⚡ Rapid Revision Sheet
Mutual Funds - Quick Summary & Formula Vault
High-yield summary covering NAV mechanics, Load adjustments, Expense Ratio thresholds, Sharpe/Treynor/Jensen evaluations, and Constant Ratio rebalancing.
1. Essential Formula Cheat Sheet
(a) Net Asset Value (NAV):
$$\mathbf{NAV = \frac{\text{Market Value of Investments} + \text{Receivables} + \text{Cash/Liquid Balances} - \text{Accrued Liabilities}}{\text{Total Number of Units Outstanding}}}$$
(b) Front-End & Exit Loads:
$$\text{Public Offer Price (POP)} = \text{NAV} \times (1 + \text{Front-End Load \%}) \quad \text{or} \quad \frac{\text{NAV}}{1 - \text{Front-End Load \%}}$$
$$\text{Repurchase Price (Redemption)} = \text{NAV} \times (1 - \text{Exit Load \%}) \quad \text{or} \quad \frac{\text{NAV}}{1 + \text{Back-End Load \%}}$$
(c) Holding Period Return & Yield:
$$R = \frac{(\text{NAV}_1 - \text{NAV}_0) + \text{Dividend} + \text{Capital Gain Distribution}}{\text{NAV}_0} \times 100$$
$$\text{Simple Annualized Return} = R \times \frac{12}{M} \quad \text{or} \quad R \times \frac{365}{\text{Days}}$$
$$\text{Effective Annualized Yield (EAY)} = (1 + r_{period})^N - 1$$
(d) Risk-Adjusted Performance Ratios:
$$\text{Sharpe Ratio (Total Risk)} = \frac{R_p - R_f}{\sigma_p}$$
$$\text{Treynor Ratio (Systematic Risk)} = \frac{R_p - R_f}{\beta_p}$$
$$\text{Jensen's Alpha (Abnormal Gain)} = R_p - [R_f + \beta_p(R_m - R_f)]$$
(e) Fama's Performance Attribution:
$$\text{Total Excess Return } (R_p - R_f) = \text{Risk Premium } [\beta_p(R_m - R_f)] + \text{Selectivity}$$
$$\text{Diversification Penalty} = \left(\frac{\sigma_p}{\sigma_m} - \beta_p
ight)(R_m - R_f)$$
$$\mathbf{\text{Net Selectivity} = \text{Gross Selectivity} - \text{Diversification Penalty} = (R_p - R_f) - \frac{\sigma_p}{\sigma_m}(R_m - R_f)}$$
2. Critical Conceptual Comparisons for Exam
| Parameter |
Open-Ended Fund |
Close-Ended Fund |
Exchange Traded Fund (ETF) |
| Subscription & Exit |
Continuous from/to AMC daily |
During NFO; later only via Stock Exchange |
Real-time intraday trading on Stock Exchange |
| Pricing |
End-of-day NAV |
Market price (often at a discount to NAV) |
Continuous market price aligned via arbitrage |
| Unit Capitalization |
Variable (expands/contracts) |
Fixed throughout tenure |
Flexible via Creation Baskets |
| Expense Ratio |
Moderate to High (1.5% - 2.25%) |
Moderate (1.0% - 1.75%) |
Very Low (0.05% - 0.50%) |
3. Master Exam Traps & Scoring Pointers
Dividend Reinvestment Units: When dividends are reinvested, always compute additional units as $\frac{\text{Total Dividend Amount}}{\text{Ex-Dividend NAV}}$. Add these to existing units for all subsequent dividend and redemption calculations.
Bonus Units vs. Dividend Equalization: When bonus units are issued (e.g. 1:5), total units increase by 20%, but the cost of bonus units is ₹ Nil for capital gains computation.
High-Water Mark Provision (Hedge Funds): Performance incentive fees (e.g. 20%) are payable only on the net wealth created above the previous historical peak, never on value already rewarded.
Constant Ratio Plan: Always rebalance back to the 50:50 benchmark by selling appreciated equity units or buying depressed equity units. This method enforces 'Buy Low, Sell High' discipline automatically.