FINM7008 Chap.2 Measuring Return and Risk From Scenarios
Measuring Return and Risk From Scenarios
From prices to rates of return
Before risk and return can be weighed, a price path has to become a rate.
This chapter covers the holding-period return, the difference between nominal and real returns, and the effective annual rate that puts different horizons on a common footing.
Scenario analysis
It then computes an expected return and a standard deviation from a set of economic states with probabilities, and separates realised excess returns from expected risk premiums.
Why it matters for the exams
Every later chapter feeds on these two numbers.
The utility score, the capital allocation line and the Sharpe ratio all start from an expected return and a standard deviation, so a slip here, such as mixing percentages and decimals or skipping the mean, carries through every calculation that follows.
What this chapter covers
- 01
Holding-period return with dividends
- 02
Nominal and real rates
- 03
Effective annual rate
- 04
Expected return from scenarios
- 05
Variance and standard deviation
- 06
Excess return and risk premium
- 07
Historical averages as estimates
Worked example · free
Mean and standard deviation from three economic states
- 1Expected return: 0.3(28) + 0.5(10) + 0.2(−15) = 8.4 + 5.0 − 3.0 = 10.4%.
- 1Deviations from the mean: 17.6, −0.4 and −25.4 percentage points.
- 1Variance: 0.3(309.76) + 0.5(0.16) + 0.2(645.16) = 222.04 squared percentage points.
- 1Standard deviation: √222.04 = 14.90%.
Key terms
- Nominal Return
- The growth rate of an investment's money value over a period.
- Real Return
- The growth rate of purchasing power, found by deflating the nominal return by inflation.
- Effective Annual Rate
- A holding-period return restated as the compounded return over one year.
- Excess Return
- The realised return on a risky portfolio minus the risk-free rate.
- Scenario Analysis
- A method that lists possible future states, their probabilities and the return in each.
- Market Risk Premium
- The expected return on the market index minus the risk-free rate.
Measuring Return and Risk From Scenarios FAQ
When is subtracting inflation from the nominal rate good enough?
Only when inflation is small. The exact real return divides one plus the nominal rate by one plus inflation; the shortcut drops a cross term that becomes large when inflation is high, so it overstates the real return in high-inflation periods.
Why annualise returns with an effective annual rate?
Returns earned over three months and over five years cannot be compared directly. The effective annual rate compounds each holding-period return to a one-year horizon, so a monthly average of 0.954% becomes 12.07% a year rather than twelve times the monthly figure.
What is the difference between an excess return and a risk premium?
An excess return is what a risky portfolio actually earned above the risk-free rate in a period. A risk premium is the expected return above the risk-free rate, a statement about the future that historical averages can only estimate.
How do I compute a standard deviation from scenarios?
Find the probability-weighted mean first, subtract it from each state's return, square each deviation, weight the squares by their probabilities and add them to get the variance. The square root of that variance, back in percentage units, is the standard deviation.
Why are expected returns described as unobservable?
Nobody knows the full list of future states or their true probabilities, so the expected return of the market or of a share can only be estimated. The lecture estimates it from past monthly returns, which is why the length of the sample window matters.
What is the market risk premium?
It is the expected return on the market portfolio minus the risk-free rate. Because the expectation cannot be observed, it is estimated from history, and the lecture's long US record shows how much such averages vary from one twenty-year era to the next.
Exam move
Work one scenario table with a calculator and one by hand, keeping variance in squared units until the last line. Then annualise a short-term bill and convert it to a real return, comparing the exact answer with the shortcut. Then set yourself a high-inflation case and confirm that the exact real return falls well below the subtraction shortcut.
When a question gives returns as decimals, keep them as decimals to the end; when it gives percentages, square percentage points and label the variance as such.
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