UTS16657 Chap.4 Measuring Risk on a Single Asset
Measuring Risk on a Single Asset
In investment the word risk is used more precisely than in everyday speech. Risk is how widely the probable gains and losses scatter around the outcome you expected, so fluctuation around an expected return can be an upside variance as readily as a downside one. The subject calls it a double-edged sword for that reason.
You cannot avoid it; you can identify where it comes from, understand its nature and decide how much of it you are being paid to carry.
The sources split by controllability. External sources cannot be controlled: economic risk covering output, inflation and the cash rate, political risk covering government decisions, and property market risk covering local demand and supply.
Internal sources largely can be: management risk, property-specific risk covering lease structure, tenancy mix and building features, and financial risk covering leverage, the loan-to-value ratio, the loan period and the debt coverage ratio.
Liquidity risk sits across the line and matters enormously for property.
Quantifying the spread means squaring the deviations from the mean, averaging them into a variance, and taking the square root to return the answer to the units of the returns themselves.
Where the distribution is roughly bell-shaped, the empirical rule converts the number into a statement about outcomes: about 68% of returns land within one standard deviation of the mean, about 95% within two and virtually all within three.
Real return distributions are not that well behaved and investors are not indifferent between the tails, which is why the probability of landing under the mean carries its own name, downside risk.
Because a return figure alone cannot rank two investments, the two quantities are combined into a ratio.
The coefficient of variation is risk per unit of return and lower is better; the return-risk index is its reciprocal and higher is better. They always agree, and they routinely reverse the ranking a headline return would give. Finally, two things distort a measured risk figure: appraisal-based valuation smooths a series and understates its volatility, and a geared series measures something different from an ungeared one.
What this chapter covers
- 01
Risk defined as variability rather than as the chance of loss
- 02
External and internal sources, and which can be controlled
- 03
Variance, standard deviation, and why the square root is needed
- 04
Reading a standard deviation through the empirical rule
- 05
Annualising a risk figure with the square root of time
- 06
Coefficient of variation, and its reciprocal the return-risk index
- 07
Appraisal smoothing and why direct property looks safer than it is
A full risk calculation, from six monthly observations to an annual figure
- +1Mean: (4.1 − 2.3 + 5.8 + 1.2 − 3.7 + 6.9) ÷ 6 = 12.0 ÷ 6 = 2.00% per month.
- +1Deviations from the mean, in percentage points: 2.1, −4.3, 3.8, −0.8, −5.7 and 4.9. They sum to zero, which is a free check that the mean is right.
- +1Square each deviation in decimals and total them: 0.000441 + 0.001849 + 0.001444 + 0.000064 + 0.003249 + 0.002401 = 0.009448.
- +1Divide by n − 1 and take the root: 0.009448 ÷ 5 = 0.0018896, and √0.0018896 = 4.3470% per month.
- +1Annualise each one with its own rule. The return compounds: (1.02)12 − 1 = 26.82%. The risk scales with the square root of time: 4.3470 × √12 = 15.0583%.
Key terms
- Standard deviation
- The square root of the variance of a return series, expressing the spread of outcomes in the same units as the returns themselves. It is the subject's working definition of investment risk.
- Empirical rule
- The reading that, for a roughly bell-shaped distribution, roughly 68% of outcomes fall no further than one standard deviation from the mean, about 95% within two and virtually all within three.
- Downside risk
- The chance of a return falling below the mean. Standard deviation charges equally for both tails, which is its main limitation given that investors prefer a unit of upside to a unit of downside.
- Coefficient of variation
- The standard deviation divided by the expected return, reporting risk per unit of return, where a lower figure is preferred.
- Return-risk index
- The expected return divided by the standard deviation, reporting return per unit of risk, where a higher figure is preferred. A negative value signals suboptimal performance rather than a ranking.
- Appraisal smoothing
- The reduction in measured volatility that follows from valuing an asset periodically rather than pricing it continuously, because movements between valuation dates never enter the series.
- Liquidity risk
- The risk of being unable to exit a position at a fair price when required. It is significant for direct property, partly controllable through the choice of vehicle, and invisible to a standard deviation.
- Financial risk
- The controllable component of risk created by the funding structure, covering the level of leverage, the loan-to-value ratio, the loan period and the debt coverage ratio.
Measuring Risk on a Single Asset FAQ
Why is risk defined as variability rather than as the chance of losing money?
Because variability is what can be measured and what actually matters for combining assets. A definition based only on loss would ignore the upside, and the subject is explicit that fluctuation around an expected return can be an upside variance as easily as a downside one. Defining risk as the spread also makes it arithmetic, which is what allows the portfolio variance formula, the efficient frontier and beta to exist.
The concern about losses has its own separate name, downside risk, and it is a recognised limitation of treating both tails alike.
An unlisted fund shows a much lower standard deviation than a listed trust holding similar assets. Is it safer?
Not on that evidence. The unlisted fund is valued periodically by a valuer, so its series is appraisal-based and smoothed: movements between valuation dates never appear, and the measured standard deviation is biased downward. The listed trust is priced continuously by a market, so every movement is captured, and its series may also carry gearing at the trust level.
A defensible comparison either matches the measurement frequency or notes that the unlisted fund carries liquidity risk that a standard deviation does not measure at all.
Can the coefficient of variation disagree with the return-risk index?
No, because they are reciprocals of the same pair of inputs. If one prefers an asset the other must prefer the same asset, and the only difference is the direction in which they are read.
The reason the subject uses both is that they make different sentences natural: the coefficient of variation is the answer to how much risk you are taking per unit of return, and the index is the answer to how much return you are buying per unit of risk. Both break down when the return is negative.
How many observations should I use?
More than the six in the worked example, which is a teaching size chosen so every line can be shown. A standard deviation estimated from a handful of periods is itself very uncertain and one unusual month can dominate it.
The individual report asks for ten years of monthly data, which is a hundred and twenty observations, and whenever you report a risk figure you should state how many observations it rests on so the reader knows what weight to place on it.
Exam move
Do the six-observation calculation by hand at least twice before you let a spreadsheet do it, because the deviation column summing to zero is the only free check you get and you will not notice it in a formula. Then spend your time on the two things markers actually ask about: translating a standard deviation into a sentence using the empirical rule, and explaining why a smoothed series understates risk.
Both are short-answer material and neither requires a calculator.
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