Skip to content

NISM-Series-V-A: Mutual Fund Distributors · Mutual Fund Scheme Performance

Standard Deviation, Beta and Tracking Error Explained

Updated 11 October 2026 · Fact-checked

Standard deviation measures how much a scheme's returns swing around its average. Beta measures how much a scheme moves relative to the market or benchmark. Tracking error measures how far an index fund's returns stray from its index. Higher values mean more volatility or more deviation.

Understand Risk Measures: Standard Deviation, Beta and Tracking Error

Risk in a mutual fund is not only the chance of loss. It is also how uncertain the return is. Three measures help you put numbers on this: standard deviation, beta and tracking error.

Standard deviation shows how widely a scheme's returns are spread around their average (mean) return. A scheme with a high standard deviation has returns that jump up and down a lot. A scheme with a low one is steadier. It measures total volatility, which covers both upward and downward swings. It does not say whether the swings were good or bad.

Beta measures sensitivity to the market. The market (or benchmark) has a beta of 1. A scheme with beta above 1 tends to move more than the market. A scheme with beta below 1 tends to move less. If beta is 1.2 and the market rises 10%, the scheme is expected to rise about 12%. The same works on the way down, so a 10% fall suggests about a 12% fall. Beta captures only market-related risk, not the scheme's own specific risk.

Tracking error applies mainly to passive schemes such as index funds and ETFs. These aim to copy an index. Tracking error is the standard deviation of the difference between the scheme's returns and the index returns. A low tracking error means the fund follows its index closely. A high one means it strays. Causes include expenses, cash holdings, delays in investing inflows, and transaction costs.

The key contrast: standard deviation and beta describe how risky a scheme is. Tracking error describes how well a scheme copies its benchmark. For an index fund, a lower tracking error is better.

Key formulas to remember

Standard deviation
Higher standard deviation = wider spread of returns around the average = higher volatility
Measures total risk. It is not a measure of return, and it is not a prediction of loss.
Beta of the market
Market (benchmark) beta = 1
Beta > 1: more volatile than market. Beta < 1: less volatile. Beta = 1: moves with market.
Expected move using beta
Expected scheme change ≈ Beta × Market change
A rough estimate. Works for both rises and falls.
Tracking error
Tracking error = standard deviation of (Scheme return − Index return)
Lower is better for an index fund or ETF.
Range using standard deviation (rule of thumb)
Average return ± 1 standard deviation covers roughly 68% of outcomes if returns are normally distributed
Only an approximation. It holds under a normal distribution assumption.

How to solve Risk Measures: Standard Deviation, Beta and Tracking Error questions

Most questions ask you to identify the measure, read its value, or compare two schemes. Use this method.

  1. 1Read what the question asks: total volatility, market sensitivity, or closeness to an index.
  2. 2Match it: total volatility → standard deviation; market sensitivity → beta; closeness to index → tracking error.
  3. 3Check the scheme type. Tracking error is relevant mainly to index funds and ETFs.
  4. 4If beta is given, compare it with 1 to decide if the scheme is more or less volatile than the market.
  5. 5For a calculation, multiply beta by the market change. Keep the sign (rise or fall).
  6. 6When comparing two schemes, pick the higher number as riskier for standard deviation and beta. For tracking error, pick the lower number as better.
  7. 7Check the option wording for traps such as 'return' instead of 'volatility', or 'guaranteed'.

Quickest way: Match the keyword to the measure

When to use it: Use when the question is a definition or a comparison and time is short.

  1. Spot the keyword: 'spread' or 'total risk' means standard deviation.
  2. 'Sensitivity', 'relative to market' or 'compared with 1' means beta.
  3. 'Index fund', 'deviation from index' or 'replication' means tracking error.
  4. For a beta calculation, multiply beta by the market move and check the direction.
  5. Eliminate options that say a higher value means higher return or lower risk.

Common mistakes in Risk Measures: Standard Deviation, Beta and Tracking Error

  • Thinking a high standard deviation means a high return.

    Students link risk with reward too tightly.

    Fix: Standard deviation only shows how widely returns vary. It says nothing about whether the average return is high.

  • Saying beta measures total risk.

    Beta and standard deviation both sound like risk numbers.

    Fix: Beta measures only sensitivity to market movements. Total volatility is standard deviation.

  • Ignoring direction when using beta.

    Students remember the rise case and forget the fall.

    Fix: Beta works both ways. With beta 1.2, a 10% market fall suggests about a 12% fall.

  • Treating a high tracking error as good.

    Students assume a larger number means more skill.

    Fix: For an index fund the goal is to copy the index. Lower tracking error means better replication.

  • Applying tracking error to an actively managed scheme as the main quality test.

    Students apply one measure everywhere.

    Fix: Tracking error mainly assesses passive funds. Active funds are judged on risk and return against the benchmark.

  • Believing the market beta is 0.

    Students confuse it with a risk-free asset.

    Fix: The market or benchmark has beta 1. A risk-free asset has a beta of about 0.

Worked examples

Example 1

A scheme has a beta of 1.3. The benchmark is expected to rise 8%. What is the scheme's expected rise, and is the scheme more or less volatile than the market?

Show the solution
  1. Expected change ≈ Beta × Market change.
  2. 1.3 × 8% = 10.4%.
  3. Beta of 1.3 is above 1, so the scheme is more volatile than the market.

Answer: Expected rise is about 10.4%; the scheme is more volatile than the market.

Example 2

Index Fund A has a tracking error of 0.3% and Index Fund B has a tracking error of 1.2%. Both track the same index. Which follows the index more closely, and what does it indicate?

Show the solution
  1. Tracking error measures how much the fund's returns deviate from the index.
  2. A lower figure means smaller deviations.
  3. 0.3% is lower than 1.2%.
  4. So Fund A follows the index more closely.

Answer: Fund A follows the index more closely, as its lower tracking error shows smaller deviation from the index.

Exam tips

  • Learn the one-line meaning of each measure. Many questions are pure definition checks.
  • Remember market beta is 1 and compare any given beta with it.
  • Watch for options claiming a measure guarantees returns or removes risk. They are wrong.
  • For index funds, lower tracking error is better. Expect a comparison of two funds.
  • Read whether the market is rising or falling before applying beta.

Practice questions from Mutual Fund Scheme Performance

Risk Measures: Standard Deviation, Beta and Tracking Error in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Risk Measures: Standard Deviation, Beta and Tracking Error: frequently asked questions

What does standard deviation tell you about a mutual fund?

It tells you how widely the fund's returns vary around its average return. A higher figure means more volatility and less predictable returns. It does not tell you the direction of the swings.

What is the difference between standard deviation and beta?

Standard deviation measures total volatility of the scheme's own returns. Beta measures how sensitive the scheme is to market movements, with the market at 1. A scheme can have a high standard deviation yet a modest beta.

What is tracking error in an index fund?

It is the standard deviation of the gap between the fund's returns and the index's returns. It shows how closely the fund copies the index. A lower tracking error means closer tracking.

Does a beta below 1 mean a scheme cannot fall?

No. A beta below 1 only means the scheme is expected to move less than the market. It can still fall when the market falls, just by a smaller amount.