Glossary

An option traded on its own expiry day ("zero days to expiry"). Its price is almost all gamma and theta, so it behaves like a lottery ticket on the day's move. SEBI's FY26 study (released 20 Aug 2026) reports that 59% of index-option turnover was in contracts on their expiry day.

The part of a security's return on an event day not explained by a model of normal returns, usually the market model: $AR_{i\tau} = R_{i\tau} - \hat\alpha_i - \hat\beta_i R_{m\tau}$, with $\hat\alpha_i, \hat\beta_i$ estimated on a pre-event estimation window. Its variance includes the estimation error of the fitted parameters.

The expense ratio implicitly paid for the part of a fund that differs from its index: $[c - (1 - AS)c_I]/AS$ for fund cost $c$, active share $AS$ and index cost $c_I$ (Miller 2007; M06B (6B.33)).

Half the sum of absolute differences between a fund's and its benchmark's weights, $\tfrac12\sum_i|w_{p,i} - w_{b,i}|$: 0 for the index, 1 for a portfolio with no common holdings (Cremers and Petajisto 2009).

The loss a liquidity provider suffers by trading with counterparties who know more than she does. In the Glosten–Milgrom model the bid–ask spread exists exactly to cover this expected loss to informed traders; a resting limit order is exposed to it whenever news arrives before it can be cancelled.

An order entered with a broker outside market hours and sent to the exchange at the next session's open. It is a broker convenience, not a separate exchange order type.

An optimal-execution model in which a trader liquidates $X$ shares over a horizon $T$, trading off expected impact cost (permanent and temporary impact, linear in trading rate) against the variance of price risk with risk aversion $\lambda$. The optimal holdings follow $x(t) = X\sinh(\kappa(T-t))/\sinh(\kappa T)$ with $\kappa = \sqrt{\lambda\sigma^2/\eta}$: more risk aversion front-loads the trading.

The company that manages a mutual fund's schemes under an agreement with the trustee and earns the management fee. Its revenue is roughly AUM × fee yield, its costs are mostly fixed, so its profits move more than the market (M06B Proposition 6B.5.1).

An option that may be exercised at any time up to expiry. An American call on a non-dividend-paying stock is never optimally exercised early, so it is worth the same as the European call; American puts can be worth more. NSE index and stock options are European.

A qualified institutional buyer allotted shares in an Indian IPO before the issue opens to the public, at a price within the band, subject to a lock-in. The anchor lock-in expiries (30 and 90 days after allotment) are dated supply events for the stock.

A VWAP whose sums start at a chosen event (an earnings day, a breakout bar, a crash low) rather than at the session open. On daily bars it is computed with the typical price $(H+L+C)/3$ as a proxy for each day's trade prices.

A life insurer's measure of new business: regular first-year premiums plus one tenth of single premiums written in the period, so that regular- and single-premium products are comparable.

A fund that buys stocks and sells their futures, earning the futures basis (the cash-and-carry return of M07 · 7.1). Its risk resembles a money-market fund's, but it is taxed as equity-oriented.

An autoregressive moving-average model, ARMA($p,q$): $X_t = c + \sum_{i=1}^p \phi_i X_{t-i} + \varepsilon_t + \sum_{j=1}^q \theta_j\varepsilon_{t-j}$ with white-noise $\varepsilon_t$. It is the baseline linear model for forecasting a stationary series; the squared shocks of a GARCH(1,1) follow an ARMA(1,1).

The Additional Surveillance Measure and Graded Surveillance Measure frameworks under which Indian exchanges place stocks with unusual price, volume or fundamental characteristics into stages carrying tighter price bands, higher margins or trade-for-trade settlement. The lists change frequently; check the exchange's current list. Not covered in detail in the notes.

An option whose strike is approximately equal to the current price of the underlying, $K \approx S$ (desks often use the forward, $K \approx F$). ATM options have the highest time value, vega, and (near expiry) gamma; ATM gamma grows like $1/(\sigma S\sqrt{2\pi\tau})$ as $\tau \to 0$.

A test of the null of a unit root, based on the $t$-statistic of $\gamma$ in $\Delta y_t = \gamma y_{t-1} + \sum_j \delta_j\Delta y_{t-j} + e_t$ (with optional constant and trend). Under the null the statistic has a non-standard Dickey–Fuller distribution, so Student-$t$ critical values are wrong; with a constant the 5% critical value is about $-2.86$.

A model $X_t = c + \sum_{i=1}^p \phi_i X_{t-i} + \varepsilon_t$. An AR(1) is stationary iff $|\phi| < 1$, with autocorrelations $\rho_k = \phi^k$, forecast $\mathbb E_t X_{t+h} = \mu + \phi^h(X_t - \mu)$ and half-life $\ln 0.5/\ln\phi$; an AR($p$) is stationary iff the roots of its characteristic polynomial lie outside the unit circle.

A moving average (simple or exponential) over $n$ bars of the true range $\mathrm{TR} = \max(H, C_{-1}) - \min(L, C_{-1})$, the bar's range extended to include any gap from the previous close; it is a volatility estimate in price units. Under Brownian motion $\hat\sigma \approx \mathrm{ATR}/(1.596\,S)$ per bar, so stops set in ATR multiples have roughly the same stop-out probability across stocks.

A simulation of a trading rule on historical data, producing the returns the rule would have earned after costs. A valid backtest uses only information available at each decision time (no look-ahead), point-in-time universes (no survivorship bias), realistic costs and fills, and reports how many variants were tried.

A futures curve whose prices fall with maturity, so that near futures (and spot) are above deferred futures; in the cost-of-carry relation the convenience yield exceeds interest plus storage. M07 states it for one contract as $F < S$ (when $q > r$); M10 defines it by the slope of the curve, $F_t(T)$ decreasing in $T$. A long who rolls in backwardation earns a positive roll yield.

A procedure that estimates the number and dates of multiple structural breaks in a regression by minimising the sum of squared residuals over all admissible partitions, with sup-F type tests for the number of breaks. It is the tool when break dates are unknown and there may be more than one.

The Nifty Bank index of the most liquid large Indian bank stocks, maintained by NSE Indices, and the underlying of NSE's Bank Nifty futures and options. Lot size 30 and no weekly expiry, as of the 5 Nov 2026 NSE F&O bhavcopy.

The capped part of a mutual fund's expenses under the 2026 Regulations: management fee and recurring expenses including distribution commission, excluding statutory levies, brokerage up to the permitted limit and transaction costs. Caps run from 2.10% (first ₹500 cr of an equity scheme) down to 0.95%; 0.90% for index funds and ETFs (M06B Table 6B.1).

The unconditional frequency of an outcome in a reference class, used as the prior before case-specific evidence. For an individual Indian F&O trader, SEBI's studies give a base rate of loss close to 0.9; in forecasting, always forecasting the base rate is perfectly calibrated but has no resolution.

The futures price minus the spot price, $b = F - S$ (the course's convention; Hull uses $S - F$). It is about $S(r-q)\tau$ for a financial future, positive in contango, and converges to zero at expiry; a hedger's effective price is the futures price locked in minus the basis at close-out.

One hundredth of a percentage point, $10^{-4}$. Trading costs, spreads, yields and rate changes are quoted in basis points: a ₹1 lakh intraday NSE round trip costs about 8.27 bp at the charges of 6 Nov 2026.

The risk that the basis at the time a hedge is closed differs from what was expected, so that a futures hedge does not lock in a known price. It arises when the hedge is lifted before expiry, or when the hedged asset differs from the futures' underlying (cross-hedging).

Revising probabilities on new evidence by Bayes' rule, $P(s\mid n) \propto P(n\mid s)P(s)$. In odds form, posterior odds = prior odds × likelihood ratio, so log-odds add across independent pieces of evidence; the course uses it to update scenario probabilities and forecast-journal entries.

A probit-based score built from eight ratios of two consecutive years of financial statements (receivables, gross margin, asset quality, sales growth, depreciation, SG&A, accruals, leverage), designed to flag earnings manipulation. The usual flag is $M > -1.78$; it is a screen for further forensic work, not proof.

A multiple-testing rule that sorts $m$ $p$-values and rejects the hypotheses with the $k$ smallest, where $k$ is the largest index with $p_{(k)} \le k\alpha/m$. Under independence it controls the false discovery rate at $m_0\alpha/m \le \alpha$; it is less conservative than Bonferroni.

A model in which skilled managers face decreasing returns to scale and investors supply money until expected net alpha is zero. Flows chase past performance, net returns do not persist, and the skill is paid to the manager as fees (Berk and Green 2004; M06B Proposition 6B.7.1).

The slope of an asset's return on the market's return, $\beta_i = \operatorname{Cov}(R_i, R_M)/\operatorname{Var}(R_M)$. In the CAPM it sets the asset's risk premium; in hedging it converts a portfolio's value into a number of index futures; in event studies it is a parameter of the market model.

Changing a portfolio's market beta from $\beta$ to a target $\beta^\star$ with index futures: trade $N = (\beta^\star - \beta)V_P/V_F$ contracts, where $V_P$ is the portfolio value and $V_F$ the value of one futures contract. A negative $N$ means selling futures; $\beta^\star = 0$ is a full hedge.

A factor that is long low-beta stocks and short high-beta stocks, each leg scaled to beta one, so the portfolio has zero beta: $(r_L - r_f)/\beta_L - (r_H - r_f)/\beta_H$. It exploits the empirical flatness of the security market line relative to the CAPM.

NSE's end-of-day file of prices, volumes and open interest for every traded contract. The F&O bhavcopy (UDiFF format) has one row per contract with fields such as ClsPric, SttlmPric, OpnIntrst (in units) and TtlTradgVol (in contracts) and NewBrdLotQty (lot size). Bhavcopy prices are not adjusted for corporate actions.

The difference between the best ask (lowest resting sell price) and the best bid (highest resting buy price); their average is the mid. A trader who buys at the ask and sells at the bid pays the spread on a round trip; microstructure models attribute it to order-processing, inventory and adverse-selection costs.

A discrete model in which the underlying moves up by $u$ or down by $d$ each step. Any claim is replicated by $\Delta = (V_u - V_d)/(S(u-d))$ shares plus cash, giving risk-neutral probability $p = (e^{(r-q)\Delta t} - d)/(u-d)$. The Cox–Ross–Rubinstein tree sets $u = e^{\sigma\sqrt{\Delta t}}$, $d = 1/u$, prices American options by backward induction, and converges to Black–Scholes with error $O(1/n)$.

Black's (1976) formula for European options on a futures or forward price $F$: $c = e^{-r\tau}[F N(d_1) - K N(d_2)]$ with $d_{1,2} = [\ln(F/K) \pm \tfrac12\sigma^2\tau]/(\sigma\sqrt\tau)$. The course prices Nifty options off the Nifty future and MCX options on futures with it, avoiding a separate dividend or carry estimate.

The model in which the underlying follows geometric Brownian motion with constant volatility $\sigma$ and the rate $r$ and yield $q$ are constant. Delta hedging gives the PDE $V_t + \tfrac12\sigma^2S^2V_{SS} + (r-q)SV_S - rV = 0$, solved by $c = Se^{-q\tau}N(d_1) - Ke^{-r\tau}N(d_2)$, $d_{1,2} = [\ln(S/K) + (r - q \pm \tfrac12\sigma^2)\tau]/(\sigma\sqrt\tau)$.

A large trade executed in a separate exchange window rather than in the normal order book. Under SEBI's circular of 8 Oct 2025 (effective 7 Dec 2025) the minimum order is ₹25 crore, with a morning window 08:45–09:00 and an afternoon window 14:05–14:20, a ±3% band around a reference price and compulsory delivery.

A multiple-testing rule that rejects hypothesis $i$ only if $p_i \le \alpha/m$ when $m$ hypotheses are tested. It controls the family-wise error rate at $\alpha$ under any dependence, at the cost of power; at $\alpha = 5\%$ the required $|t|$ rises from 1.96 for one test to about 3.48 for 100.

An issue of $a$ new fully paid shares for every $b$ held, capitalised from reserves, with no cash changing hands. The theoretical ex-price is $P_c\,b/(a+b)$; an index divisor does not change, and a price series must be adjusted by the factor $b/(a+b)$ before the ex-date.

The IPO pricing process in which investors bid quantities at prices within a published band and the issue price is set from the resulting demand. In India the book is split by investor category (QIB, non-institutional, retail) with prescribed allocation shares.

Order inflow divided by revenue recognised in the period. By the order-book identity (M06A Proposition 6A.21), the order book grows if and only if book-to-bill exceeds 1; it is the leading indicator for capital-goods and defence companies.

Measures of how many stocks participate in a market move, such as the number of advancing minus declining stocks, the advance–decline ratio, or the share of stocks above a moving average. In a one-factor model the expected advancing share is $\frac1N\sum_i\Phi(\beta_i f/s_i)$, so breadth largely restates the index move.

The difference between a nominal bond yield and the real yield on an inflation-indexed bond of the same maturity, $b = i - r^{\text{real}}$. By the Fisher relation it approximates expected inflation plus an inflation risk premium.

The win rate at which a system with average win $W$ (in units of the initial risk $R$), average loss $1R$ and round-trip cost $c$ (in $R$) has zero expectancy: $p^* = (1+c)/(1+W)$.

A close (or trade) above the highest high, or below the lowest low, of a look-back window, used as an entry signal. As a hypothesis it says that returns after such a close are higher than unconditional returns; it must be tested against a random-walk null and after costs.

The mean squared error of probability forecasts of binary events, $\mathrm{BS} = \frac1N\sum_i (p_i - y_i)^2$, between 0 (perfect) and 1. It is strictly proper, bounded, and decomposes (Murphy) into reliability minus resolution plus uncertainty.

A continuous-time process $W_t$ with $W_0 = 0$, continuous paths and independent Gaussian increments $W_t - W_s \sim N(0, t-s)$. Arithmetic Brownian motion with drift models log-wealth in M03 and log-price for barrier (stop and target) problems in M04A; geometric Brownian motion models prices.

India's older national stock exchange (formerly the Bombay Stock Exchange), owner of the Sensex. Its clearing corporation is the Indian Clearing Corporation Ltd (ICCL). BSE's Sensex weekly options expire on Thursdays (since 1 Sep 2025).

A trade or trades by one client in one stock on one day totalling more than 0.5% of the company's listed shares, executed in the normal market. The exchange publishes the client name, quantity and price after the close; the reason for the trade is not disclosed.

A company's repurchase of its own shares, either by a tender offer (shareholders tender shares at a fixed price, accepted pro rata by an acceptance ratio) or through open-market purchases on the exchange over a period. It is EPS-accretive iff the earnings yield at the buyback price exceeds the after-tax return on the cash used, and it transfers value to remaining holders iff the price paid is below intrinsic value per share. India's buyback tax regime changed in Oct 2024 and again from Apr 2026.

A position long one expiry and short another on the same underlying, in futures (a bet on the change in the far–near price difference, i.e. the carry) or in options (mainly a bet on the term structure of implied volatility and on time decay).

A forecaster is calibrated if, among all occasions on which she forecasts probability $f$, the event occurs with frequency $f$: $\Pr(Y = 1 \mid p = f) = f$. Calibration is the reliability term of the Murphy decomposition; it is necessary but cheap, since always forecasting the base rate is calibrated.

A mechanism that collects orders over a period and executes them together at one price, chosen to maximise executable volume $\min\{D(p), S(p)\}$, then to minimise imbalance, then to stay closest to a reference price. NSE and BSE set the open (pre-open session) and, since 3 Aug 2026, the official close (closing auction session) this way.

The right, not the obligation, to buy the underlying at the strike $K$ on (European) or before (American) expiry. Its payoff at expiry is $(S_T - K)^+$; the buyer pays a premium and can lose at most that premium.

The Capital Asset Pricing Model: in equilibrium each asset's expected excess return is proportional to its market beta, $\mu_i - r_f = \beta_i(\mu_M - r_f)$. The course derives it from mean–variance optimisation and uses it to build a cost of equity.

The return from holding a position if prices do not change. For futures it is the net cost of carry ($r - q$, or $r + u - y$ for commodities) embedded in the basis; for currencies it is the interest differential $i - i^*$, and the carry-trade excess return is $(i - i^*) - \Delta s$.

Current and savings account deposits as a share of a bank's total deposits. These deposits pay little or no interest, so a high CASA ratio means cheap funding and a higher net interest margin; NBFCs have no CASA.

Buying the underlying with borrowed money and selling it forward, locking in $F_0 - S_0e^{(r-q)T}$; the reverse cash-and-carry sells the underlying and buys forward. Together they force $F_0 = S_0e^{(r-q)T}$ for investment assets; for consumption commodities only the upper bound $F_0 \le S_0e^{(r+u)T}$ is enforceable.

India's two securities depositories, Central Depository Services (India) Ltd and National Securities Depository Ltd. They hold securities in dematerialised form and move them between demat accounts on settlement; investors access them through a depository participant.

The rate of change of an option's delta with the passage of time, $\partial\Delta/\partial t$ (equivalently $-\partial\Theta/\partial S$ up to sign convention), also called delta decay. It matters for overnight and expiry-day hedging, when delta drifts toward 0 or 1 even if spot does not move. Not named in the notes; it is one of the cross terms of the Taylor expansion of option value.

An $F$-test of whether regression coefficients differ before and after a known break date: $F = [(\mathrm{SSR}_R - \mathrm{SSR}_1 - \mathrm{SSR}_2)/k]/[(\mathrm{SSR}_1 + \mathrm{SSR}_2)/(n-2k)]$. Choosing the date from the data invalidates its critical values; use a sup-F test for unknown dates.

A limit on how far a stock's price may move in a day from the previous close; orders outside the band are rejected. Stocks without derivatives have fixed bands of 2%, 5%, 10% or 20%; F&O stocks have dynamic bands (initially 10%) that the exchange can widen in steps.

The central counterparty that becomes buyer to every seller and seller to every buyer through novation, nets obligations, collects margins and guarantees settlement, backed by a settlement guarantee fund. NSE's is NSE Clearing Ltd; BSE's is ICCL.

The single-price call auction that sets the official closing price of NSE and BSE stocks, live since 3 Aug 2026 for stocks with derivatives. From 7 Dec 2026 it runs 15:30–15:40 with a random end of order entry between 15:38 and 15:40, followed by a post-close session at the closing price.

The official end-of-day price of a security. Before Aug 2026 NSE's close was the VWAP of trades between 15:00 and 15:30; since 3 Aug 2026 (F&O stocks) it is set by the closing auction, so NSE and BSE can publish different closes. Derivative expiry settlement uses a separate last-30-minute VWAP.

A broker product code for delivery-based equity trades: shares bought under CNC are paid for in full and delivered into the demat account at settlement. It is a broker margin category, not an exchange order type.

Mukherjea's (Marcellus) screen for consistent compounders: revenue growth of at least 10% and ROCE of at least 15% in every one of the last 10 years (for lenders, loan-book growth and ROE of at least 15%), with the portfolio held untouched for 10 years. It tests every year, not the CAGR.

A risk measure $\rho$ on losses satisfying monotonicity, translation invariance ($\rho(L + c) = \rho(L) + c$), positive homogeneity and subadditivity ($\rho(L_1 + L_2) \le \rho(L_1) + \rho(L_2)$). Expected Shortfall is coherent; Value-at-Risk is not, because it can fail subadditivity.

Two or more integrated (unit-root) series are cointegrated if some linear combination $\beta'y_t$ of them is stationary. The combination is the long-run equilibrium (the spread of a pair), and by the Granger representation theorem deviations from it are corrected through an error-correction model.

A long position hedged with a bought put below the price and a sold call above it, often at near-zero net premium: losses below the put strike and gains above the call strike are given up. M14 · 14.19 compares it with a protective put, a put spread and short futures on a stock portfolio.

A tax on non-agricultural commodity derivatives traded on an exchange, levied under Chapter VII of the Finance Act, 2013: 0.01% of the sale value of futures and 0.05% of the premium on the sale of options (as of Nov 2026). It is the commodity counterpart of STT; agricultural commodities are exempt.

A futures curve whose prices rise with maturity, with deferred futures above near futures and spot; in the cost-of-carry relation interest plus storage exceed the convenience yield. M07 states it for one contract as $F > S$ (when $r > q$); M10 by the curve slope, $F_t(T)$ increasing in $T$. A long who rolls in contango pays a negative roll yield.

The legal confirmation a broker issues for each day's executed trades, listing prices, quantities and every charge (brokerage, STT, exchange charges, SEBI fee, stamp duty, GST). It shows the statutory costs of a trade but not the market impact.

The implicit benefit, expressed as a continuous yield $y$, of holding the physical commodity rather than a futures contract: the ability to keep production running or meet unexpected demand. It enters $F_0 = S_0e^{(r+u-y)T}$, is implied by $y = r + u - \ln(F/S)/T$, and is high when inventories are low.

The property that a futures price approaches the spot price as expiry nears, so the basis goes to zero at expiry ($b_T = 0$), enforced by delivery or cash settlement against the spot. Convergence is only as good as the agreement between the futures settlement price and the cash price used.

The second-order sensitivity of a bond's price to its yield, $C = P^{-1}\,\partial^2P/\partial y^2$. With modified duration it gives $\Delta P/P \approx -D_{\text{mod}}\Delta y + \tfrac12 C\,\Delta y^2$; positive convexity means prices rise more for a yield fall than they fall for an equal yield rise.

The reduction in a strategy's return, or Sharpe ratio, caused by trading costs: net mean $\mu_n = \mu_g - c\cdot\mathrm{TO}$ for cost $c$ per unit of turnover $\mathrm{TO}$. For $N$ trades a year the Sharpe drag is $\sqrt N c/\sigma_t$, which is why short holding periods need much larger per-trade edges.

The net cost of holding the underlying until the delivery date: financing at $r$, plus storage $u$, minus income $q$ or convenience yield $y$. The cost-of-carry relation $F_0 = S_0e^{(r+u-y)T}$ (with $F_0 = S_0e^{(r-q)T}$ for financial assets) links futures to spot. Indian brokers also quote "cost of carry" as the annualised basis.

The return shareholders require, used to discount equity cash flows. The course builds an INR cost of equity as $k_e = (y_{\text{G-sec}} - \text{default spread}) + \beta(\text{ERP}_{\text{mature}} + \text{CRP})$ from Damodaran's India inputs (July 2026), or reads it from the Gordon model as $D_1/P_0 + g$.

A long position in the underlying combined with a short call. It earns the call premium and gives up upside above the strike; by put–call parity its payoff equals that of a short put plus cash, so it is a short-volatility position.

The no-arbitrage relation between spot and forward exchange rates and the two interest rates: $F = S(1 + r_dT)/(1 + r_fT)$. Borrowing in one currency, converting, lending in the other and hedging with a forward must earn nothing; bid–ask spreads turn the equality into a band.

The Consumer Price Index, a measure of the price of a fixed basket of consumer goods and services; its growth rate is headline retail inflation. In India it is the RBI's target variable: 4% with a band of 2–6% for Apr 2026–Mar 2031 (notified 25 Mar 2026, per the notes).

The gross margin of refining crude oil into products, measured from futures or spot prices. The 3-2-1 crack per barrel of crude is $(2P_{\text{gasoline}} + P_{\text{distillate}} - 3P_{\text{crude}})/3$; refiners' margins (GRM) and oil marketing companies' earnings move with it.

The block of ETF units (often tens of thousands) that the AMC issues or redeems, usually in exchange for the index basket plus a cash component. Only market makers and large investors deal in it; others trade units on the exchange.

A bank's provisions for loan losses over average assets (or loans) for a period. It is the most cyclical line in the bank ROA tree, $\text{ROA} = (\text{NIM} + \text{fees} - \text{opex} - \text{credit cost})(1-\tau)$.

The observed rise of correlations between assets in high-volatility periods, which removes diversification when it is most needed. Part of the rise is a conditioning artefact: selecting on high market variance mechanically raises measured correlation (the Forbes–Rigobon bias), so a genuine breakdown must be separated from it.

The share of deposits Indian banks must hold as unremunerated balances with the RBI: 3.00% as of 6 Nov 2026. A CRR cut releases reserves and acts like a rate cut at the short end without changing the repo rate. (In M08, CRR also abbreviates the Cox–Ross–Rubinstein binomial tree.)

The sum of a security's abnormal returns over an event window, $CAR_i = \sum_{\tau \in \text{window}} AR_{i\tau}$. Its variance includes estimation error; the standardised CAR is $t$-distributed under the null, and cross-sectional tests (J1, Patell, BMP) aggregate CARs across events.

The excess of a country's payments for imports of goods and services, net income and transfers over its receipts, which must be financed by capital inflows or reserves. India's CAD widens roughly one-for-one with the oil import bill; a CAD financed by portfolio flows makes the rupee vulnerable.

A test for parameter instability based on the cumulative sum of standardised recursive residuals, $W_r = \hat\sigma^{-1}\sum_{t \le r} w_t$; the null of stability is rejected when the path crosses bounds that widen linearly with $r$. It detects breaks without specifying their date.

The time (3 pm for most schemes) by which an application and, for purchases, the money must reach the scheme for that day's NAV to apply; later transactions get a later NAV. Forward pricing of this kind prevents investors from trading on known price moves (M06B · 6B.2).

A classification of macro regimes by the surprise in growth (rising or falling) and inflation (rising or falling): goldilocks, reflation, deflationary bust and stagflation, each with assets that tend to do well. Bridgewater's All Weather portfolio holds risk-balanced assets for all four; the mapping failed in 2022 and March 2026 when stocks and bonds fell together.

Finding apparently significant results by searching many rules, parameters or datasets and reporting the best, without accounting for the search. The relevant family is every rule that could have been tried; White's Reality Check, the deflated Sharpe ratio and PBO are the corrections.

Valuation as the present value of expected future cash flows: free cash flow to the firm discounted at WACC (then subtract net debt), or free cash flow to equity at the cost of equity. A two-stage DCF projects explicit cash flows for $N$ years and adds a Gordon terminal value $F_N(1+g_T)/(W - g_T)$.

The probabilistic Sharpe ratio evaluated against the Sharpe ratio expected from the best of $N$ skill-less trials, $\mathrm{DSR} = \mathrm{PSR}(S_0)$ with $S_0 \approx \sqrt V[(1-\gamma)\Phi^{-1}(1 - 1/N) + \gamma\Phi^{-1}(1 - 1/(Ne))]$. It is the probability that the selected strategy's true Sharpe exceeds what selection alone would produce.

Removal of a company's shares from an exchange. A voluntary delisting in India runs by reverse book building: public shareholders bid the prices at which they will sell, and the discovered price is where the acquirer's holding with shares tendered at or below it reaches 90% (SEBI Delisting Regulations 2021, as amended 25 Sep 2024).

For a stock and day, deliverable quantity divided by traded quantity, from NSE's full bhavcopy. Shares bought and sold by the same client on the same day net out and are not delivered, so it is mechanically higher where intraday trading is light; compare a stock with its own history.

The sensitivity of an option's value to the underlying price, $\Delta = \partial V/\partial S$: $e^{-q\tau}N(d_1)$ for a call and $-e^{-q\tau}N(-d_1)$ for a put under Black–Scholes. It is the hedge ratio in shares, and the position delta is the sum of signed leg deltas.

Holding $-\Delta$ units of the underlying against an option so the combined position is insensitive to small price moves, rebalanced as delta changes. A delta-hedged long option earns $\tfrac12\Gamma S^2(\sigma_r^2 - \sigma_i^2)\,dt$: it profits iff realised volatility exceeds the implied volatility it was bought at.

The second-order Taylor expansion of a book's value for scenario P&L: $\Delta V \approx \sum_i\Delta_i\Delta S_i + \tfrac12\sum_{ij}\Gamma_{ij}\Delta S_i\Delta S_j + \sum_k\mathcal V_k\Delta\sigma_k + \Theta\Delta t$. It understates losses on short options when the move goes toward the strike and overstates them far beyond it; full revaluation avoids both errors.

An account in which securities are held in dematerialised (electronic) form with a depository (NSDL or CDSL), opened through a depository participant. Shares bought on the exchange are credited to it at settlement (T+1).

The split of a listed company into two or more listed companies, with shareholders receiving $q$ shares of the resulting company for each parent share. Value conservation gives $P_{\text{cum}} = P_{\text{ex}} + qP_{\text{child}}$; the tax cost basis is apportioned by book value transferred, and the parent's ex-price is found in a special pre-open session.

An agent of a depository (NSDL or CDSL), usually the broker, through which an investor opens and operates a demat account. DPs charge a fee per scrip per sell day for debiting shares.

Domestic institutional investors: Indian mutual funds, insurers, pension funds, banks and similar institutions. NSE publishes provisional daily DII (and FII) net buying in the cash market, and DII is one of the four categories in the participant-wise OI file.

Two plans of the same scheme with the same portfolio. The regular plan is sold through a distributor and carries a higher expense ratio, the difference paying the distributor's trail commission; the direct plan has no commission. A gap of 0.6 point a year costs about 7% of a 20-year SIP's corpus (M06B Worked example 6B.3).

The tendency to sell winners too early and hold losers too long, measured by Odean's proportion of gains realised exceeding the proportion of losses realised. Prospect theory's value function, concave for gains and convex for losses relative to the purchase price, generates it.

A cash payment per share to holders on the record date. The theoretical ex-dividend price is $P_c - d$, and the dividend adjustment factor for a price series is $1 - d/P_c$. Since 1 Apr 2020 Indian dividends are taxed in the investor's hands at slab rates.

Annual dividends per share divided by the share price. For an index it is the continuous yield $q$ in the forward price $F_0 = S_0e^{(r-q)T}$ and option formulas; in the Gordon model the dividend yield plus growth equals the cost of equity.

The number $D$ that converts free-float market capitalisation into an index level, $I = M/D$. When constituents, share counts or free-float factors change, $D' = D\cdot M'/M$ keeps the index continuous; splits and bonuses need no change.

Stephen Jen's heuristic that the US dollar strengthens in two states, global risk-off (safe-haven demand and dollar funding stress) and US outperformance (higher US rates and growth), and weakens in between, during synchronised global growth.

The fall of wealth (or log-wealth) from its running maximum: $D_t = M_t - X_t$ with $M_t = \sup_{u \le t}X_u$. For Brownian log-wealth with drift $m$ and volatility $s$, the stationary drawdown exceeds $d$ with probability $e^{-2md/s^2}$.

The present-value-weighted average time to a bond's cash flows, $D_{\text{mac}} = \sum_k t_k PV_k/P$, in years. It measures interest-rate sensitivity together with modified duration. (In M03, "duration" also denotes the expected length of a gambler's-ruin game.)

A settlement design in which securities move if and only if the corresponding cash moves. Clearing corporations with depositories settle on a DvP basis; the absence of DvP in government-securities settlement made the 1992 securities scam possible.

ICE's US Dollar Index, a geometric average of six exchange rates against the dollar with weights EUR 57.6%, JPY 13.6%, GBP 11.9%, CAD 9.1%, SEK 4.2% and CHF 3.6% (base March 1973 = 100). It contains neither the yuan nor the rupee.

Earnings before interest, taxes, depreciation and amortisation, a proxy for operating cash profit before capital spending. EV/EBITDA, enterprise value over EBITDA, is a capital-structure-neutral multiple used for cyclicals such as metals and cement, ideally on mid-cycle (normalised) EBITDA.

The hypothesis that prices fully reflect available information, in weak (past prices), semi-strong (public information) or strong (all information) form. Formally, excess returns are a martingale difference sequence, so no $\mathcal F_t$-measurable predictor is correlated with the next excess return; it constrains mean forecasts far more than variance forecasts.

In purged cross-validation, dropping a further $\lceil\epsilon N\rceil$ observations immediately after each test block from the training set (typically $\epsilon = 0.01$), because their features overlap the test period through trailing windows and serial correlation.

A two-step cointegration test: regress one series on the other by OLS, then apply a Dickey–Fuller test to the residuals. Because the residuals are fitted, the critical values are more negative than DF's: about $-3.34$ at 5% for a pair with a constant, against $-2.86$.

The value of a firm's operating business to all capital providers: equity market value plus net debt (debt minus excess cash), with adjustments for minorities and other claims. DCF on FCFF at WACC estimates it directly.

A portfolio in which every asset contributes the same share of total volatility, $RC_i = w_i(\Sigma w)_i/\sigma$ equal for all $i$. It is found by the convex problem $\min \tfrac12 y'\Sigma y - \sum_i b_i\ln y_i$, $w = y/\mathbf 1'y$, and equals inverse-volatility weighting iff the correlation matrix has equal row sums.

The interest-rate sensitivity of a stock valued by the Gordon model: modified duration $1/(r - g) = P/D_1$. Low-dividend-yield growth stocks have long durations, which is why they, like long bonds, fall when real yields rise.

The expected return of the equity market in excess of the risk-free rate. The course uses Damodaran's July 2026 inputs for India: a mature-market ERP plus a country risk premium of 2.72%, total 6.92%.

For Indian tax, a fund with at least 65% in listed domestic equity (hedged arbitrage positions count). Gains are taxed like listed shares: 20% if held 12 months or less, 12.5% above ₹1.25 lakh a year otherwise (rates as of 2026-27).

A model in which changes in cointegrated series respond to the lagged deviation from equilibrium: $\Delta y_t = \alpha\beta'y_{t-1} + \sum_i\Gamma_i\Delta y_{t-i} + \varepsilon_t$ (the VECM). The loadings $\alpha$ give the speed at which each series corrects the spread.

A fund whose units trade on the exchange; new units are created and redeemed with the AMC only in creation units, by market makers or by investors dealing above ₹25 cr. Arbitrage between the two markets keeps the price near iNAV within a cost band (M06B Proposition 6B.9.1).

The percentage by which an ETF's traded price exceeds (premium) or falls short of (discount) its iNAV. Without frictions it is bounded by the cost of creating or redeeming units, $I(1 - C_r) \le P \le I(1 + C_c)$ (M06B (6B.26)).

A method that measures the price effect of an event by estimating normal returns on an estimation window, computing abnormal returns over an event window, aggregating them into CARs across firms, and testing them with statistics (J1, Patell, BMP) whose size depends on clustering and variance changes.

The extra variance the option market prices for a known event (results, policy decision), extracted from two expiries straddling it: $m^2 = (\sigma_1^2 - \sigma_2^2)T_1T_2/(T_2 - T_1)$ when both expire after the event. The implied expected absolute event move is $m\sqrt{2/\pi}$.

The first trading day on which a share trades without the right to a declared dividend, bonus, split or rights entitlement. Under T+1, brokers state that the ex-date equals the record date, so buying on the ex-date does not give the benefit; check NSE's corporate-actions page for each case.

A charge on units redeemed within a stated period, credited to the scheme (not the AMC) and capped at 3% of NAV. It transfers value from short-term leavers to the remaining holders.

The expected profit per trade in R-multiples, $E = p\bar W - (1-p)\bar L$, with win rate $p$, average win $\bar W$ and average loss $\bar L$. For a driftless price no stop, target or trailing rule changes it from zero; with drift $\mu$ it equals $\mu$ times expected exposure time.

The average loss given that the loss exceeds VaR: $\mathrm{ES}_c = -E[r \mid r \le q_{1-c}(r)]$ (also called CVaR). For a normal return it is $-\mu + \sigma\varphi(\Phi^{-1}(c))/(1-c)$; it is coherent, always at least VaR, and harder to backtest because it is not elicitable.

The last trading day of a derivative contract, when it is settled. On expiry day ATM gamma and theta peak, an extra 2% ELM applies to short index options (since 20 Nov 2024), calendar-spread margin benefit is removed (since 1 Feb 2025), and from 7 Dec 2026 expiring index contracts stop trading at 15:30.

A margin collected over and above the VaR or SPAN margin to cover losses beyond the modelled scenarios, charged as a percentage of notional; for derivatives it is also called exposure margin (about 2% of notional for index derivatives is the commonly quoted figure, not re-verified in the notes). An additional 2% ELM applies to short index options on their expiry day since 20 Nov 2024.

A period during which a stock's derivatives can only be traded to reduce positions, triggered when market-wide futures-equivalent open interest exceeds 95% of the market-wide position limit (MWPL). The MWPL formula and futures-equivalent basis were revised from 1 Oct 2025 (reported; verify the current circular). The exchange publishes the ban list each evening.

The nominal value per share stated in a company's charter (e.g. ₹1, ₹2, ₹10). It matters for splits (which reduce it) and for dividends declared as a percentage of it, not for valuation. For a bond it is the principal repaid at maturity.

Holding long–short portfolios sorted on stock characteristics (value, size, momentum, quality, low volatility or beta) to earn the premia associated with them. A factor return must be built with correct timing (characteristics known before the holding period), and its premium tested for significance, crowding and crash risk.

The expected proportion of false rejections among all rejections in a family of tests. Controlling it (Benjamini–Hochberg) tolerates some false discoveries in exchange for power, unlike family-wise error control.

The probability of at least one false rejection among $m$ tests; with $k$ independent tests at level $\alpha$ it is $1 - (1-\alpha)^k$. Bonferroni and Holm control it at $\alpha$ under any dependence.

The cash available to shareholders after operating needs, reinvestment and net payments to debt holders: FCFF minus after-tax interest plus net borrowing. Discounted at the cost of equity, it values the equity directly; with clean surplus it equals dividends net of new equity.

The cash generated by operations after taxes and reinvestment, available to all capital providers: $\text{FCFF} = \text{NOPAT} + \text{D\&A} - \text{capex} - \Delta\text{NWC} = \text{NOPAT} - \Delta\text{NOA}$. It equals the cash paid to debt and equity holders, and is discounted at WACC.

Foreign institutional investors, now registered by SEBI as foreign portfolio investors (FPIs). Their daily net cash-market flows, published provisionally by NSE, and their positions in the participant-wise OI file are watched as drivers of the Nifty and the rupee; a short index future held by an FII is often a hedge of its cash holdings.

The relation between nominal and real interest rates and expected inflation: $(1 + i) = (1 + r)(1 + \pi^e)$, approximately $i \approx r + \pi^e$.

The upward bias in correlation measured in high-volatility periods: if the market's variance rises by a factor $1 + \delta$ with an unchanged linear relation, conditional correlation becomes $\rho^* = \rho\sqrt{(1+\delta)/(1 + \delta\rho^2)} > \rho$. "Contagion" must be measured after removing it.

A dated record of one's probabilistic forecasts, each with the exact question, resolution criterion and date, probability, base rate used, rationale and later updates, scored with Brier and log scores when resolved. Detecting a skill difference $d$ against a baseline needs roughly $(1.96\,s/d)^2$ questions.

The foreign-currency assets, gold, SDRs and IMF reserve position held by the central bank. The RBI uses them to intervene in the rupee market; selling dollars absorbs rupees and tightens domestic liquidity unless sterilised.

An agreement to buy or sell an asset at a fixed price $K$ on a future date, settled once at maturity. The no-arbitrage forward price is $F_0 = S_0e^{(r-q)T}$ (or $(S_0 - I)e^{rT}$ with discrete dividends); an existing long forward is worth $(F_t - K)e^{-r\tau}$.

The empirical failure of uncovered interest parity: in the Fama regression $\Delta s_{t+1} = a + b(f_t - s_t) + \varepsilon$, the slope $b$ is typically below 1 and often negative, so high-interest currencies tend not to depreciate enough to offset the rate differential, and carry trades earn positive average returns with crash risk.

The implied variance for the period between two expiries, $\sigma_{1,2}^2 = (\sigma_2^2\tau_2 - \sigma_1^2\tau_1)/(\tau_2 - \tau_1)$, from total implied variances $w_i = \sigma_i^2\tau_i$. Absence of calendar arbitrage requires it to be non-negative.

Betting a fraction $c$ of the Kelly fraction, $f = cf^*$. It achieves about $2c - c^2$ of the maximal excess growth with $c$ times the volatility, and the probability of ever falling to a fraction $x$ of initial wealth is $x^{2/c-1}$; half Kelly gives 75% of the growth with half the volatility.

The fraction of a company's shares available to ordinary investors, excluding promoter holdings, government strategic stakes and locked-in shares; NSE expresses it as the investible weight factor (IWF). Nifty 50 weights are by free-float market capitalisation $\sum_i P_iN_if_i$.

A scheme that invests in other mutual fund schemes or ETFs, domestic or foreign. Its expense cap includes the underlying schemes' weighted expense ratio. Gold and silver FoFs hold the AMC's own ETF; international FoFs are subject to the overseas investment limits.

An exchange-traded forward with standardised terms, guaranteed by a clearing corporation and marked to market daily so that gains and losses are paid each day. With deterministic interest rates futures and forward prices are equal; with stochastic rates the futures price is $\mathbb E^{\mathbb Q}[S_T]$.

A Government of India dated security (bond), issued through RBI auctions and the benchmark for INR risk-free yields. The 10-year G-sec yield, less a default spread, is the starting point of the course's INR cost of equity.

The probability that a random walk with up-probability $p$ and down-probability $q$, starting at $a$, hits 0 before $N$: $P_a = (\rho^a - \rho^N)/(1 - \rho^N)$ with $\rho = q/p$. With $N = \infty$ and $p > q$ it is $\rho^a$; with fixed-fractional betting ruin is replaced by bounded losses, $P(\text{ever} \le xW_0) \le x^\theta$.

The rate of change of delta with the underlying, $\Gamma = \partial^2V/\partial S^2 = e^{-q\tau}\varphi(d_1)/(S\sigma\sqrt\tau)$ under Black–Scholes. Long options are long gamma; the theta–gamma identity ties gamma gains to time decay, and ATM gamma grows like $\tau^{-1/2}$ toward expiry.

The difference between a day's open and the previous close, $g_t = \ln(O_t/C_{t-1})$; a full gap up has $O_t > H_{t-1}$. An up-gap is filled if the day's low reaches $C_{t-1}$. Under a random walk a gap of size $g$ fills with probability $2\Phi(-|g|/\sigma_{in})$, so "gaps get filled" is largely noise.

A model of conditional variance $\sigma_t^2 = \omega + \alpha\varepsilon_{t-1}^2 + \beta\sigma_{t-1}^2$. It is covariance-stationary iff $\alpha + \beta < 1$, with unconditional variance $\omega/(1-\alpha-\beta)$; forecasts revert to it geometrically at rate $\alpha + \beta$, and it reproduces volatility clustering and excess kurtosis.

Gross domestic product, the value of final goods and services produced in an economy in a period. Its nominal growth $g_n$ sets, against the interest rate $i$, whether debt ratios fall or compound: $d_{t+1} = d_t(1+i)/(1+g_n) - pb_t$.

The price model $dS = \mu S\,dt + \sigma S\,dW$, solved by $S_T = S_0e^{(\mu - \sigma^2/2)T + \sigma W_T}$. $S_T$ is lognormal with mean $S_0e^{\mu T}$ and median $S_0e^{(\mu-\sigma^2/2)T}$; it is the Black–Scholes model of the underlying.

Caldara and Iacoviello's (2022) index of the share of articles in major newspapers that discuss geopolitical threats or acts, scaled so the 1985–2019 average is 100. Sub-indices separate threats (war, nuclear, terror threats, build-ups) from acts (war onset, escalation, terror acts).

A sequential-trade model in which a competitive market maker quotes $a = E[V \mid \text{buy}]$ and $b = E[V \mid \text{sell}]$, updated by Bayes' rule. The spread exists because some traders are informed: it equals the market maker's expected loss to them, and prices converge to the true value as trades reveal information.

The premium over the issue price at which IPO shares are informally quoted before listing in an unregulated grey market. It has no legal standing or settlement guarantee and is thin and easily manipulated; the course does not treat it as evidence.

Gross non-performing assets as a share of gross loans. A loan is non-performing when interest or principal has been overdue beyond the RBI's regulatory threshold. With provision coverage PCR, the net NPA ratio is $\text{GNPA}(1 - \text{PCR})/(1 - \text{GNPA}\cdot\text{PCR})$.

The landed INR price of gold implied by the international price: $P_{10g} = (P_{oz} + q)/31.1034768 \times 10 \times X \times (1+d)$, with $X$ the USDINR rate, $q$ a premium or discount and $d$ basic customs duty plus AIDC; GST of 3% is added at retail. It lets one reproduce MCX gold prices and decompose rupee gold returns into gold, currency and duty parts.

The price of gold divided by the price of silver per ounce. It is often traded as mean-reverting, but no arbitrage anchors it; a test needs ADF critical values, a half-life with honest confidence intervals and attention to small-sample bias.

The value of a cash flow growing at constant rate $g$ forever, discounted at $r > g$: $V = c_1/(r - g)$. For equity, $P_0 = D_1/(k_e - g)$, so $k_e = D_1/P_0 + g$; it gives the terminal value in a DCF, justified multiples, and an equity duration of $1/(r-g)$.

The partial derivatives of an option's value with respect to its inputs: delta and gamma (underlying), vega (volatility), theta (time) and rho (interest rate), plus higher-order ones such as vanna, vomma and charm. The course quotes vega per 1.00 of volatility and theta per year unless it says "per vol point" or "per day".

The argument that prices cannot be perfectly informative: if they were, nobody would pay to gather information, and then prices could not reflect it. In equilibrium prices are noisy enough that informed traders just recover the cost of their information.

A broker-side conditional order that waits on the broker's server, sometimes for up to a year, and sends a limit order to the exchange when its trigger price is hit. The exchange does not see it until then, so it has no queue position.

The percentage deducted from the market value of a security pledged as collateral to compute its collateral value. Indian clearing corporations set haircuts aligned with each security's VaR margin rate and publish them daily; brokers may apply larger ones.

The expected time for a deviation from the mean to halve. For an AR(1) with coefficient $\varphi$ it is $-\ln 2/\ln\varphi$ periods; for an Ornstein–Uhlenbeck process with speed $\kappa$ it is $\ln 2/\kappa$; for a GARCH variance forecast it is $\ln 0.5/\ln(\alpha + \beta)$. Estimates from short samples are biased and imprecise.

The recursive filter for a Markov regime-switching model (parameters depend on a hidden state following a Markov chain; state $j$ lasts $1/(1 - p_{jj})$ periods on average) that updates the probabilities of each regime: $\xi_{t\mid t} \propto \xi_{t\mid t-1}\odot f(y_t)$, $\xi_{t+1\mid t} = P'\xi_{t\mid t}$, and yields the likelihood. Filtered probabilities use only past data; smoothed (Kim) probabilities use the whole sample and are look-ahead in a backtest.

Tails of a return distribution that decay more slowly than the normal's, typically like a power law $P(|X| > x) \sim Cx^{-\alpha}$. Moments of order $p \ge \alpha$ are infinite; daily index returns have a tail index near 3, so sample kurtosis is unreliable.

The share of the spot position's variance removed by the minimum-variance hedge, equal to $\rho^2$, the squared correlation between spot and futures price changes.

The number of futures per unit of spot exposure that minimises the variance of the hedged position, $h^* = \rho\sigma_S/\sigma_F = \operatorname{Cov}(\Delta S, \Delta F)/\operatorname{Var}(\Delta F)$; the number of contracts is $N^* = h^*Q_A/Q_F$. In pairs trading the hedge ratio is the cointegrating coefficient, estimated by OLS, TLS or a Kalman filter.

The maximum-likelihood estimator of the tail index $\alpha$ of a Pareto-type tail from the $k$ largest observations: $\hat\alpha_k = [\frac1k\sum_{i \le k}\ln X_{(i)} - \ln X_{(k+1)}]^{-1}$, with standard error about $\alpha/\sqrt k$. The choice of $k$ trades variance against bias (Hill plot).

A step-down multiple-testing rule: sort $p$-values and reject while $p_{(k)} \le \alpha/(m - k + 1)$, stopping at the first failure. It controls the family-wise error rate at $\alpha$ and is uniformly more powerful than Bonferroni.

The result that, in competitive equilibrium, the net price of an exhaustible resource rises at the rate of interest, $p_t - c = (p_0 - c)e^{rt}$, so that owners are indifferent between extracting now and later. Real oil prices have not followed it.

An order with a disclosed quantity: only part of the order is displayed in the book and the rest is hidden, refreshing after the visible part fills. It reduces information leakage at the cost of queue priority for the hidden part.

A scheme option that pays out part of the NAV from time to time; called the dividend option before 2021. The payout can include the investor's own capital and is taxed as income at slab rates; the growth option defers tax to redemption at capital-gains rates.

The difference between the value of a paper portfolio traded at the decision price and the realised portfolio, decomposed into delay cost, execution (impact) cost, opportunity cost of unfilled quantity, and fees. It is the benchmark that Almgren–Chriss optimises.

The stock-borrow fee at which shorting through SLB and shorting through a single-stock future cost the same: $b_{\text{imp}} = r - q - \ln(F/S)/T$. A future trading well below carry value signals expensive borrowing and crowded shorts.

The volatility that, put into Black–Scholes or Black-76, reproduces an option's market price. It exists and is unique because the price is strictly increasing in $\sigma$; it depends on the price used (LTP or mid), the forward and the time convention, and is computed by Newton's method from the Manaster–Koehler start with a Brent fallback.

An option with positive intrinsic value: a call with $S > K$, a put with $S < K$ (desks often compare with the forward). ITM stock options on NSE are exercised automatically at expiry and physically settled.

An ETF's net asset value per unit computed during the trading day from live prices of its basket. It is the benchmark against which an ETF's traded price shows a premium or discount.

An open-ended scheme that holds an index's securities in index weights (at least 95% of assets) and is bought and redeemed at NAV. It lags the index by its tracking difference (M06B · 6B.8).

Cash-settled futures on a stock index such as the Nifty 50 or Bank Nifty. Their fair price is $S e^{(r-q)T}$; they are the standard instrument for beta hedging and for a short index view, and futures plus cash replicate the total-return index.

NSE's volatility index: the square root of the 30-calendar-day variance-swap rate implied by near- and next-month Nifty OTM option quotes, using the VIX methodology adapted from CBOE, with the relevant-tenor NSE MIBOR as the rate. It is quoted in annualised percentage points and is an implied, not a realised, volatility.

Annualised active return divided by tracking error: the reward per unit of active risk (M06B (6B.19)).

The collateral a trader must post before opening a futures or short-option position, sized to cover a large one-day loss (SPAN plus exposure margin for Indian derivatives). In India the full initial margin must be maintained at all times, including at intraday peak-margin snapshots.

An order validity that fills whatever can be filled on arrival and cancels the rest; it never rests in the book. It is not accepted in NSE's pre-open session.

An initial public offering: the first sale of a company's shares to the public, with listing on an exchange. An Indian IPO combines a fresh issue (new shares) and/or an offer for sale by existing holders, and is priced by book building within a price band.

The average first-day return of IPOs, the listing price above the issue price. Rock's winner's-curse model explains it: uninformed investors receive more of the bad issues, so issues must be priced below expected value to keep them in the market. Long-run post-IPO returns are on average weak.

A short strangle with long wings: short an OTM put and an OTM call, and long a further-OTM put and call. It is short volatility with maximum loss capped at the wing width minus the credit, which also caps its scenario margin.

International Securities Identification Number, the 12-character code that identifies a security uniquely across exchanges and depositories (Indian equities begin with "INE"). Not discussed in the notes; data joins across NSE, BSE and depository records use it.

The chain rule of stochastic calculus: for $dX = a\,dt + b\,dW$ and smooth $f(t,x)$, $df = (f_t + af_x + \tfrac12b^2f_{xx})\,dt + bf_x\,dW$. The extra $\tfrac12b^2f_{xx}$ term, from $(dW)^2 = dt$, produces volatility drag and the Black–Scholes PDE.

The share of past days in a trailing window whose implied volatility was below today's, $\mathrm{IVP}_t = \frac1{n-1}\#\{s : t-n < s < t,\ \sigma_s < \sigma_t\}$. Under exchangeability it is uniform whatever the distribution of IV.

Today's implied volatility located between the trailing window's minimum and maximum, $\mathrm{IVR}_t = (\sigma_t - \min\sigma)/(\max\sigma - \min\sigma)$. Unlike IV percentile its distribution depends on the distribution of IV, and a single spike compresses it for a year.

The intercept of a regression of a fund's excess returns on the market's excess returns (or on several factors): the average return not explained by factor exposure (Jensen 1968; M06B (6B.18)).

A maximum-likelihood test of the number of cointegrating relations $r$ in a VAR, from the eigenvalues of a reduced-rank regression: the trace statistic $-T\sum_{i>r}\ln(1 - \hat\lambda_i)$ and the maximum-eigenvalue statistic $-T\ln(1 - \hat\lambda_{r+1})$. It handles more than two series and does not need a choice of dependent variable.

The recursive optimal estimator of a hidden linear-Gaussian state, here a time-varying hedge ratio $b_t$ following a random walk: predict $P_{t\mid t-1} = P_{t-1\mid t-1} + Q$, compute the gain $K_t = P_{t\mid t-1}x_t/F_t$, update $b_{t\mid t} = b_{t\mid t-1} + K_te_t$. In steady state it is an exponentially weighted estimator.

Sizing bets to maximise expected log wealth, which maximises the long-run growth rate almost surely. For a binary bet with odds $b$ and win probability $p$, $f^* = p - q/b$; in continuous time $f^* = (\mu - r)/\sigma^2$ with growth $r + S^2/2$. Betting twice Kelly gives zero excess growth, and estimation error argues for fractions below 1.

The standardised fourth moment $\kappa = E(X-\mu)^4/\sigma^4$, equal to 3 for a normal; excess kurtosis is $\kappa - 3$ (the course writes $\kappa$ for kurtosis and $K$ for excess kurtosis). Stochastic volatility raises it, and with a tail index near 3 its sample estimate is unreliable.

The price impact per unit of net order flow in Kyle's (1985) model, $\lambda = \sigma_v/(2\sigma_u)$, where $\sigma_v$ is the uncertainty of the asset's value and $\sigma_u$ the volatility of noise trading. The insider trades $\beta = \sigma_u/\sigma_v$ per unit of private information and half of it is revealed by the price.

The RBI's Liquidity Adjustment Facility corridor for overnight rates: floor at the Standing Deposit Facility (repo − 25 bp) and ceiling at the Marginal Standing Facility (repo + 25 bp). The weighted average call rate, the operating target, sits near the floor in liquidity surplus and near the ceiling in deficit.

Market timing exploits stale fund prices with frequent round trips; late trading, which is illegal, places orders after the pricing time at that time's NAV. Both transfer wealth from long-term holders; they were the subject of the US mutual fund scandal of 2003 (M06B · 6B.12.4).

Contamination of a model's evaluation by information from the test period, for example when overlapping labels or trailing features in the training set span the test window. Ordinary k-fold cross-validation leaks on financial time series; purging and embargoing remove it.

Estimating a covariance matrix as a convex combination $\delta F + (1-\delta)S$ of the sample covariance $S$ and a structured target $F$ (such as constant correlation), with the intensity $\delta^* = \mathbb E\|S - \Sigma\|^2/(\mathbb E\|S - \Sigma\|^2 + \|\Sigma - F\|^2)$ that minimises expected squared error. It stabilises mean–variance weights.

The ratio of position size to equity, $\lambda = V/E$. Static leverage magnifies returns linearly; constant (rebalanced) leverage on GBM gives log growth $c + \lambda(\mu - c) - \tfrac12\lambda^2\sigma^2$ with borrowing cost $c$, so volatility drag grows with $\lambda^2$, and a margin call arrives at a computable price before the planned drawdown.

An order to buy at or below, or sell at or above, a specified price. If it cannot trade on arrival it rests in the book and supplies liquidity; it controls price but not execution, and it gives others a free option to trade against it on news.

The continuous limit order book: the set of resting buy and sell limit orders, matched under price-time priority, with each trade at the resting (maker's) price. Between the auctions, every NSE and BSE trade happens in it.

A volatility function $\sigma_{\text{loc}}(S,t)$ such that the diffusion $dS = (r-q)S\,dt + \sigma_{\text{loc}}S\,dW$ reproduces every European option price on the surface. Dupire's formula gives it from call prices: $\sigma_{\text{loc}}^2 = [\partial_TC + (r-q)K\partial_KC + qC]/[\tfrac12K^2\partial_K^2C]$.

The continuously compounded return $r_t = \ln(P_t/P_{t-1}) = \ln(1 + R_t)$. Log returns add over time (a $k$-period log return is the sum of one-period ones), while simple returns add across assets in a portfolio.

The logarithmic scoring rule for probability forecasts, scored as a loss: $-\frac1N\sum_i\ln p_i(y_i)$, the average negative log probability given to what happened. It is strictly proper and unbounded (a probability of 0 on an event that occurs scores $+\infty$), and is tied to a Kelly bettor's log-wealth growth.

The distribution of $e^X$ for normal $X$. Under GBM, $S_T$ is lognormal: $\ln S_T \sim N(\ln S_0 + (\mu - \sigma^2/2)T, \sigma^2T)$, so its mean exceeds its median and $P(S_T < E S_T) = \Phi(\sigma\sqrt T/2) > \tfrac12$.

Using at time $t$ information that was not available at $t$: same-bar closes for same-bar decisions, restated fundamentals, revised index membership, smoothed regime probabilities, or vendor-adjusted prices. An event-driven backtest that only reads data timestamped before each decision provably avoids it.

The asymmetry in prospect theory by which losses weigh more than equal gains; Tversky and Kahneman (1992) estimate the loss coefficient at 2.25, so $v(x) = -2.25(-x)^{0.88}$ for losses.

The number of units of the underlying in one derivatives contract. Nifty 65 and Bank Nifty 30, as of the 5 Nov 2026 NSE F&O bhavcopy (field NewBrdLotQty); SEBI keeps index contract values in a ₹15–20 lakh band, so lots change as the index moves. Read the lot from the bhavcopy of the date you trade.

The RBI scheme under which resident Indian individuals may remit up to an annual limit abroad for permitted purposes, including overseas investment. Not covered in the notes; it is the channel through which residents invest in foreign markets and is part of the rupee's capital-account plumbing.

Gains on listed equity held more than 12 months with STT paid, taxed at 12.5% on gains above ₹1.25 lakh a year without indexation (transfers from 23 Jul 2024; as of 6 Nov 2026, before surcharge and cess). Long-term losses can be set off only against long-term gains.

The positive root $\theta$ of $E(1 + fX)^{-\theta} = 1$ for fixed-fractional betting with per-bet return $X$. It bounds the probability of ever falling to a fraction $x$ of initial wealth, $P \le x^\theta$; $\theta = 1$ at the Kelly fraction and $\theta \approx 2/c - 1$ at $c$ times Kelly.

In a limit order book, the maker is the resting order that supplied liquidity and the taker is the arriving marketable order that removed it. The trade prints at the maker's price; the taker pays the spread and the maker bears adverse selection.

A demand for additional collateral when an account's equity falls below the required margin. In the textbook model it is triggered at a maintenance level below initial margin; in India every futures MTM loss is collected daily and the full margin must be maintained at all times. For a leveraged position the trigger is a computable price.

The discount of price to estimated intrinsic value required before buying. The course states it as a probability: buy only if the price is below a low quantile $q_\alpha$ of a Monte Carlo distribution of intrinsic value, which accounts for uncertainty in growth, margins and the discount rate.

Using shares already held as collateral for trading margin: under SEBI's pledge/re-pledge framework (mandatory from 1 Sep 2020, per broker notices) the shares stay in the client's demat account, marked as pledged to the broker and re-pledged to the clearing corporation, and count at market value less a haircut. For derivatives, at least half the margin must be in cash or cash equivalents (secondary sources).

A regulated arrangement in which a broker funds part of a client's purchase of delivery shares, which are pledged to the broker; the client pays an initial margin and interest on the funded amount. For Group I F&O stocks the margin is VaR + 3 × ELM and for other Group I stocks and equity ETFs VaR + 5 × ELM (SEBI master circular as reproduced 18 Jun 2026), so permitted leverage falls as volatility rises.

Revaluing a position at the day's settlement price and paying or receiving the change in cash. For futures the daily variation margin is $m_t = Q(F_t - F_{t-1})$; the cash flows sum to the forward's P&L, but their timing makes the cash demands path-dependent.

The adverse move in price caused by one's own trading, split into a temporary part that decays after the trade and a permanent part that reflects information. It is the largest cost of large orders, does not appear on the contract note, and is concave in size (the square-root law).