NISM-Series-XXI-A: Portfolio Management Services (PMS) Distributors · Performance Measurement and Evaluation of Portfolio Managers

Risk Measures: Standard Deviation, Beta and Tracking Error

Q: What is the difference between standard deviation and beta?

Standard deviation measures total volatility of a portfolio's returns, including risk specific to its holdings. Beta measures only how sensitive the portfolio is to market movements. A concentrated portfolio can have a high standard deviation but a modest beta.

Q: What does maximum drawdown mean in PMS?

It is the largest fall in portfolio value from a peak to a later low, before a new peak is made. It shows the worst loss a client would have faced. It is shown as a percentage of the peak.

Q: How is downside deviation different from standard deviation?

Standard deviation counts all swings from the average, up and down. Downside deviation counts only returns below a chosen minimum level. It therefore focuses on the risk of loss.

Updated 11 October 2026 · Fact-checked

Standard deviation measures total volatility of returns. Beta measures sensitivity to the market, so it captures only market risk. Tracking error is the standard deviation of the difference between portfolio and benchmark returns. Downside deviation counts only bad returns. Maximum drawdown is the largest peak-to-trough fall.

Understand Risk Measures: Standard Deviation, Beta and Tracking Error

Return alone does not tell you how good a portfolio manager is. You also need to know how much risk was taken to earn it. Risk measures put a number on that risk.

Standard deviation measures how far returns swing around their average. A higher number means a more volatile portfolio. It treats upside and downside swings alike. It is a measure of total risk: market risk plus the risk specific to the stocks held.

Beta measures how much a portfolio moves when the market moves. The market (benchmark) has a beta of 1. A beta of 1.2 means the portfolio tends to move 20% more than the market. A beta of 0.8 means it tends to move 20% less. Beta captures only systematic (market) risk. A well-diversified portfolio has little specific risk, so beta describes most of its risk.

Tracking error is the standard deviation of the active return, which is portfolio return minus benchmark return. A low tracking error means the portfolio stays close to its benchmark. A high one means the manager takes large active bets. Downside deviation is like standard deviation but uses only returns below a chosen minimum, so it focuses on losses. Maximum drawdown is the largest fall from a peak value to a later low, before a new peak is reached. It shows the worst loss an investor would have lived through.

For a PMS client, these numbers help judge whether the manager's returns were worth the risk taken.

Key formulas to remember

Standard deviation (σ): σ = √[ Σ(R − average R)² ÷ (n − 1) ]; Uses sample data, so divide by n − 1. Higher σ means higher total risk. Annualising monthly σ: multiply by √12.
Beta (β): β = Covariance(Rp, Rm) ÷ Variance(Rm); Market beta is 1. β > 1 is aggressive, β < 1 is defensive. It measures only systematic risk.
Beta from correlation: β = ρ × (σp ÷ σm); ρ is the correlation between portfolio and market returns.
Tracking error: TE = standard deviation of (Rp − Rb); Rb is the benchmark return. It is not the simple difference of the two returns.
Active return: Active return = Rp − Rb; This is the series whose standard deviation gives tracking error.
Maximum drawdown: MDD = (Trough value − Peak value) ÷ Peak value; Shown as a negative percentage or as a fall in percent. Peak must come before the trough.

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

Use this method for any question on risk measures.

1Identify what the question asks: total risk, market risk, risk relative to benchmark, downside risk or worst fall.
2Match it to the measure: standard deviation for total risk, beta for market risk, tracking error for benchmark-relative risk, downside deviation for losses only, drawdown for peak-to-trough fall.
3Write the matching formula and list the numbers given.
4For beta from σ and ρ, use β = ρ × σp ÷ σm. Do not mix up which σ is on top.
5For drawdown, find the highest value first, then the lowest value after it. Compute (trough − peak) ÷ peak.
6Check the answer is sensible: beta is not negative for a normal equity portfolio, and drawdown is never positive.
7Read all four options and drop any that use the wrong measure.

Quickest way: Match the keyword to the measure

When to use it: Use for definition and concept questions, which are common in this topic.

Total risk or volatility points to standard deviation.
Sensitivity to market or systematic risk points to beta.
Deviation from benchmark or active risk points to tracking error.
Only negative returns or losses points to downside deviation.
Peak to trough or worst loss points to maximum drawdown.
For numbers, do the one-line formula and test it against the options.

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

Saying beta measures total risk.
Both beta and standard deviation are called risk measures, so they get blurred.
Fix: Beta is only market (systematic) risk. Standard deviation is total risk.
Calling tracking error the difference between portfolio and benchmark return.
The word 'tracking' suggests a simple gap.
Fix: That gap is active return. Tracking error is the standard deviation of that active return.
Assuming a high standard deviation means the manager is bad.
Students link risk with poor quality.
Fix: High σ only means high volatility. Judge it against the return earned.
Thinking a beta of 0.8 means the portfolio loses 0.8% always.
Beta is read as a fixed number rather than a relative one.
Fix: It means the portfolio tends to move 0.8 times the market move, on average.
Measuring drawdown from the starting value instead of the peak.
Students assume the first value is the reference.
Fix: Always use the highest value before the fall as the base.
Believing standard deviation separates up and down moves.
Risk is thought of as only loss.
Fix: Standard deviation counts both. Only downside deviation focuses on losses.

Worked examples

Example 1

A portfolio has a correlation of 0.9 with the benchmark. The portfolio's standard deviation is 20% and the benchmark's is 15%. What is the portfolio's beta?

Show the solution

Use β = ρ × (σp ÷ σm).
ρ = 0.9, σp = 20, σm = 15.
σp ÷ σm = 20 ÷ 15 = 1.3333.
β = 0.9 × 1.3333 = 1.2.

Answer: Beta = 1.2. The portfolio tends to move 20% more than the market.

Example 2

A PMS portfolio is valued at ₹10,00,000, rises to ₹14,00,000, falls to ₹10,50,000, then recovers to ₹13,00,000. What is the maximum drawdown?

Show the solution

Find the peak: ₹14,00,000.
Find the lowest value after that peak: ₹10,50,000.
Fall = 14,00,000 − 10,50,000 = ₹3,50,000.
Drawdown = 3,50,000 ÷ 14,00,000 = 0.25, which is 25%.

Answer: Maximum drawdown is 25%, measured from the ₹14,00,000 peak.

Exam tips

Expect definition questions that ask which measure fits a situation. Learn the keyword matches.
Watch for options that swap beta and standard deviation, or tracking error and active return.
Remember the benchmark beta is 1, and use that to judge aggressive or defensive portfolios.
In drawdown questions, the peak must come before the trough. Ignore later highs.
Index funds and closet trackers have low tracking error. Active concentrated portfolios have high tracking error.

Practice questions from Performance Measurement and Evaluation of Portfolio Managers