FINC2011 Chap.7 Risk, Return and Diversification
Risk, Return and Diversification
The risk and return chapter measures realised and expected performance, distinguishes arithmetic from geometric averages, and moves from stand-alone volatility to portfolio variance. It calculates covariance and correlation, shows how asset weights determine expected return, and explains why joint movement determines diversification benefit.
It closes by separating systematic market exposure from company-specific risk that a broad portfolio can reduce.
What this chapter covers
- 01
Realised return with dividends and price change
- 02
Expected return across possible states
- 03
Arithmetic and geometric averages
- 04
Variance and standard deviation
- 05
Covariance and correlation
- 06
Portfolio weights, return and volatility
- 07
Systematic and diversifiable risk
Worked example · free
Measure a two-asset portfolio
- 1Confirm weights sum to one and compute expected return as 0.45 times 0.11 plus 0.55 times 0.07, giving 8.8%.
- 2Calculate the weighted variance terms: 0.45 squared times 0.16 squared plus 0.55 squared times 0.09 squared.
- 2Add twice the weight product times correlation and both volatilities as the covariance contribution.
- 1Take the square root of total variance to obtain portfolio volatility of about 10.16%.
Key terms
- Arithmetic Average
- The simple mean of periodic returns, often used as an estimate for one future period.
- Geometric Average
- The compound periodic return linking beginning wealth to ending wealth across multiple periods.
- Covariance
- A measure of the direction and scale with which two asset returns vary together.
- Diversifiable Risk
- Company-specific or narrow exposure that can be reduced by combining securities with imperfectly related returns.
Risk, Return and Diversification FAQ
Why are arithmetic and geometric returns different?
Arithmetic average takes a simple mean and is useful for a single-period expectation. Geometric average captures compounding across time. Volatility creates a gap because a loss needs a larger percentage gain to recover, so geometric average is normally lower for a fluctuating return series.
What role does correlation play in diversification?
Correlation standardises co-movement. When correlation is below one, asset returns do not rise and fall in perfect lockstep, so some fluctuations offset and portfolio volatility falls. Expected portfolio return remains the same weighted average when only correlation changes.
Can diversification remove every risk?
No. It can reduce company-specific events such as a product failure or isolated operational disruption. Broad shocks affecting interest rates, economic activity, or market returns remain systematic. Beta relates an asset to that market co-movement rather than measuring all stand-alone volatility.
Exam move
Calculate each realised return from beginning price, ending price, and dividends before averaging anything. Practise both arithmetic and geometric averages on the same series and explain which question each answers. For a two-asset portfolio, write expected return and variance on separate lines, check weights sum to one, and keep percentages as decimals until the final report.
Recalculate volatility at correlations of one, zero, and a negative value to see the diversification direction. Sort news events into systematic and diversifiable risk, then explain what a broad portfolio can remove. End every result with one sentence about centre, spread, or co-movement. Separate future distributions from historical samples.
An expected return uses stated probabilities or forecasts, while an arithmetic historical average summarises observations; neither label should be omitted. For geometric averages, build cumulative wealth from one-plus-return factors and apply the correct root. Explain why volatility creates a gap between arithmetic and compound growth.
In a two-asset calculation, write the two stand-alone variance contributions and the covariance contribution on separate lines. Check the sign of the cross-term against correlation and test the boundary at correlation equal to one, where long-only portfolio volatility should equal the weighted average of individual volatilities.
Change correlation while holding weights and expected returns fixed; expected portfolio return should not move. Then change a weight and report both return and volatility because risk responds nonlinearly. Run a stress case with higher correlation to test whether the diversification benefit depends on an unstable estimate.
For qualitative news, identify whether the shock is issuer-specific or common across many assets before labelling it diversifiable or systematic. Keep beta distinct from total standard deviation: one focuses on market co-movement, the other includes all dispersion. A strong final sentence states expected reward, total uncertainty, and what diversification can reduce without promising that loss has been eliminated.
Use a three-pass drill: calculate the base portfolio, predict the direction after one input changes, and then recompute. Change correlation, a weight, and one asset volatility in separate rounds. Keeping all other inputs fixed makes the source of each risk movement visible and strengthens interpretation under unfamiliar numbers.
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