NISM Professor

Risk

Also written Risk (investment definition) · Investment risk · Total risk

The possibility that actual returns turn out different from what was expected — measured as the dispersion of returns around their own average, and not the same thing as uncertainty.

In plain language

In ordinary speech, risk means exposure to a danger. In investing it means something narrower and more useful: the variability of the outcome.

An investment that will certainly return 7% has no risk. An investment that will return 7% on average, but anywhere between −15% and +30% in any given year, is risky — and it is risky in both directions. The upside counts. Risk is the spread, not the loss.

The workbook is also careful to separate risk from uncertainty, and this is a distinction examiners like. When nothing at all is known about what drives the variation in an outcome, that is uncertainty. When there is theoretical or empirical knowledge about the factors that cause the variation — enough to attach numbers to them — that is risk. Risk is known uncertainty. As research and evidence accumulate, phenomena migrate from the first bucket to the second.

How it works

Risk becomes measurable the moment you can write down the possible returns and their probabilities. The standard measure is the variance of expected returns, and its square root, the standard deviation.

Take the workbook's own illustration. A security is equally likely — probability 0.25 each — to return 8%, 10%, 12% or 14%.

Expected return = (8 + 10 + 12 + 14) ÷ 4 = 11%

Deviations:  −3%, −1%, +1%, +3%
Variance    = 0.25(0.0009 + 0.0001 + 0.0001 + 0.0009) = 0.0005
Standard deviation = √0.0005 = 2.24%

Computed from forecast probabilities like this, the answer is ex-ante risk. Computed from a history of actual returns, it is ex-post risk. They are the same arithmetic on different inputs, and they routinely disagree.

That single number is total risk. It says how much the return moves, but nothing about why. The why is the taxonomy: business risk, financial risk, liquidity risk, market risk, interest rate risk, exchange rate risk, political risk, regulatory risk, country risk. A manager measures total risk and then manages the sources.

The formula

Variance (σ²) = Σ [Rᵢ − E(Rᵢ)]² × Pᵢ

Standard deviation (σ) = √Variance

where Rᵢ is a possible rate of return and Pᵢ its probability.

A worked example

An investor is shown two Category III AIF schemes, each expecting 14% a year on a Rs 1 crore commitment.

ScenarioProbabilityScheme AScheme B
Good year0.3022%44%
Normal year0.5014%12%
Bad year0.202%−12%
Expected return14.0%14.4%

Scheme A: 0.30(22) + 0.50(14) + 0.20(2) = 6.6 + 7.0 + 0.4 = 14.0% Scheme B: 0.30(44) + 0.50(12) + 0.20(−12) = 13.2 + 6.0 − 2.4 = 16.8% — higher, but look at the spread.

A's outcomes on Rs 1 crore run from Rs 1.02 crore to Rs 1.22 crore. B's run from Rs 88 lakh to Rs 1.44 crore.

The standard deviations: A is about 6.9%, B about 20.4% — roughly three times the dispersion for two and a half percentage points of extra expected return. An investor who needs the money in eighteen months and an endowment with a thirty-year horizon should reach different conclusions from the same table, and that is the whole point of stating an objective in terms of both risk and return.

Why NISM asks about it

Chapter 1, section 1.4.3, defines risk and lists its types; Chapter 3, section 3.4, turns the definition into variance and standard deviation. Expect the definitional question ("risk is the dispersion around the expected return"), the risk-versus-uncertainty distinction, and at least one computation that hands you a probability table and asks for expected return, variance or standard deviation. The framing sentence the workbook repeats — "risk leads return", not the other way around — is itself examinable.

Common exam traps

  • Risk is not the chance of losing money. It is dispersion in both directions. A fund that beat its forecast by 20% was risky too.
  • Risk is not uncertainty. Uncertainty is variability whose causes are unknown; risk is variability whose causes are understood well enough to quantify. The workbook's phrase is "risk is known uncertainty".
  • Variance is in squared units and standard deviation is not. A variance of 0.0005 is a standard deviation of 2.24%, not 0.05%.
  • Ex-ante risk uses probabilities; ex-post risk uses history. A question that gives you scenarios and probabilities wants the first. One that gives you five years of returns wants the second.
  • Total risk is not the risk that gets paid for. Only the non-diversifiable part earns a return — see systematic-risk — which is why two funds with identical standard deviations can deserve different returns.
  • The risk–return line is drawn straight in every textbook exhibit, but the workbook says outright that the real relationship is non-linear and differs between individuals.

Where this is taught

Free preparation for NISM Series XIX-E

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