Mutual Funds: formula sheet

Key formulas

Net Asset Value (NAV) per unit

NAV = (Market value of fund's assets − Liabilities) ÷ Number of units outstanding

Liabilities include accrued expenses. Detailed NAV problems are in the NAV Calculation topic.

Three-tier structure

Three tiers: Sponsor, Trust (Trustees), AMC

The sponsor settles the trust. The AMC is appointed by the sponsor (or the trustees, if so authorised) and approved by SEBI; the trustees supervise it. Custodian, registrar and auditor are support parties.

Open-ended vs close-ended test

Open-ended: continuous entry and exit at NAV-based price. Close-ended: fixed term, exit via exchange listing or maturity repurchase.

Use liquidity and maturity as the deciding features.

ETF price relationship

ETF market price ≈ NAV per unit

Arbitrage by large participants keeps the price close to NAV, but a small premium or discount can exist.

Net assets

Net assets = Market value of investments + Other assets − Liabilities − Accrued expenses

Use market value on the valuation date. Other assets include cash, bank balance and receivables.

NAV per unit

NAV per unit = Net assets ÷ Number of units outstanding

Units outstanding means units in issue on the valuation date, after any new issue or redemption.

Market value of an equity holding

Market value = Number of shares × Market price per share

Do this for each security, then add up.

Closing net assets (end of period)

Closing net assets = Opening net assets + Income and gains − Expenses − Distribution paid

Use when the question asks NAV at the end of a period. Gains include unrealised appreciation in market value. Expenses include accrued unpaid amounts as well as those paid in cash.

Total units from investment amount

Units = Amount invested ÷ NAV per unit (or the applicable price)

Useful when units are issued at a given NAV. Load, if any, changes the price applied.

Sale (issue) price, load on NAV

Sale price = NAV × (1 + entry load %)

Use when the question says load is a percentage of NAV, which is the default reading.

Repurchase (redemption) price, load on NAV

Repurchase price = NAV × (1 − exit load %)

Exit load is deducted from NAV. Repurchase price is below NAV.

Sale price, load on sale price

Sale price = NAV ÷ (1 − entry load %)

Use only when the load is stated as a percentage of the sale price itself.

Repurchase price, load on repurchase price

Repurchase price = NAV ÷ (1 + exit load %)

Use only if the exit load is stated as a percentage of the repurchase price. This is rare.

NAV per unit

NAV = (Market value of assets − Liabilities) ÷ Units outstanding

Compute this first if NAV is not given.

Amount invested and units

Units = Amount invested ÷ Sale price; Redemption proceeds = Units × Repurchase price

Use for investor-level questions.

Absolute (holding period) return

Return % = [(NAV₁ − NAV₀) + Dividend + Capital gain distribution] ÷ NAV₀ × 100

Per unit basis. NAV₀ is the opening NAV, or the offer price if an entry load applies and you paid it.

Simple annualised return

Annualised return = Absolute return × (12 ÷ months held)

Use 365 ÷ days if the period is given in days.

Effective annual yield (compounded)

Effective yield = (1 + Absolute return)^(12 ÷ months held) − 1

Absolute return as a decimal. Use when the question says effective or compounded.

Return with reinvestment

Return % = (Total units at end × NAV₁ − Amount invested) ÷ Amount invested × 100

Units added on reinvestment = Distribution ÷ Ex-distribution NAV on reinvestment date.

Total distribution per unit

Distribution per unit = Face value × Distribution % (when the distribution is declared as a percentage)

When a distribution is given as a percentage, apply it to face value, not NAV. When it is given in rupees per unit, use that figure directly.

Net-of-load redemption return

Return % = (Exit price + Distributions − Purchase price) ÷ Purchase price × 100

Purchase price includes entry load. Exit price is NAV less exit load.

Sharpe ratio

Sharpe = (Rp − Rf) ÷ σp

σp is the standard deviation of the fund's returns. Higher is better. Measures reward per unit of total risk.

Treynor ratio

Treynor = (Rp − Rf) ÷ βp

Uses beta. Reward per unit of systematic risk. Higher is better. Needs a positive beta to rank sensibly.

Jensen alpha

α = Rp − [Rf + βp × (Rm − Rf)]

Positive alpha means superior performance after adjusting for beta. It is in percentage points, not a ratio.

Required return (CAPM)

Required return = Rf + β × (Rm − Rf)

The benchmark return used inside Jensen alpha.

Fama net selectivity

Net selectivity = Rp − [Rf + (σp ÷ σm) × (Rm − Rf)]

Like Jensen alpha but the benchmark uses total risk (σp ÷ σm) instead of beta.

Information ratio

IR = (Rp − Rb) ÷ Tracking error

Rb is the benchmark return. Tracking error is the standard deviation of (Rp − Rb).

Fund return for a period

Rp = (NAV end − NAV start + Distributions) ÷ NAV start

Add dividends or distributions paid in the period. Use the same period for Rf and Rm.

Units bought in SIP

Units = Instalment amount ÷ NAV (or ÷ purchase price if entry load applies)

Use the NAV of the date of each instalment. Fractional units are allowed unless the question says otherwise.

Average cost per unit

Average cost = Total amount invested ÷ Total units acquired

This is the harmonic mean of NAVs when instalments are equal. Do not use the simple average of NAVs.

Closing value of holding

Value = Total units × Closing NAV (less exit load if redeemed)

Use the repurchase price if the question asks for the amount realised on redemption.

Absolute return

Return % = (Closing value + Withdrawals or dividends received − Amount invested) ÷ Amount invested × 100

Include all cash taken out earlier, such as SWP withdrawals.

Annualised return (single investment)

Annual return = (Closing value ÷ Opening value)^(1/n) − 1, n in years

For SIP with many instalments, a simple division is not accurate. Use it only if the question asks for an approximate or absolute figure.

Units redeemed in SWP

Units sold = Withdrawal amount ÷ NAV (or ÷ repurchase price if exit load applies)

Balance units = Opening units − Units sold.

Entry and exit price

Sale price = NAV × (1 + entry load %); Repurchase price = NAV × (1 − exit load %)

Apply the load the question states. Do not assume a load if none is given.

Quick revision

• NAV per unit = (Market value of investments + Other assets − Liabilities) ÷ Units outstanding.
• Use net assets after deducting accrued expenses and fees payable before dividing by units.
• Entry load raises the sale price: Sale price = NAV ÷ (1 − entry load %) only when load is stated on the price; if stated on NAV, Sale price = NAV × (1 + load %). Read the question wording.
• Exit load lowers the repurchase price: Repurchase price = NAV × (1 − exit load %).
• Total return = (Closing NAV − Opening NAV + Distributions) ÷ Opening NAV.
• Sharpe ratio = (Fund return − Risk-free rate) ÷ Standard deviation of the fund.
• Treynor ratio = (Fund return − Risk-free rate) ÷ Beta of the fund.
• Jensen's alpha = Fund return − [Risk-free rate + Beta × (Market return − Risk-free rate)].
• A higher Sharpe or Treynor ratio is better; a positive alpha means the fund beat what its beta required.
• Sharpe uses total risk and suits a standalone investment; Treynor uses systematic risk and suits a well-diversified portfolio.
• In SIP, a fixed amount buys more units when NAV is low and fewer when NAV is high.
• Units bought = Amount invested ÷ NAV on that date; units redeemed = Amount withdrawn ÷ NAV on that date.

Common mistakes

• Saying the AMC holds the assets of the scheme. Fix: Remember that the trust holds the assets for unit holders, and the AMC only manages them under trustee oversight.
• Treating the sponsor as the fund manager. Fix: The sponsor only sets up the fund and the trust. The AMC does the investing.
• Using cost price of investments instead of market value Fix: Always value the portfolio at market price on the valuation date. Use cost only for gain or return calculations.
• Forgetting to deduct accrued or unpaid expenses Fix: Treat every expense payable on the valuation date as a liability and deduct it before dividing by units.
• Applying the load to the wrong base, for example using NAV ÷ (1 − load) when the load is on NAV. Fix: Underline the phrase that states the base. If it says nothing, treat the load as a percentage of NAV.
• Adding exit load to NAV, or subtracting entry load from it. Fix: Remember the order: entry load adds, exit load subtracts. Sale price ≥ NAV ≥ repurchase price.
• Applying the dividend percentage to NAV instead of face value. Fix: A dividend of 10% on a ₹10 face value unit is ₹1 per unit. When the distribution is given as a percentage, apply it to face value. When it is given in rupees per unit, use that figure directly.
• Ignoring entry load in the cost base. Fix: If you paid the offer price, use it as the cost. Read the question for 'invested' amounts and loads.
• Dividing Rp by σ or β without subtracting Rf. Fix: Always write (Rp − Rf) first as its own column before dividing.
• Using beta in Sharpe or standard deviation in Treynor. Fix: Remember: Sharpe goes with total risk (σ); Treynor goes with Treynor's T for the 'Trend' of the market, that is beta.

Exam tips

• Draw a small box diagram of Sponsor, Trust and AMC in theory answers. It earns presentation marks and saves words.
• In case MCQs, look for the investor's objective, risk appetite and liquidity need before choosing the scheme type.
• For differences, always give 4 to 5 points in a table-like list rather than long paragraphs.
• Link the scheme choice to the facts given. A generic list of features scores less than a reasoned recommendation.
• Keep ETF, index fund and fund of funds separate. Examiners test this distinction.
• Write the NAV statement in three blocks: investments at market value, other assets, liabilities. It makes the working easy to follow and earns step marks even if one figure is wrong.
• In case-scenario MCQs, check each number for whether it is a market price, cost, or face value. Only market price goes into NAV.
• If units were issued or redeemed during the period, recompute units outstanding before dividing. This is a frequent trap.