CMA Final · Strategic Financial Management

Mutual Funds: formula sheet

Full chapter guide

Key formulas

Three-tier structure: Sponsor → Trust (trustees) → AMC; Sponsor creates the trust; trustees hold assets for unit holders; AMC is appointed by trustees to manage schemes.
Net Asset Value per unit: NAV = (Market value of assets − Liabilities) ÷ Number of units outstanding; Used to price units. Detailed calculations are in the NAV topic.
Investor's return from a unit: Return = (Closing NAV − Opening NAV + Distributions) ÷ Opening NAV; Simple one-period return. Distributions are dividends or income paid out in the period.
Role split: Investment decisions: AMC | Oversight: Trustees | Safekeeping: Custodian | Records: Registrar; Exam questions often ask who does what. Keep these separate.
Net Asset Value (NAV) per unit: NAV = (Market value of fund's investments + Other assets − Liabilities) ÷ Number of units outstanding; Open-ended schemes transact at NAV-linked prices. ETFs trade at market price, which may be above or below NAV.
Tracking error (concept): Tracking error = standard deviation of (Fund return − Index return); Lower tracking error means the passive fund follows its index more closely.
Structure rule: Open-ended: continuous entry and exit | Close-ended: fixed tenure, exit on exchange or at maturity | Interval: entry and exit only at set intervals; Use this one-line rule to answer difference questions.
Passive fund rule: Index fund: bought from AMC at NAV | ETF: traded on exchange at market price; Both track an index; the difference is how you buy and sell.
Net assets: Net assets = Market value of investments + Cash and bank + Accrued income receivable − Liabilities and accrued expenses; Use market value on the valuation date, not cost. Include only dues that are payable.
NAV per unit: NAV per unit = Net assets ÷ Units outstanding; Use the unit count at the same date as the net assets.
Units issued at NAV: New units = Amount received ÷ NAV per unit; NAV stays unchanged immediately after issue. Net assets and units both rise.
Units redeemed at NAV: Units redeemed = Amount paid ÷ NAV per unit; Net assets fall by the payout and units fall by the units cancelled. NAV is unchanged if there is no load.
NAV after a dividend payout: NAV after dividend = (Net assets − Total dividend paid) ÷ Units outstanding; Total dividend = dividend per unit × units. NAV falls by the dividend per unit.
Change in net assets over a period: Closing net assets = Opening net assets + Gain in market value + Income received − Expenses − Dividend paid ± Net unit sales; A quick way to roll NAV forward when the full portfolio is not given.
Sale price (with entry load): Sale price = NAV × (1 + entry load %); Price the investor pays per unit. If there is no entry load, sale price = NAV.
Repurchase price (with exit load): Repurchase price = NAV × (1 − exit load %); Price the investor receives per unit. If there is no exit load, repurchase price = NAV.
NAV from sale price: NAV = Sale price ÷ (1 + entry load %); Use when the question gives the sale price and asks for NAV.
NAV from repurchase price: NAV = Repurchase price ÷ (1 − exit load %); Use when the repurchase price is given.
NAV per unit: NAV = (Market value of investments + other assets − liabilities) ÷ Units outstanding; Liabilities include accrued expenses. Expenses charged under the expense ratio reduce net assets.
Expense ratio: Expense ratio = Annual scheme expenses ÷ Average net assets × 100; Ongoing cost, already inside NAV. Not a load.
Single-period return: Return % = [(NAV₁ − NAV₀) + Dividend + Capital gain distribution] ÷ NAV₀ × 100; NAV₀ is the opening NAV. Use the distributions actually received in the period.
Return with reinvestment: Return % = [(Units after reinvestment × NAV₁) − (Units at start × NAV₀)] ÷ (Units at start × NAV₀) × 100; Use when dividends are reinvested at a given NAV and extra units are allotted.
Annualised return: Annualised return = (1 + r)^(12 ÷ months) − 1, or simple: r × (12 ÷ months); Use the method the question asks for. If not stated, say which one you used.
Sharpe ratio: Sharpe = (Rp − Rf) ÷ σp; σp is the standard deviation of fund returns. Measures excess return per unit of total risk.
Treynor ratio: Treynor = (Rp − Rf) ÷ βp; Measures excess return per unit of systematic risk.
Jensen's alpha: α = Rp − [Rf + βp × (Rm − Rf)]; Positive alpha means the fund beat the CAPM-required return.
Units allotted per instalment: Units = Amount invested ÷ NAV (or purchase price) on that date; If an entry load applies, divide by the purchase price (NAV + load), not NAV. Use the number of decimals given in the question.
Average cost per unit: Average cost per unit = Total amount invested ÷ Total units acquired; This is the harmonic mean of NAVs when equal amounts are invested each time.
Simple average NAV: Simple average NAV = Σ NAV ÷ n; Use only for comparison. It is not your cost. The average cost is lower unless all NAVs are equal.
Value of holding: Value = Total units × Current NAV; Use the NAV on the valuation date. Use redemption price if exit load applies.
Return on SIP (absolute): Absolute return = (Value of holding − Total invested) ÷ Total invested × 100; This is not annualised. Because instalments are invested for different periods, do not treat it as an annual rate.
Ex-dividend NAV: NAV after payout = NAV before payout − Dividend per unit; Needed for the dividend option and reinvestment problems.
Units remaining after SWP: Units left = Units held − Σ (Amount withdrawn ÷ NAV on withdrawal date); Each withdrawal redeems units at that day's NAV (less exit load, if any).

Quick revision

A mutual fund pools investor money and invests it under a professional manager; SEBI regulates the industry.
Structure: sponsor sets up a trust, trustees oversee it, and an asset management company manages the schemes.
Open-ended schemes allow entry and exit at any time; close-ended schemes have a fixed maturity.
Equity funds seek growth with higher risk; debt funds seek income with lower risk; hybrid funds mix both.
NAV per unit = (Market value of investments + other assets − liabilities) ÷ units outstanding.
Sale price = NAV + entry load; repurchase price = NAV − exit load.
Load percentages are applied to NAV unless the question says otherwise.
Return = (Closing NAV − Opening NAV + distributions) ÷ Opening NAV.
In a SIP, units bought = instalment ÷ NAV on that date; total units × final NAV gives the value.
Average cost per unit in a SIP = total amount invested ÷ total units held.
Always state the recommendation at the end of a comparison question.
Check whether the question asks for annual or period return before you finish.

Common mistakes

Saying the sponsor manages the investments. Fix: The sponsor only promotes the fund and sets up the trust. The AMC manages the schemes.
Treating the AMC as the owner of the fund's assets. Fix: The assets are held by the trust for unit holders. The AMC is only the manager.
Saying close-ended units cannot be sold at all before maturity. Fix: Write that units are not redeemed by the fund before maturity but can be sold on a stock exchange, often at a discount to NAV.
Treating an ETF and an index fund as identical. Fix: State the differences: ETF trades on an exchange at market price all day and needs a demat account; index fund is bought from the AMC at end-of-day NAV.
Using cost of investments instead of market value Fix: Read the question for the market or current price. Value every holding at that price on the valuation date.
Forgetting to deduct accrued expenses or fees payable Fix: Before dividing, scan the whole question for expenses, fees and dues. Deduct every unpaid one.
Subtracting the load percentage when working back to NAV from the sale price. Fix: Divide: NAV = sale price ÷ (1 + load). Check by multiplying back.
Adding the entry load to the repurchase price or deducting the exit load from the sale price. Fix: Entry load goes with buying (sale price). Exit load goes with redeeming (repurchase price).
Ignoring the dividend and using only the NAV change Fix: Always add dividends and capital gain distributions to the NAV change before dividing.
Dividing by closing NAV instead of opening NAV Fix: The base for return is the amount invested at the start, the opening NAV.

Exam tips

Learn the three tiers as a chain with one function each. Examiners test roles directly in MCQs.
In written answers, include SEBI's role. Many students stop after sponsor, trustees and AMC.
Use the case details in application questions: the investor's amount, time, risk appetite.
Give a balanced view when asked for advantages and limitations. A one-sided list loses marks.
Keep structure theory short and move to NAV, load and return calculations, which carry more numerical marks.
For difference questions, always write a two-column comparison with at least five bases. Add an example for each side.
In MCQs, watch the keywords: 'exchange traded', 'NFO only', 'lock-in', 'tracks an index'. Each points to a specific scheme type.
In case questions, quote the investor's horizon and risk appetite in your answer. That is where marks are given.