free rate is tangent to the efficient frontier. It offers the highest Sharpe ratio and, under CAPM assumptions, equals the market portfolio held by all investors.

State the separation theorem (two-fund separation).

All investors hold a combination of just two funds: the risk-free asset and the same optimal risky (market) portfolio. Their attitude to risk only determines the proportions, not the composition of the risky portfolio.

List the key assumptions underlying Modern Portfolio Theory and CAPM.

Investors are rational and risk-averse; they care only about mean and variance over one period; markets are frictionless (no taxes/transaction costs); information is free and available to all; investors can borrow and lend unlimited amounts at the risk-free rate; and they have homogeneous expectations.

Give two key criticisms of Modern Portfolio Theory / CAPM.

(1) Assumptions are unrealistic (no frictionless markets, no single risk-free rate, returns are not normally distributed). (2) Variance treats upside and downside equally, betas are unstable, and the true market portfolio is unobservable (Roll's critique).

State the Capital Asset Pricing Model (CAPM) equation.

$$E(R_{i}) = R_{f} + \beta_{i}\,(E(R_{M}) - R_{f})$$ The expected return on an asset equals the risk-free rate plus beta times the equity market risk premium.

What does beta ($\beta$) measure in the CAPM?

Beta measures an asset's systematic risk: its sensitivity to movements in the overall market. $$\beta_{i} = \frac{Cov(R_{i}, R_{M})}{\sigma_{M}^{2}}$$ The market itself has $\beta = 1$.

Interpret beta values of $\beta = 1$, $\beta > 1$ and $\beta < 1$.

$\beta = 1$: moves in line with the market. $\beta > 1$: more volatile/aggressive than the market (amplifies moves). $\beta < 1$: less volatile/defensive than the market. $\beta < 0$: moves opposite to the market.

What is the Security Market Line (SML) and how does it differ from the CML?

The SML is the graphical representation of CAPM, plotting expected return against beta (systematic risk). It applies to all assets and portfolios, whereas the CML uses total risk ($\sigma$) and applies only to efficient portfolios.

Under CAPM, what does it mean if an asset plots above the SML?

It is undervalued: it offers a higher expected return than required for its level of systematic risk, so investors should buy it. An asset plotting below the SML is overvalued.

What is the alpha ($\alpha$) of an investment?

Alpha is the return earned in excess of that predicted by CAPM for the asset's beta: $$\alpha = R_{actual} - [R_{f} + \beta(R_{M} - R_{f})]$$ Positive alpha indicates outperformance after adjusting for systematic risk.

How does Arbitrage Pricing Theory (APT) differ from CAPM?

APT is a multi-factor model: expected return is driven by several systematic risk factors, each with its own beta, rather than a single market factor. It makes fewer assumptions and does not require the market portfolio, but does not specify which factors to use.

Write the general form of a multi-factor (APT) return model.

$$E(R_{i}) = R_{f} + \beta_{i1}F_{1} + \beta_{i2}F_{2} + \dots + \beta_{in}F_{n}$$ where each $F_{k}$ is a systematic risk-factor premium and $\beta_{ik}$ is the asset's sensitivity to that factor.

Name the three factors in the Fama-French three-factor model.

(1) Market risk premium (as in CAPM), (2) Size factor SMB (Small Minus Big), and (3) Value factor HML (High Minus Low book-to-market). These explain returns better than CAPM's single market factor.

Give examples of macroeconomic factors used in multi-factor models.

Inflation, GDP/industrial production growth, interest rates, the yield curve slope (term spread), credit spreads, exchange rates and commodity/oil prices.

Define the Efficient Market Hypothesis (EMH).

The EMH states that asset prices fully and instantly reflect all available information, so it is impossible to consistently earn abnormal risk-adjusted returns; prices follow a random walk and the best estimate of value is the current market price.

Describe the three forms of market efficiency.

Weak form: prices reflect all past price/volume data (technical analysis fails). Semi-strong form: prices reflect all publicly available information (fundamental analysis fails). Strong form: prices reflect all information, public and private (even insiders cannot outperform).

What does weak-form market efficiency imply for technical analysis?

It implies technical analysis (studying past prices and chart patterns) cannot consistently generate abnormal returns, because all historical price information is already reflected in current prices.

What does semi-strong form efficiency imply, and how is it tested?

It implies neither technical nor fundamental analysis of public information can beat the market. It is tested using event studies that measure how quickly prices adjust to new public information such as earnings announcements.

What is behavioural finance and how does it challenge the EMH?

Behavioural finance studies how psychological biases cause investors to act irrationally, leading to mispricing, bubbles and anomalies. It challenges the EMH assumption of fully rational investors and explains why markets may not always be efficient.

Distinguish between cognitive biases and emotional biases.

Cognitive biases stem from faulty reasoning/information-processing errors and can often be corrected with education and advice. Emotional biases arise from feelings and impulses, are harder to correct, and usually have to be accommodated rather than eliminated.

Define the cognitive biases: anchoring, confirmation, and representativeness.

Anchoring: over-relying on an initial reference point. Confirmation: seeking information that supports existing beliefs and ignoring contradictory evidence. Representativeness: judging probability by similarity to a stereotype, leading to over-extrapolation.

What are the cognitive biases of availability and conservatism?

Availability bias: overweighting easily recalled or recent/vivid information when estimating probabilities. Conservatism bias: clinging to prior views and being slow to update beliefs in light of new information.

Describe the emotional biases of loss aversion and overconfidence.

Loss aversion: feeling losses roughly twice as strongly as equivalent gains, so investors hold losers too long and sell winners too early (disposition effect). Overconfidence: overestimating one's knowledge/ability, leading to excessive trading and under-diversification.

Explain the emotional biases of regret aversion and herding.

Regret aversion: avoiding decisions for fear of a poor outcome causing regret, leading to inaction or following the crowd. Herding: mimicking the actions of a larger group rather than acting on independent analysis, which can inflate bubbles and crashes.

What are the implications of behavioural biases for markets?

Collective biases can cause market anomalies, mispricing, excess volatility, momentum, overreaction/underreaction, and asset-price bubbles and crashes. They imply markets are not always perfectly efficient and create potential, though hard-to-exploit, opportunities.