Risk adjusted return
The return an investment earns for each unit of risk it takes on, rather than the return looked at on its own — in this paper, measured through the Sharpe ratio.
In plain language
A fund that returns 16% is not automatically the better choice over one that returns 12%. The real question is how much risk each one took to get there.
Risk adjusted return answers exactly that: how much return did an investment produce, per unit of the risk it exposed the investor to. The workbook's tool for measuring it is the Sharpe ratio.
How it works
Sharpe ratio = (Investment return − Risk-free rate) ÷ Standard deviation.
The workbook's own example: a risk-free rate of 5%, a scheme return of 14%, and a standard deviation of 4%, giving a Sharpe ratio of (14% − 5%) ÷ 4% = 2.25.
Among a group of comparable schemes, the workbook's rule is to prefer the one with the highest Sharpe ratio, because it is generating more return for every unit of risk taken — not necessarily the one with the highest raw return.
A worked example
Ms Iyer is comparing two hybrid mutual funds for the growth portion of her retirement portfolio, with the risk-free rate at 6%:
| Fund P | Fund Q | |
|---|---|---|
| Return | 12% | 16% |
| Standard deviation | 3% | 8% |
| Sharpe ratio | (12−6)/3 = 2.00 | (16−6)/8 = 1.25 |
Fund Q has the higher headline return, 16% against Fund P's 12%. But on a risk-adjusted basis, Fund P wins, with a Sharpe ratio of 2.00 against Q's 1.25 — it earned nearly as much excess return per unit of risk while carrying less than half of Q's volatility. For a retiree who cannot afford a bad year, that is the more relevant comparison than the raw return alone.
Why NISM asks about it
Chapter 5, section 5.3.3 (Sharpe Ratio), introduces risk adjusted return and gives the formula with the 5%/14%/4% worked example. Expect a direct Sharpe ratio computation, and a question comparing two schemes where the higher raw return does not have the higher Sharpe ratio.
Common exam traps
- Subtract the risk-free rate before dividing — dividing the raw return straight by the standard deviation, skipping the risk-free rate, is the standard error.
- A higher Sharpe ratio is preferred over a higher raw return when comparing schemes — the workbook is explicit about this ranking rule.
- The full mechanics of the ratio, and its comparison with the Treynor ratio, are covered on the dedicated Sharpe ratio page — this entry covers the broader idea of risk-adjusted return that the Sharpe ratio is one measure of.
Check yourself
1.A scheme has returned 11 percent with a standard deviation of 3 percent. The risk-free rate of return is 5 percent. What is its Sharpe ratio?
- a)3.67
- b)1.20
- c)2.00
- d)0.50
Show the answer
Answer: (c) 2.00
"Sharpe Ratio = (Investment Return − Risk Free rate of Return) / Standard Deviation."
(11 − 5) ÷ 3 = 6 ÷ 3 = 2.00.
The workbook's own example follows the same method: (14 percent − 5 percent) ÷ 4 percent = 2.25.
Where the wrong answers come from:
- 3.67 = 11 ÷ 3 — the risk-free rate has been left out. The Sharpe ratio measures excess return over the risk-free rate.
- 1.20 = 6 ÷ 5 — the excess return divided by the risk-free rate instead of the standard deviation.
- 0.50 = 3 ÷ 6 — the formula turned upside down.
Why it matters: it is "a measure of risk adjusted return" — the return "for each unit of risk taken" — and "from a group of comparable schemes, investors ought to prefer the scheme with the HIGHEST Sharpe ratio."
Where this is taught
Free preparation for NISM Series XVIIRelated terms
- BetaHow sharply a share moves relative to the market index — beta 1 moves with the index, above 1 amplifies it, below 1 dampens it. The standard measure of systematic risk.
- Sharpe ratioReturn earned above the risk-free rate divided by standard deviation — how much reward an investment produced for each unit of total risk its holder had to live with.
- Standard deviationA measure of how far returns typically stray from their own average — the standard statistic for total risk, counting company-specific and market-wide causes alike.
- Treynor ratioRisk premium per unit of market risk — the return a scheme earned above the risk-free rate, divided by its beta rather than by its standard deviation.
- Tax-adjusted returnThe return an investor actually keeps after tax is deducted — the figure that tells them what income is really available to spend, unlike the pre-tax rate quoted on the product.
- Percentage returnReturn expressed as a percentage of the amount invested rather than in rupees, which puts every investment on a base of Rs 100 and makes holdings of different sizes comparable.
- Peer group comparisonJudging a fund against other similar actively managed funds rather than against an index — popular, but only sound if the funds follow comparable strategies and their risk is compared alongside their return.
- Investment styleThe consistent approach a fund manager takes to picking securities inside a given mandate — such as a credit quality or interest-rate sensitivity in debt, or a market-cap segment in equity.