Mutual Fund Scheme Performance: formula sheet

Key formulas

Absolute return

Absolute return (%) = (Final value − Initial value) ÷ Initial value × 100

Ignores time. Suitable for periods up to one year.

CAGR

CAGR = (Final value ÷ Initial value)^(1/n) − 1

n is the number of years. Only for a single investment with no interim cash flows.

Future value check

Final value = Initial value × (1 + CAGR)^n

Use it to test which option is correct by working forward.

Annualising a short-period return (simple)

Annualised return = Return for the period × (365 ÷ number of days)

Simple annualisation, no compounding. Use only if the question says so.

XIRR condition

Σ [Cash flow ÷ (1 + XIRR)^(days from first date ÷ 365)] = 0

Investments are negative, redemption or current value is positive. Solved by trial or software.

Rule of 72 (approximation)

Years to double ≈ 72 ÷ annual rate (%)

A rough guide only, not exact.

Absolute NAV return

(Ending NAV − Beginning NAV) ÷ Beginning NAV × 100

Use for growth option, or when no dividend is paid.

Dividend adjusted return (no reinvestment)

(Ending NAV − Beginning NAV + Dividend per unit) ÷ Beginning NAV × 100

Dividend is added back as cash received. Use when the question says dividend was not reinvested.

Units bought on reinvestment

Dividend per unit × Units held ÷ Ex-dividend NAV

Use the NAV after the dividend, not the NAV before.

Total return with reinvestment

(Total units at end × Ending NAV − Initial investment) ÷ Initial investment × 100

Total units = original units + reinvested units + bonus units.

Bonus units

Units after bonus = Units before × (1 + bonus ratio)

For a 1:1 bonus, units double and NAV roughly halves.

CAGR (for periods over 1 year)

[(Ending value ÷ Beginning value)^(1 ÷ years) − 1] × 100

Annualises a multi-year return.

TRI versus PRI

TRI return = price return + dividend income reinvested

For the same index and period, TRI return is normally higher than or equal to PRI return.

Excess return over benchmark

Excess return = Scheme return − Benchmark return

Positive means the scheme outperformed. Use the TRI return for the benchmark.

Benchmark selection rule

Benchmark must match the scheme's investment universe, style and asset class

Example: large cap scheme with a large cap index; debt scheme with a debt index.

SEBI requirement

Scheme performance is compared with TRI of the benchmark

If a TRI is not available for an index, PRI may be used until a TRI is available.

Standard deviation

Higher standard deviation = wider spread of returns around the average = higher volatility

Measures total risk. It is not a measure of return, and it is not a prediction of loss.

Beta of the market

Market (benchmark) beta = 1

Beta > 1: more volatile than market. Beta < 1: less volatile. Beta = 1: moves with market.

Expected move using beta

Expected scheme change ≈ Beta × Market change

A rough estimate. Works for both rises and falls.

Tracking error

Tracking error = standard deviation of (Scheme return − Index return)

Lower is better for an index fund or ETF.

Range using standard deviation (rule of thumb)

Average return ± 1 standard deviation covers roughly 68% of outcomes if returns are normally distributed

Only an approximation. It holds under a normal distribution assumption.

Excess return

Excess return = Rp − Rf

Rp is scheme return, Rf is risk-free return. Both must be for the same period and in the same form (for example, annualised).

Sharpe ratio

Sharpe ratio = (Rp − Rf) ÷ σp

σp is the standard deviation of scheme returns. Measures return per unit of total risk. Higher is better.

Treynor ratio

Treynor ratio = (Rp − Rf) ÷ βp

βp is scheme beta. Measures return per unit of market risk. Higher is better.

Expected return (CAPM)

Expected return = Rf + β × (Rm − Rf)

Rm is the market (benchmark) return. Used to find alpha.

Jensen's alpha

Alpha = Rp − [Rf + β × (Rm − Rf)]

Positive means outperformance after adjusting for beta. Negative means underperformance. Zero means return matched the risk taken.

Absolute return

(Ending NAV − Beginning NAV) ÷ Beginning NAV × 100

Used for periods up to one year. Adjust for dividends or income distribution if paid.

CAGR

CAGR = (Ending NAV ÷ Beginning NAV)^(1 ÷ n) − 1

Used for periods longer than one year, where n is the number of years.

Excess return over benchmark

Scheme return − Benchmark return

A positive value means the scheme outperformed. Compare the same period and use the Total Return Index version of the benchmark.

Portfolio turnover ratio

Lower of purchases or sales of securities ÷ Average AUM

Shows trading activity. Higher turnover generally means higher transaction costs.

Disclosure warning

Past performance may or may not be sustained in future

Past returns must carry this caution and must never be presented as assured or guaranteed.

Quick revision

• Absolute return = (end value − start value) ÷ start value, and it ignores time.
• CAGR gives the yearly compounded rate between two values over a period.
• XIRR is used when cash flows happen on different dates, as in SIPs.
• Returns shown for periods under one year are generally absolute; longer periods are annualised.
• Dividend payouts reduce NAV, so scheme returns must be adjusted for them.
• A Total Return Index includes dividends, so it is the fairer benchmark.
• Standard deviation measures how much returns vary around their average.
• Beta measures sensitivity to the market; a beta above 1 means more volatile than the market.
• Tracking error shows how closely a scheme follows its benchmark; it matters most for index funds.
• Sharpe ratio divides excess return over the risk-free rate by standard deviation.
• Treynor ratio divides excess return over the risk-free rate by beta.
• Alpha is the return earned above what the risk taken would explain.

Common mistakes

• Using CAGR for a SIP Fix: Instalments are invested for different durations. Use XIRR for any series of dated cash flows.
• Treating absolute return as an annual rate Fix: Absolute return covers the whole period. Annualise it with CAGR if the period is more than a year.
• Ignoring the dividend and using only the NAV change. Fix: Always check for a dividend in the question. If one is paid, add it back.
• Dividing by the ending NAV instead of the beginning NAV. Fix: The base of any return is the amount you started with, which is the beginning NAV.
• Saying PRI includes dividends Fix: Remember: Total Return = price plus dividends. Price Return = price only.
• Choosing a broad market index for a sector or small cap scheme Fix: Match the index to the scheme's actual universe and style.
• Thinking a high standard deviation means a high return. Fix: Standard deviation only shows how widely returns vary. It says nothing about whether the average return is high.
• Saying beta measures total risk. Fix: Beta measures only sensitivity to market movements. Total volatility is standard deviation.
• Dividing the scheme return by risk without subtracting the risk-free rate. Fix: Write Rp − Rf first, every time, before touching the denominator.
• Mixing up Sharpe and Treynor denominators. Fix: Sharpe uses standard deviation (total risk). Treynor uses beta (market risk).

Exam tips

• Look for the trap option equal to the absolute return when a CAGR question is asked.
• If the question mentions monthly instalments or several dates, the intended answer is XIRR, not CAGR.
• Convert months to years before using n.
• V-A has no negative marking, so always attempt every question, but still eliminate options by compounding.
• Remember the definitions: CAGR for one investment, XIRR for irregular or periodic cash flows.
• Look first at the option name. Growth means no dividend adjustment is needed.
• Reinvestment questions use the ex-dividend NAV. Wrong options are often built with the cum-dividend NAV.
• After a bonus issue, compare value (units × NAV), not NAV.