Risk Measures — Standard Deviation, Beta, Sharpe Ratio
Risk measures put numbers on how much a fund's returns have varied and how much return came with that variation. This lesson explains standard deviation, beta, the Sharpe, Sortino and Treynor ratios, the Information Ratio and maximum drawdown.
Two ways of measuring variation
Standard deviation measures volatility: how widely a fund's returns have spread around their own average. Two funds can have the same average return while one swings far more from period to period; that fund has the higher standard deviation.
Beta measures something narrower: sensitivity to the benchmark. A beta above 1 means the fund has tended to move more than its benchmark, up or down; below 1, less. A beta of 1.2 means it has tended to move 1.2 times as much. Beta is estimated from past data, and the actual move in any period can differ.
Return per unit of risk
Risk-adjusted ratios ask how much return a fund earned for the risk it carried. Each starts with the return above the risk-free rate and divides it by a different measure of risk.
The Sharpe ratio divides by standard deviation: (return − risk-free rate) ÷ standard deviation. The Treynor ratio divides by beta: (return − risk-free rate) ÷ beta.
The Sortino ratio is like the Sharpe ratio but uses downside deviation, which counts only returns below a chosen target, often the risk-free rate. Returns above the target do not add to the risk figure.
Measured against the benchmark
The Information Ratio is (portfolio return − benchmark return) ÷ the standard deviation of that excess return. It relates how far a scheme was ahead of or behind its benchmark to how much that gap varied.
Under the SEBI Master Circular for Mutual Funds, the Information Ratio is disclosed daily for equity schemes, measured against the Tier 1 benchmark.
Drawdown, and reading the numbers
Maximum drawdown is the largest peak-to-trough fall over a period.
All these measures are worked out from past data, and none has a fixed pass mark. A figure has meaning only when compared between similar schemes over the same period, and it changes when the period changes.
Rules at a glance
Same average, different spread (illustrative)
Assumed figures: over three years Fund A returns 8%, 10% and 12%, and Fund B returns −10%, 10% and 30%. The simple average of the three yearly figures is 10% for both.
Fund A's returns sit within 2 percentage points of that average; Fund B's sit up to 20 percentage points away. Fund B's spread, and so its standard deviation, is ten times as large.
Sharpe, Treynor and Information Ratio (illustrative)
- Assumed figures, for arithmetic only, with a risk-free rate of 7%. Fund P: return 15%, standard deviation 20%, beta 1.25. Fund Q: return 13%, standard deviation 12%, beta 0.8.
- Sharpe ratio, Fund P = (15 − 7) ÷ 20 = 8 ÷ 20 = 0.40. Fund Q = (13 − 7) ÷ 12 = 6 ÷ 12 = 0.50.
- Treynor ratio, Fund P = (15 − 7) ÷ 1.25 = 6.4. Fund Q = (13 − 7) ÷ 0.8 = 7.5.
- Information Ratio: a portfolio returns 16% against a benchmark return of 13%, and the standard deviation of the excess return is 5%. Information Ratio = (16 − 13) ÷ 5 = 0.60.
- Beta: with a beta of 0.8, a 10% fall in the benchmark suggests a fall of about 0.8 × 10% = 8%, and a 10% rise suggests a rise of about 8%.
Result. Fund P had the higher return, but Fund Q had the higher Sharpe ratio (0.50 against 0.40) and Treynor ratio (7.5 against 6.4) over this period.
Key points
- Standard deviation measures how widely returns have spread around their average.
- Beta measures sensitivity to the benchmark: above 1, the fund has tended to move more than the benchmark; below 1, less.
- Sharpe divides the return above the risk-free rate by standard deviation; Treynor divides it by beta; Sortino uses downside deviation.
- The Information Ratio divides the excess return over the benchmark by the standard deviation of that excess return.
- None of these measures has a fixed pass mark; they are compared between similar schemes over the same period.
Common misunderstandings
- There is no fixed pass mark for a Sharpe ratio or any other measure: a figure is read only against similar schemes over the same period.
- Beta is not the same as standard deviation: beta is sensitivity to the benchmark, standard deviation is the spread of the fund's own returns.
- The ratio that uses beta is the Treynor ratio, not the Sortino ratio: Sortino uses downside deviation.
Questions people ask
What does a Sharpe ratio of 0.40 mean?
The fund earned 0.40 units of return above the risk-free rate for each unit of volatility over the period measured.
Why does the Sortino ratio leave out returns above the target?
Because downside deviation counts only returns below the chosen target, so returns above it do not add to the risk figure.
Do these measures predict future risk?
No. They are worked out from past data, and the figures change with the period chosen.
What this lesson relies on
- SEBI Master Circular for Mutual Funds, 20 March 2026 — Information Ratio and its daily disclosure for equity schemes
- Standard definitions of standard deviation, beta, Sharpe, Sortino and Treynor ratios and maximum drawdown (plain mathematics)
This lesson was reviewed independently against these sources on 8 October 2026. Rules change: check the current regulation, scheme document or policy wording before relying on any figure. This is education, not advice.