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Intermediate/Risk Management/Lesson 47 of 60

Risk-Adjusted Returns

Comparing returns after accounting for the risk taken (Sharpe ratio).

Why it matters

A high return earned by taking wild risk is not automatically better than a slightly lower return earned smoothly. Two funds can both report strong numbers, yet one may have lurched up and down so violently that most investors would have sold in a panic along the way. What matters is not the raw return on its own, but the return you earned for each unit of risk you carried.

Judging return per unit of risk is how professionals separate genuine skill from luck. A manager who delivers 14 percent by swinging wildly has not done better than one who delivers 12 percent in a near straight line. Risk-adjusted return puts both on the same honest footing, so you can pick the fund that works hardest for the risk it takes rather than the one with the loudest headline.

An everyday way to picture it

Two drivers leave the same office for the same airport and arrive within minutes of each other. The first weaved through traffic at high speed, braking hard and cutting across lanes. The second drove smoothly and stayed in one lane the whole way. They reached at almost the same time, but only one of them risked a crash to get there.

Judged on arrival time alone, the two drivers look equal. Judged on the risk taken to arrive, the smooth driver clearly did better. Investing works the same way. Reaching a given return by taking wild risk is not the same as reaching it calmly, even when the final number matches, because the wild ride is the one that shakes you out before you get there.

What the numbers are really telling you

Raw returns mislead because they say nothing about the ride. A number like 18 percent tells you the destination but hides whether the path was a gentle slope or a cliff edge. To compare two funds fairly, you divide the reward by the risk. The standard measure is the Sharpe ratio: take the portfolio return, subtract the risk-free rate, and divide by the standard deviation of returns, which is just how much the returns bounce around their own average.

Sharpe ratio:
Sharpe ratio = (portfolio return - risk-free rate) ÷ standard deviation of returns

The risk-free rate is the yardstick because no sensible investor takes risk for a return they could already earn safely. In India that rate comes from short-term government debt, usually the yield on a treasury bill, often proxied by the RBI repo rate, and it sits in the region of 6 to 7 percent. Only the return earned above that risk-free rate counts as reward for taking risk, which is why the formula subtracts it first.

The Sharpe ratio has one weakness: it treats upside swings and downside swings as equally bad. But investors do not lose sleep when a fund jumps up. The Sortino ratio fixes this by dividing only by downside volatility, the size of the falls, and ignoring the upside bounce. A fund that looks jumpy only because it keeps surprising on the upside can score poorly on Sharpe yet strongly on Sortino.

Sortino ratio:
Sortino ratio = (portfolio return - risk-free rate) ÷ downside volatility

The clearest case is two funds with the same headline return. If both return 12 percent with a risk-free rate of 6 percent, the steadier one earned that return more efficiently and wins on a risk-adjusted basis.

FundReturnVolatilitySharpe ratio
Fund X12%8%(12 - 6) ÷ 8 = 0.75
Fund Y12%15%(12 - 6) ÷ 15 = 0.40

Same return, very different ratios. Fund X turns the risk it takes into far more reward per unit, so a careful investor prefers it even though the headline 12 percent is identical on both.

See it for yourself

Set a return and a volatility for two funds, choose a risk-free rate, and watch which one wins on return per unit of risk.

Fund A return12%
Fund A volatility8%
Fund B return18%
Fund B volatility15%
Risk-free rate4%
In India this tracks short-term government debt, usually 6 to 7 percent.
Fund A Sharpe ratio
1.00
Fund A returns 12 percent at 8 percent volatility, a good risk-adjusted result.
Fund B Sharpe ratio
0.93
Fund B returns 18 percent at 15 percent volatility, a below average risk-adjusted result.
Winner on risk-adjusted return: Fund A

Fund A earns 1.00 of return for every unit of risk, more than the other fund. Even if the other fund shows a higher headline return or a lower volatility, Fund A turns the risk it takes into reward more efficiently, and that is exactly what risk-adjusted return rewards.

Rank three funds by Sharpe ratio

Three funds, three different mixes of return and risk. Change the risk-free rate and watch the ranking re-sort.

Risk-free rate4%
RankFundReturnVolatilitySharpe ratio
1Fund C12%9%0.89
2Fund A10%8%0.75
3Fund B14%15%0.67
Best fund right now
Fund C
The highest return does not always top the list. The winner is whichever fund pays the most return for each unit of risk, which is why a steadier fund can outrank a higher returning one.

A steady fund versus a wild one over time

Give each fund a return and a volatility, then compare where they land and how far each one fell along the way.

Steady fund return12%
Steady fund volatility8%
Wild fund return15%
Wild fund volatility25%
Years invested5
Steady fund, value after 5 years
₹1,87,675
Worst drop along the way
0.0%
Sharpe ratio
1.00
Wild fund, value after 5 years
₹2,08,241
Worst drop along the way
0.0%
Sharpe ratio
0.44
The point of the simulation

The wild fund can sometimes finish ahead, but look at its worst drop. That deeper fall is the moment most investors give up and sell. The steady fund usually carries a higher Sharpe ratio, which is the calmer, more repeatable way to grow money.

Worked example: which fund really won

Two funds, one risk-free rate of 6 percent. Fund A returns 14 percent but swings hard at 20 percent volatility. Fund B returns only 12 percent but is far steadier at 10 percent volatility. The headline says Fund A. The Sharpe ratio disagrees.

StepFund AFund B
Return14%12%
Volatility20%10%
Return above risk-free14 - 6 = 812 - 6 = 6
Sharpe ratio8 ÷ 20 = 0.406 ÷ 10 = 0.60

Fund A earns 0.40 of return for each unit of risk. Fund B earns 0.60. Fund B wins on a risk-adjusted basis, even though its headline return is two percentage points lower, because it produced that return with half the volatility.

So you decide. Do you chase the bigger headline number, or take the fund that pays more per unit of risk?

Remember this

Sharpe ratioWhat it signalsHow to read it
Below 0The fund returned less than risk-free cashYou took risk and were not paid for it
0 to 1Modest reward for the risk carriedCommon, but check whether a steadier option exists
1 to 2Good risk-adjusted returnSolid reward for each unit of risk
Above 2Excellent risk-adjusted returnRare, and hard to sustain over long periods

In short: do not chase the biggest headline return. Compare the return each fund earns for every unit of risk, and prefer the one that pays you more per unit of risk. That is the difference between earning a lot and earning it well.