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

Unit 2 — Investment Risk, Return and Portfolio Theory syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Unit 2 — Investment Risk, Return and Portfolio Theory in Investment Management Certificate (IMC), not a summary of it.

1. 1

   Risk and Return Fundamentals

   3 topics

   • Measuring investment risk
     • Standard deviation and variance of returns
     • Downside risk and value at risk
   • Sources of risk
     • Systematic versus unsystematic risk
     • Market, credit, liquidity and operational risk
   • The risk-return trade-off
     • Risk premium and the risk-free rate
     • Investor risk attitudes and utility
2. 2

   Modern Portfolio Theory

   4 topics

   • Diversification
     • Effect of correlation on portfolio risk
     • The benefits and limits of diversification
   • The efficient frontier
     • Mean-variance optimisation
     • The minimum-variance portfolio
   • The capital market line
     • Combining risky assets with the risk-free asset
     • The market portfolio
   • Assumptions and criticisms
     • Reliance on historical estimates
     • Non-normal returns
3. 3

   Asset Pricing Models

   3 topics

   • The Capital Asset Pricing Model
     • Beta and the security market line
     • Required return and alpha
   • Multi-factor models
     • Arbitrage pricing theory
     • Fama-French factors
   • Market efficiency
     • Weak, semi-strong and strong forms
     • Anomalies and behavioural finance
4. 4

   Behavioural Finance

   3 topics

   • Cognitive biases
     • Anchoring and overconfidence
     • Representativeness and availability
   • Emotional biases
     • Loss aversion and the disposition effect
     • Herding and regret
   • Implications for markets
     • Bubbles and momentum
     • Challenges to the efficient market hypothesis

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

22 of 50 cards from the Unit 2 — Investment Risk, Return and Portfolio Theory deck — real questions with worked answers.

1. How is the holding period return (HPR) of an investment calculated?

   $$HPR = \frac{(P_{1} - P_{0}) + D_{1}}{P_{0}}$$ where $P_{0}$ is the start price, $P_{1}$ the end price and $D_{1}$ the income (dividend) received during the period. It captures both capital gain and income.

2. What is the formula for the expected return of a single asset using a probability distribution?

   $$E(R) = \sum_{i=1}^{n} p_{i} R_{i}$$ the probability-weighted average of all possible returns $R_{i}$ with probabilities $p_{i}$.

3. Define variance as a measure of investment risk and give its formula.

   Variance measures the dispersion of returns around the mean (expected return). $$\sigma^{2} = \sum_{i=1}^{n} p_{i}\,(R_{i} - E(R))^{2}$$ A higher variance means greater volatility and risk.

4. How does standard deviation relate to variance, and why is it often preferred?

   Standard deviation is the square root of variance: $\sigma = \sqrt{\sigma^{2}}$. It is preferred because it is expressed in the same units (percentage returns) as the asset, making it more interpretable as a risk measure.

5. What does the coefficient of variation measure and how is it calculated?

   It measures risk per unit of return, allowing comparison of investments with different expected returns. $$CV = \frac{\sigma}{E(R)}$$ Lower $CV$ indicates a better risk-return profile.

6. In the IMC, what is the distinction between systematic and unsystematic risk?

   Systematic (market) risk affects the whole market and cannot be diversified away (e.g. interest rates, recession). Unsystematic (specific/idiosyncratic) risk is unique to a company or sector and can be eliminated through diversification.

7. List the main sources of investment risk a portfolio is exposed to.

   Market risk, interest rate risk, inflation (purchasing power) risk, credit/default risk, liquidity risk, currency (FX) risk, business/sector risk, political/regulatory risk and event risk.

8. What is interest rate risk and which assets are most exposed to it?

   Interest rate risk is the risk that changing interest rates alter an asset's value. Bonds are most exposed: when rates rise, bond prices fall. Longer-duration and lower-coupon bonds are more sensitive.

9. What is liquidity risk?

   The risk that an investor cannot buy or sell an asset quickly at a fair price, often forcing a sale at a discount. It is higher for thinly traded securities, property and small-cap stocks.

10. State the risk-return trade-off principle.

    To obtain a higher expected return, an investor must accept a higher level of risk. Rational, risk-averse investors require additional expected return (a risk premium) as compensation for bearing additional risk.

11. What is a risk premium?

    The excess return demanded by investors over the risk-free rate for holding a risky asset: $$\text{Risk premium} = E(R) - R_{f}$$ It compensates the investor for taking on systematic risk.

12. What does it mean for a rational investor to be 'risk averse'?

    A risk-averse investor prefers more certain outcomes to less certain ones of equal expected value, and will only accept higher risk if compensated by higher expected return. Their utility curves are concave.

13. How is the covariance between two assets' returns defined?

    $$Cov(A,B) = \sum_{i=1}^{n} p_{i}\,(R_{A,i} - E(R_{A}))(R_{B,i} - E(R_{B}))$$ It measures how the returns of two assets move together; positive means they tend to move in the same direction.

14. What is the correlation coefficient and what range can it take?

    $$\rho_{AB} = \frac{Cov(A,B)}{\sigma_{A}\,\sigma_{B}}$$ It standardises covariance and ranges from $-1$ (perfect negative correlation) to $+1$ (perfect positive correlation), with $0$ meaning no linear relationship.

15. How does correlation affect the benefit of diversification?

    The lower (more negative) the correlation between assets, the greater the reduction in portfolio risk. Diversification benefits are maximised at $\rho = -1$ and are zero when $\rho = +1$.

16. Give the formula for the variance of a two-asset portfolio.

    $$\sigma_{P}^{2} = w_{A}^{2}\sigma_{A}^{2} + w_{B}^{2}\sigma_{B}^{2} + 2 w_{A} w_{B}\,\rho_{AB}\,\sigma_{A}\sigma_{B}$$ where $w$ are the portfolio weights.

17. What is the expected return of a two-asset portfolio?

    $$E(R_{P}) = w_{A}E(R_{A}) + w_{B}E(R_{B})$$ the weighted average of the component expected returns. Unlike risk, portfolio expected return is always a simple weighted average.

18. What type of risk can diversification eliminate, and what risk remains?

    Diversification eliminates unsystematic (specific) risk by combining imperfectly correlated assets. Systematic (market) risk remains and cannot be diversified away.

19. Roughly how many securities are typically needed to achieve most diversification benefits?

    Most specific risk can be removed with around 15-30 well-chosen securities; beyond this, additional diversification yields diminishing benefits and risk approaches the systematic floor.

20. What is the efficient frontier?

    The set of optimal portfolios offering the highest expected return for each level of risk (or the lowest risk for each level of expected return). It forms the upper boundary of the feasible (opportunity) set of risky portfolios.

21. 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.

22. 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.

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