Sharpe ratio decoded: same CAGR, different ride

Friend forwarded a fund factsheet on Saturday evening. Highlighted the 14 pct CAGR over five years. I asked him for the volatility number next to it. Long pause. The factsheet had it. Page four, in 8 point grey type. He had never looked.

Two funds can print the same return and be two completely different products. The CAGR is the marketing copy. The Sharpe is the receipt.

Same scenario. Two funds, both 14 pct CAGR. Fund A is a boring large cap stack at 12 pct annualised volatility. Fund B is an exciting thematic at 22 pct. Risk free rate 7 pct in both cases. Sharpe is just (Return minus RFR) divided by the volatility. Fund A . 0.58. Fund B . 0.32. Same end point on the chart, half the rupee earned per unit of risk to get there. The reason most investors quietly switch out of Fund B is not the return. It is the ride.

Reference numbers worth keeping in one place. NIFTY 50 TRI long run, Sharpe around 0.40. S and P 500 TR USD, around 0.50. Active largecap MF median in India net of fees, around 0.30. A clean quality cohort, 0.92. A systematic multi asset cohort with disciplined rebalance harvest, 1.20.

Above 1.5 over a real ten year window is rare globally. If the brochure prints 2.0, the methodology is the question. Smoothed monthly NAVs, illiquid holdings priced stale, survivorship in the cohort can all inflate the number. Real edge welcomes the audit.

Three rules to read any Sharpe by. Ask for the volatility next to every CAGR. Compare like for like . same window, same risk free rate, same return frequency. Anything above 1.5 over a decade earns the right to be questioned before it earns the right to be trusted.

The half you skip is the half that decides whether you actually hold

Redo Fund A and Fund B yourself

The arithmetic in the opening takes three numbers. Fund A: 14 minus 7 is 7 points of return above cash, divided by 12 points of volatility, gives 0.58. Fund B: the same 7 points divided by 22 gives 0.32. Fund B had to swing almost twice as hard to earn the same 7 points.

The last line is the useful one. To earn Fund A's Sharpe at its own level of swing, Fund B would need about 19.8 percent a year, not 14. Now change the risk free rate to 5.5. Both Sharpe ratios rise, Fund A to 0.71 and Fund B to 0.39, without either fund changing at all. That is why the opening insists on the same risk free rate before comparing two figures.

The denominator is not the same across the market

Volatility is the yearly swing of returns, measured as the standard deviation of daily changes scaled up to a year. It differs a lot between parts of the Indian market, which means the same return buys a very different Sharpe depending on where it came from.

Put that into the formula. An index with 21.68 percent volatility needs nearly twice the excess return of one with 11.97 to print the same Sharpe. A small cap or alpha style fund that matches a large cap fund on return has, by definition, delivered less per unit of risk. Fund B in the opening is not a made up extreme. It is roughly the gap between the calmest and the busiest NSE indices in the last two years.

Applying the audit to our own numbers

The opening says anything above 1.5 earns the right to be questioned. RupeeCase's own model strategies print numbers in that zone, so here they are, with the questions applied.

Run the three rules against them. Window: these histories are about four to five years of back test, not a real ten year window, and a short window can flatter any Sharpe. Method: they are model figures on monthly values, not live accounts, so costs and slippage are only what the model assumes. Like for like: they only compare fairly with figures on the same window and risk free rate. That is why every one of them carries the label "Model, back tested", and why I read them as an upper bound, not a forecast.

The free module on risk metrics that matter covers volatility, drawdown, Sharpe and the rest with calculators and a quiz. Sharpe treats an upside swing the same as a downside one; the two ratios that fix that are in Sharpe, Sortino and Calmar, and why the swing itself eats compounded return is in volatility drag.