JSE FX Trader cheat sheet

Ordinary shares carry residual claim on earnings and assets after all creditors and preference holders are paid; voting rights typically attach to ordinary shares only.

Dividend discount model: P0 = D1 / (r − g), valid only when r > g; the same relation rearranges to r = D1/P0 + g (Gordon growth).

Ex-dividend date: buyers on or after this date do not receive the declared dividend; the price typically drops by roughly the dividend on the ex-date.

Market capitalisation = shares in issue × price; free-float market cap excludes strategic or locked-up holdings and drives index weights in float-adjusted indices.

P/E = price / EPS; trailing EPS uses last reported 12 months, forward P/E uses forecast EPS. Earnings yield = EPS / price = 1 / P/E.

Rights issue: subscription price is set below market; theoretical ex-rights price = (N × cum price + subscription price) / (N + 1) for a 1-for-N issue.

Share buybacks reduce shares outstanding, raise EPS for unchanged earnings, and are an alternative to cash dividends for returning capital.

Stock splits and scrip issues change share count and price proportionally without changing market cap or shareholder wealth.

Direct vs indirect quote: a direct quote prices one unit of foreign currency in domestic terms; indirect quotes invert it. Always confirm the base currency before calculating.

Cross rate from two quotes: if EUR/USD = 1.10 and USD/JPY = 150, then EUR/JPY = 1.10 × 150 = 165, achieved by chaining so the intermediate currency cancels.

Forward rate from interest rate parity: F/S = (1 + r_quote) / (1 + r_base) for the quoted period; higher-yielding currency trades at a forward discount.

Covered interest arbitrage eliminates the forward premium/discount equal to the interest differential; deviations are transient and bounded by transaction costs.

Bid/offer spread is quoted from the market maker's perspective: the client buys at the offer (ask) and sells at the bid; the spread is a transaction cost.

Real exchange rate = nominal rate × (foreign price level / domestic price level); it measures competitiveness adjusted for inflation differentials.

Purchasing power parity is a long-run anchor; short-run deviations persist because of capital flows, intervention, and non-traded goods.

Carry trade earns the interest differential but is exposed to abrupt spot reversal; the payoff resembles selling a currency option.

Preference shares rank ahead of ordinary shares but behind all debt for dividends and liquidation proceeds; they are hybrid capital.

Cumulative preference shares accrue unpaid dividends as arrears that must be settled before ordinary dividends can be paid.

Non-participating preference shares receive only the stated dividend; participating shares may share in residual profits above the fixed rate.

Perpetual preference valuation: P = D / r, where D is the fixed annual dividend and r the required return; it behaves like a perpetuity.

Redeemable preference shares have a fixed redemption date and price; value = PV of dividends to redemption + PV of redemption amount.

Convertible preference shares allow conversion into ordinary shares at a set ratio; value includes an option premium over straight preference.

Dividend rate may be fixed (as a percentage of par) or floating (referenced to a benchmark such as a policy rate plus margin).

Preference dividends are usually paid before ordinary dividends, but directors may omit non-cumulative preference dividends without creating arrears.

Mean, variance, standard deviation: population variance uses divisor N, sample variance uses n − 1 to correct for estimation bias.

Correlation ρ = cov(X,Y) / (σX σY), bounded between −1 and +1; it measures linear association only, not causation.

Portfolio variance for two assets: σp² = w1²σ1² + w2²σ2² + 2 w1 w2 ρ σ1 σ2; diversification benefits rise as ρ falls.

Normal distribution: about 68% of observations within 1σ, 95% within 2σ, 99.7% within 3σ of the mean.

Standard error of the mean = σ / √n; larger samples narrow the confidence interval by the square root of n.

Regression slope β = cov(X,Y) / var(X); R² is the proportion of variance in the dependent variable explained by the model.

Z-score = (x − μ) / σ standardises a value; use it to compare observations from distributions with different means and spreads.

Skewness measures asymmetry (positive skew has a long right tail); kurtosis measures tail heaviness, with excess kurtosis above 3 indicating fat tails.

An ETF is a listed fund whose shares trade intraday on an exchange; creation and redemption in kind by authorised participants keeps price close to NAV.

NAV per share = (total assets − liabilities) / shares outstanding; premium or discount = (market price − NAV) / NAV.

Physical ETFs hold the underlying securities; synthetic ETFs gain exposure via swaps and carry counterparty risk.

Tracking difference is the realised return gap versus the index; tracking error is the volatility of that gap.

Total expense ratio covers management and administrative costs but excludes brokerage and bid-offer costs of trading the ETF itself.

Leveraged and inverse ETFs rebalance daily, so returns over longer periods deviate from a simple multiple of the index return.

Distributing ETFs pay out dividends; accumulating ETFs reinvest income inside the fund, raising NAV instead.

ETF liquidity depends on both secondary-market volume and the liquidity of underlying holdings; the creation mechanism supports arbitrage.

Bond price = Σ coupon / (1 + y)^t + face / (1 + y)^n; price and yield move inversely, with longer duration amplifying the move.

Macaulay duration is the weighted average time to cash flows; modified duration = Macaulay duration / (1 + y/m) approximates percentage price change per 1% yield change.

Convexity captures curvature: ΔP/P ≈ −D_mod × Δy + ½ × convexity × (Δy)²; positive convexity benefits the holder for large yield moves.

Clean price excludes accrued interest; dirty (full) price = clean price + accrued interest, where accrued = coupon × days since last coupon / days in period.

Yield to maturity assumes all coupons reinvested at the YTM; realised return differs if reinvestment rates change.

Duration of a zero-coupon bond equals its maturity; a par bond's duration is below maturity and a premium bond's is lower still.

Credit spread = yield on corporate bond − yield on comparable government bond; it compensates for default and liquidity risk.

Floating rate notes reset coupons to a reference rate plus spread, so their price sensitivity to rates is low between reset dates.

Price-weighted index (e.g. Dow method) weights by share price; a high-priced stock dominates regardless of company size, and a divisor adjusts for splits.

Capitalisation-weighted index weights by market cap; larger companies dominate and the index automatically reflects share issuance.

Equal-weighted indices rebalance to equal weights, giving small caps more influence and requiring periodic rebalancing trades.

Float-adjusted weighting uses only shares available to outside investors, avoiding distortion from strategic holdings.

Index divisor adjustment keeps the index level continuous when constituents change, shares are issued, or splits occur.

Total return index reinvests dividends; price index excludes them, so total return exceeds price return over time.

Rebalancing effect: additions to a major index often see buying pressure before inclusion and partial reversal afterwards.

Index futures fair value = spot × (1 + r − q)^T, where q is the dividend yield; the basis converges to zero at expiry.

Order types: market orders execute immediately at best available price; limit orders execute only at the specified price or better.

Stop orders become market orders once the trigger price is reached, so slippage is possible in fast or thin markets.

Settlement cycles vary by market (commonly T+1 or T+2); trade date and settlement date differ, affecting cash timing.

Bid-offer spread plus commission and taxes form total transaction cost; quoted spread alone understates cost for large orders.

Short selling involves borrowing securities and selling them, with a later repurchase to close; losses are theoretically unlimited.

Margin trading uses borrowed funds with a maintenance margin; a margin call forces deposit or liquidation when equity falls below the threshold.

Liquidity measures include average daily volume, quoted depth, and the price impact of a standard-sized trade.

Corporate actions (splits, dividends, mergers) adjust open orders and positions; contract specifications define the adjustment method.

A warrant is issued by the company (or a bank for covered warrants) and gives the right, not obligation, to buy or sell shares at a strike price before expiry.

Warrant premium = (warrant price + strike) − share price for a call warrant, expressed as a percentage of share price to compare issues.

Gearing (leverage) = share price / warrant price; effective gearing = gearing × delta, measuring sensitivity to the underlying.

Warrant value = intrinsic value + time value; intrinsic value of a call = max(0, share price − strike) and of a put = max(0, strike − share price).

Issuers may adjust the exercise ratio and strike for dividends, splits, and rights issues so warrant holders are not disadvantaged.

Implied volatility rises with demand and time to expiry; warrant prices fall through time decay as expiry approaches.

Covered (bank-issued) warrants are cash-settled and do not dilute share capital, unlike company-issued warrants.

Exercise style may be American (any time before expiry) or European (only at expiry); confirm before valuing.

Commodity futures price = spot × (1 + r + storage − convenience yield)^T; the cost-of-carry model links spot and futures.

Contango: futures price above spot, typical when storage costs exceed convenience yield; the futures curve slopes upward.

Backwardation: futures price below spot, often when supply is tight and convenience yield is high; the curve slopes downward.

Roll yield is positive in backwardation (sell higher near contract, buy lower far contract) and negative in contango for long positions.

Commodity indices use roll rules (e.g. monthly roll) that determine exposure to roll yield; the choice materially affects returns.

Commodities are usually traded via futures or ETFs, not physical delivery, and are priced in USD, adding currency exposure.

Gold is often treated as a store of value and safe-haven asset, with demand from jewellery, investment, and central bank reserves.

Supply is inelastic in the short run because of long production cycles, so demand shocks drive large price swings.

Ordinary shares carry residual claim on earnings and assets after all creditors and preference holders are paid; voting rights typically attach to ordinary shares only.

Dividend discount model: P0 = D1 / (r − g), valid only when r > g; the same relation rearranges to r = D1/P0 + g (Gordon growth).

Ex-dividend date: buyers on or after this date do not receive the declared dividend; the price typically drops by roughly the dividend on the ex-date.

Market capitalisation = shares in issue × price; free-float market cap excludes strategic or locked-up holdings and drives index weights in float-adjusted indices.

P/E = price / EPS; trailing EPS uses last reported 12 months, forward P/E uses forecast EPS. Earnings yield = EPS / price = 1 / P/E.

Rights issue: subscription price is set below market; theoretical ex-rights price = (N × cum price + subscription price) / (N + 1) for a 1-for-N issue.

Share buybacks reduce shares outstanding, raise EPS for unchanged earnings, and are an alternative to cash dividends for returning capital.

Stock splits and scrip issues change share count and price proportionally without changing market cap or shareholder wealth.

Direct vs indirect quote: a direct quote prices one unit of foreign currency in domestic terms; indirect quotes invert it. Always confirm the base currency before calculating.

Cross rate from two quotes: if EUR/USD = 1.10 and USD/JPY = 150, then EUR/JPY = 1.10 × 150 = 165, achieved by chaining so the intermediate currency cancels.

Forward rate from interest rate parity: F/S = (1 + r_quote) / (1 + r_base) for the quoted period; higher-yielding currency trades at a forward discount.

Covered interest arbitrage eliminates the forward premium/discount equal to the interest differential; deviations are transient and bounded by transaction costs.

Bid/offer spread is quoted from the market maker's perspective: the client buys at the offer (ask) and sells at the bid; the spread is a transaction cost.

Real exchange rate = nominal rate × (foreign price level / domestic price level); it measures competitiveness adjusted for inflation differentials.

Purchasing power parity is a long-run anchor; short-run deviations persist because of capital flows, intervention, and non-traded goods.

Carry trade earns the interest differential but is exposed to abrupt spot reversal; the payoff resembles selling a currency option.

Preference shares rank ahead of ordinary shares but behind all debt for dividends and liquidation proceeds; they are hybrid capital.

Cumulative preference shares accrue unpaid dividends as arrears that must be settled before ordinary dividends can be paid.

Non-participating preference shares receive only the stated dividend; participating shares may share in residual profits above the fixed rate.

Perpetual preference valuation: P = D / r, where D is the fixed annual dividend and r the required return; it behaves like a perpetuity.

Redeemable preference shares have a fixed redemption date and price; value = PV of dividends to redemption + PV of redemption amount.

Convertible preference shares allow conversion into ordinary shares at a set ratio; value includes an option premium over straight preference.

Dividend rate may be fixed (as a percentage of par) or floating (referenced to a benchmark such as a policy rate plus margin).

Preference dividends are usually paid before ordinary dividends, but directors may omit non-cumulative preference dividends without creating arrears.

Mean, variance, standard deviation: population variance uses divisor N, sample variance uses n − 1 to correct for estimation bias.

Correlation ρ = cov(X,Y) / (σX σY), bounded between −1 and +1; it measures linear association only, not causation.

Portfolio variance for two assets: σp² = w1²σ1² + w2²σ2² + 2 w1 w2 ρ σ1 σ2; diversification benefits rise as ρ falls.

Normal distribution: about 68% of observations within 1σ, 95% within 2σ, 99.7% within 3σ of the mean.

Standard error of the mean = σ / √n; larger samples narrow the confidence interval by the square root of n.

Regression slope β = cov(X,Y) / var(X); R² is the proportion of variance in the dependent variable explained by the model.

Z-score = (x − μ) / σ standardises a value; use it to compare observations from distributions with different means and spreads.

Skewness measures asymmetry (positive skew has a long right tail); kurtosis measures tail heaviness, with excess kurtosis above 3 indicating fat tails.

An ETF is a listed fund whose shares trade intraday on an exchange; creation and redemption in kind by authorised participants keeps price close to NAV.

NAV per share = (total assets − liabilities) / shares outstanding; premium or discount = (market price − NAV) / NAV.

Physical ETFs hold the underlying securities; synthetic ETFs gain exposure via swaps and carry counterparty risk.

Tracking difference is the realised return gap versus the index; tracking error is the volatility of that gap.

Total expense ratio covers management and administrative costs but excludes brokerage and bid-offer costs of trading the ETF itself.

Leveraged and inverse ETFs rebalance daily, so returns over longer periods deviate from a simple multiple of the index return.

Distributing ETFs pay out dividends; accumulating ETFs reinvest income inside the fund, raising NAV instead.

ETF liquidity depends on both secondary-market volume and the liquidity of underlying holdings; the creation mechanism supports arbitrage.

Bond price = Σ coupon / (1 + y)^t + face / (1 + y)^n; price and yield move inversely, with longer duration amplifying the move.

Macaulay duration is the weighted average time to cash flows; modified duration = Macaulay duration / (1 + y/m) approximates percentage price change per 1% yield change.

Convexity captures curvature: ΔP/P ≈ −D_mod × Δy + ½ × convexity × (Δy)²; positive convexity benefits the holder for large yield moves.

Clean price excludes accrued interest; dirty (full) price = clean price + accrued interest, where accrued = coupon × days since last coupon / days in period.

Yield to maturity assumes all coupons reinvested at the YTM; realised return differs if reinvestment rates change.

Duration of a zero-coupon bond equals its maturity; a par bond's duration is below maturity and a premium bond's is lower still.

Credit spread = yield on corporate bond − yield on comparable government bond; it compensates for default and liquidity risk.

Floating rate notes reset coupons to a reference rate plus spread, so their price sensitivity to rates is low between reset dates.

Price-weighted index (e.g. Dow method) weights by share price; a high-priced stock dominates regardless of company size, and a divisor adjusts for splits.

Capitalisation-weighted index weights by market cap; larger companies dominate and the index automatically reflects share issuance.

Equal-weighted indices rebalance to equal weights, giving small caps more influence and requiring periodic rebalancing trades.

Float-adjusted weighting uses only shares available to outside investors, avoiding distortion from strategic holdings.

Index divisor adjustment keeps the index level continuous when constituents change, shares are issued, or splits occur.

Total return index reinvests dividends; price index excludes them, so total return exceeds price return over time.

Rebalancing effect: additions to a major index often see buying pressure before inclusion and partial reversal afterwards.

Index futures fair value = spot × (1 + r − q)^T, where q is the dividend yield; the basis converges to zero at expiry.

Order types: market orders execute immediately at best available price; limit orders execute only at the specified price or better.

Stop orders become market orders once the trigger price is reached, so slippage is possible in fast or thin markets.

Settlement cycles vary by market (commonly T+1 or T+2); trade date and settlement date differ, affecting cash timing.

Bid-offer spread plus commission and taxes form total transaction cost; quoted spread alone understates cost for large orders.

Short selling involves borrowing securities and selling them, with a later repurchase to close; losses are theoretically unlimited.

Margin trading uses borrowed funds with a maintenance margin; a margin call forces deposit or liquidation when equity falls below the threshold.

Liquidity measures include average daily volume, quoted depth, and the price impact of a standard-sized trade.

Corporate actions (splits, dividends, mergers) adjust open orders and positions; contract specifications define the adjustment method.

A warrant is issued by the company (or a bank for covered warrants) and gives the right, not obligation, to buy or sell shares at a strike price before expiry.

Warrant premium = (warrant price + strike) − share price for a call warrant, expressed as a percentage of share price to compare issues.

Gearing (leverage) = share price / warrant price; effective gearing = gearing × delta, measuring sensitivity to the underlying.

Warrant value = intrinsic value + time value; intrinsic value of a call = max(0, share price − strike) and of a put = max(0, strike − share price).

Issuers may adjust the exercise ratio and strike for dividends, splits, and rights issues so warrant holders are not disadvantaged.

Implied volatility rises with demand and time to expiry; warrant prices fall through time decay as expiry approaches.

Covered (bank-issued) warrants are cash-settled and do not dilute share capital, unlike company-issued warrants.

Exercise style may be American (any time before expiry) or European (only at expiry); confirm before valuing.

Commodity futures price = spot × (1 + r + storage − convenience yield)^T; the cost-of-carry model links spot and futures.

Contango: futures price above spot, typical when storage costs exceed convenience yield; the futures curve slopes upward.

Backwardation: futures price below spot, often when supply is tight and convenience yield is high; the curve slopes downward.

Roll yield is positive in backwardation (sell higher near contract, buy lower far contract) and negative in contango for long positions.

Commodity indices use roll rules (e.g. monthly roll) that determine exposure to roll yield; the choice materially affects returns.

Commodities are usually traded via futures or ETFs, not physical delivery, and are priced in USD, adding currency exposure.

Gold is often treated as a store of value and safe-haven asset, with demand from jewellery, investment, and central bank reserves.

Supply is inelastic in the short run because of long production cycles, so demand shocks drive large price swings.

Ordinary shares carry residual claim on earnings and assets after all creditors and preference holders are paid; voting rights typically attach to ordinary shares only.

Dividend discount model: P0 = D1 / (r − g), valid only when r > g; the same relation rearranges to r = D1/P0 + g (Gordon growth).

Ex-dividend date: buyers on or after this date do not receive the declared dividend; the price typically drops by roughly the dividend on the ex-date.

Market capitalisation = shares in issue × price; free-float market cap excludes strategic or locked-up holdings and drives index weights in float-adjusted indices.

P/E = price / EPS; trailing EPS uses last reported 12 months, forward P/E uses forecast EPS. Earnings yield = EPS / price = 1 / P/E.

Rights issue: subscription price is set below market; theoretical ex-rights price = (N × cum price + subscription price) / (N + 1) for a 1-for-N issue.

Share buybacks reduce shares outstanding, raise EPS for unchanged earnings, and are an alternative to cash dividends for returning capital.

Stock splits and scrip issues change share count and price proportionally without changing market cap or shareholder wealth.

Direct vs indirect quote: a direct quote prices one unit of foreign currency in domestic terms; indirect quotes invert it. Always confirm the base currency before calculating.

Cross rate from two quotes: if EUR/USD = 1.10 and USD/JPY = 150, then EUR/JPY = 1.10 × 150 = 165, achieved by chaining so the intermediate currency cancels.

Forward rate from interest rate parity: F/S = (1 + r_quote) / (1 + r_base) for the quoted period; higher-yielding currency trades at a forward discount.

Covered interest arbitrage eliminates the forward premium/discount equal to the interest differential; deviations are transient and bounded by transaction costs.

Bid/offer spread is quoted from the market maker's perspective: the client buys at the offer (ask) and sells at the bid; the spread is a transaction cost.

Real exchange rate = nominal rate × (foreign price level / domestic price level); it measures competitiveness adjusted for inflation differentials.

Purchasing power parity is a long-run anchor; short-run deviations persist because of capital flows, intervention, and non-traded goods.

Carry trade earns the interest differential but is exposed to abrupt spot reversal; the payoff resembles selling a currency option.

Preference shares rank ahead of ordinary shares but behind all debt for dividends and liquidation proceeds; they are hybrid capital.

Cumulative preference shares accrue unpaid dividends as arrears that must be settled before ordinary dividends can be paid.

Non-participating preference shares receive only the stated dividend; participating shares may share in residual profits above the fixed rate.

Perpetual preference valuation: P = D / r, where D is the fixed annual dividend and r the required return; it behaves like a perpetuity.

Redeemable preference shares have a fixed redemption date and price; value = PV of dividends to redemption + PV of redemption amount.

Convertible preference shares allow conversion into ordinary shares at a set ratio; value includes an option premium over straight preference.

Dividend rate may be fixed (as a percentage of par) or floating (referenced to a benchmark such as a policy rate plus margin).

Preference dividends are usually paid before ordinary dividends, but directors may omit non-cumulative preference dividends without creating arrears.

Mean, variance, standard deviation: population variance uses divisor N, sample variance uses n − 1 to correct for estimation bias.

Correlation ρ = cov(X,Y) / (σX σY), bounded between −1 and +1; it measures linear association only, not causation.

Portfolio variance for two assets: σp² = w1²σ1² + w2²σ2² + 2 w1 w2 ρ σ1 σ2; diversification benefits rise as ρ falls.

Normal distribution: about 68% of observations within 1σ, 95% within 2σ, 99.7% within 3σ of the mean.

Standard error of the mean = σ / √n; larger samples narrow the confidence interval by the square root of n.

Regression slope β = cov(X,Y) / var(X); R² is the proportion of variance in the dependent variable explained by the model.

Z-score = (x − μ) / σ standardises a value; use it to compare observations from distributions with different means and spreads.

Skewness measures asymmetry (positive skew has a long right tail); kurtosis measures tail heaviness, with excess kurtosis above 3 indicating fat tails.

An ETF is a listed fund whose shares trade intraday on an exchange; creation and redemption in kind by authorised participants keeps price close to NAV.

NAV per share = (total assets − liabilities) / shares outstanding; premium or discount = (market price − NAV) / NAV.

Physical ETFs hold the underlying securities; synthetic ETFs gain exposure via swaps and carry counterparty risk.

Tracking difference is the realised return gap versus the index; tracking error is the volatility of that gap.

Total expense ratio covers management and administrative costs but excludes brokerage and bid-offer costs of trading the ETF itself.

Leveraged and inverse ETFs rebalance daily, so returns over longer periods deviate from a simple multiple of the index return.

Distributing ETFs pay out dividends; accumulating ETFs reinvest income inside the fund, raising NAV instead.

ETF liquidity depends on both secondary-market volume and the liquidity of underlying holdings; the creation mechanism supports arbitrage.

Bond price = Σ coupon / (1 + y)^t + face / (1 + y)^n; price and yield move inversely, with longer duration amplifying the move.

Macaulay duration is the weighted average time to cash flows; modified duration = Macaulay duration / (1 + y/m) approximates percentage price change per 1% yield change.

Convexity captures curvature: ΔP/P ≈ −D_mod × Δy + ½ × convexity × (Δy)²; positive convexity benefits the holder for large yield moves.

Clean price excludes accrued interest; dirty (full) price = clean price + accrued interest, where accrued = coupon × days since last coupon / days in period.

Yield to maturity assumes all coupons reinvested at the YTM; realised return differs if reinvestment rates change.

Duration of a zero-coupon bond equals its maturity; a par bond's duration is below maturity and a premium bond's is lower still.

Credit spread = yield on corporate bond − yield on comparable government bond; it compensates for default and liquidity risk.

Floating rate notes reset coupons to a reference rate plus spread, so their price sensitivity to rates is low between reset dates.

Price-weighted index (e.g. Dow method) weights by share price; a high-priced stock dominates regardless of company size, and a divisor adjusts for splits.

Capitalisation-weighted index weights by market cap; larger companies dominate and the index automatically reflects share issuance.

Equal-weighted indices rebalance to equal weights, giving small caps more influence and requiring periodic rebalancing trades.

Float-adjusted weighting uses only shares available to outside investors, avoiding distortion from strategic holdings.

Index divisor adjustment keeps the index level continuous when constituents change, shares are issued, or splits occur.

Total return index reinvests dividends; price index excludes them, so total return exceeds price return over time.

Rebalancing effect: additions to a major index often see buying pressure before inclusion and partial reversal afterwards.

Index futures fair value = spot × (1 + r − q)^T, where q is the dividend yield; the basis converges to zero at expiry.

Order types: market orders execute immediately at best available price; limit orders execute only at the specified price or better.

Stop orders become market orders once the trigger price is reached, so slippage is possible in fast or thin markets.

Settlement cycles vary by market (commonly T+1 or T+2); trade date and settlement date differ, affecting cash timing.

Bid-offer spread plus commission and taxes form total transaction cost; quoted spread alone understates cost for large orders.

Short selling involves borrowing securities and selling them, with a later repurchase to close; losses are theoretically unlimited.

Margin trading uses borrowed funds with a maintenance margin; a margin call forces deposit or liquidation when equity falls below the threshold.

Liquidity measures include average daily volume, quoted depth, and the price impact of a standard-sized trade.

Corporate actions (splits, dividends, mergers) adjust open orders and positions; contract specifications define the adjustment method.

A warrant is issued by the company (or a bank for covered warrants) and gives the right, not obligation, to buy or sell shares at a strike price before expiry.

Warrant premium = (warrant price + strike) − share price for a call warrant, expressed as a percentage of share price to compare issues.

Gearing (leverage) = share price / warrant price; effective gearing = gearing × delta, measuring sensitivity to the underlying.

Warrant value = intrinsic value + time value; intrinsic value of a call = max(0, share price − strike) and of a put = max(0, strike − share price).

Issuers may adjust the exercise ratio and strike for dividends, splits, and rights issues so warrant holders are not disadvantaged.

Implied volatility rises with demand and time to expiry; warrant prices fall through time decay as expiry approaches.

Covered (bank-issued) warrants are cash-settled and do not dilute share capital, unlike company-issued warrants.

Exercise style may be American (any time before expiry) or European (only at expiry); confirm before valuing.

Commodity futures price = spot × (1 + r + storage − convenience yield)^T; the cost-of-carry model links spot and futures.

Contango: futures price above spot, typical when storage costs exceed convenience yield; the futures curve slopes upward.

Backwardation: futures price below spot, often when supply is tight and convenience yield is high; the curve slopes downward.

Roll yield is positive in backwardation (sell higher near contract, buy lower far contract) and negative in contango for long positions.

Commodity indices use roll rules (e.g. monthly roll) that determine exposure to roll yield; the choice materially affects returns.

Commodities are usually traded via futures or ETFs, not physical delivery, and are priced in USD, adding currency exposure.

Gold is often treated as a store of value and safe-haven asset, with demand from jewellery, investment, and central bank reserves.

Supply is inelastic in the short run because of long production cycles, so demand shocks drive large price swings.

Ordinary shares carry residual claim on earnings and assets after all creditors and preference holders are paid; voting rights typically attach to ordinary shares only.

Dividend discount model: P0 = D1 / (r − g), valid only when r > g; the same relation rearranges to r = D1/P0 + g (Gordon growth).

Ex-dividend date: buyers on or after this date do not receive the declared dividend; the price typically drops by roughly the dividend on the ex-date.

Market capitalisation = shares in issue × price; free-float market cap excludes strategic or locked-up holdings and drives index weights in float-adjusted indices.

P/E = price / EPS; trailing EPS uses last reported 12 months, forward P/E uses forecast EPS. Earnings yield = EPS / price = 1 / P/E.

Rights issue: subscription price is set below market; theoretical ex-rights price = (N × cum price + subscription price) / (N + 1) for a 1-for-N issue.

Share buybacks reduce shares outstanding, raise EPS for unchanged earnings, and are an alternative to cash dividends for returning capital.

Stock splits and scrip issues change share count and price proportionally without changing market cap or shareholder wealth.

Direct vs indirect quote: a direct quote prices one unit of foreign currency in domestic terms; indirect quotes invert it. Always confirm the base currency before calculating.

Cross rate from two quotes: if EUR/USD = 1.10 and USD/JPY = 150, then EUR/JPY = 1.10 × 150 = 165, achieved by chaining so the intermediate currency cancels.

Forward rate from interest rate parity: F/S = (1 + r_quote) / (1 + r_base) for the quoted period; higher-yielding currency trades at a forward discount.

Covered interest arbitrage eliminates the forward premium/discount equal to the interest differential; deviations are transient and bounded by transaction costs.

Bid/offer spread is quoted from the market maker's perspective: the client buys at the offer (ask) and sells at the bid; the spread is a transaction cost.

Real exchange rate = nominal rate × (foreign price level / domestic price level); it measures competitiveness adjusted for inflation differentials.

Purchasing power parity is a long-run anchor; short-run deviations persist because of capital flows, intervention, and non-traded goods.

Carry trade earns the interest differential but is exposed to abrupt spot reversal; the payoff resembles selling a currency option.

Preference shares rank ahead of ordinary shares but behind all debt for dividends and liquidation proceeds; they are hybrid capital.

Cumulative preference shares accrue unpaid dividends as arrears that must be settled before ordinary dividends can be paid.

Non-participating preference shares receive only the stated dividend; participating shares may share in residual profits above the fixed rate.

Perpetual preference valuation: P = D / r, where D is the fixed annual dividend and r the required return; it behaves like a perpetuity.

Redeemable preference shares have a fixed redemption date and price; value = PV of dividends to redemption + PV of redemption amount.

Convertible preference shares allow conversion into ordinary shares at a set ratio; value includes an option premium over straight preference.

Dividend rate may be fixed (as a percentage of par) or floating (referenced to a benchmark such as a policy rate plus margin).

Preference dividends are usually paid before ordinary dividends, but directors may omit non-cumulative preference dividends without creating arrears.

Mean, variance, standard deviation: population variance uses divisor N, sample variance uses n − 1 to correct for estimation bias.

Correlation ρ = cov(X,Y) / (σX σY), bounded between −1 and +1; it measures linear association only, not causation.

Portfolio variance for two assets: σp² = w1²σ1² + w2²σ2² + 2 w1 w2 ρ σ1 σ2; diversification benefits rise as ρ falls.

Normal distribution: about 68% of observations within 1σ, 95% within 2σ, 99.7% within 3σ of the mean.

Standard error of the mean = σ / √n; larger samples narrow the confidence interval by the square root of n.

Regression slope β = cov(X,Y) / var(X); R² is the proportion of variance in the dependent variable explained by the model.

Z-score = (x − μ) / σ standardises a value; use it to compare observations from distributions with different means and spreads.

Skewness measures asymmetry (positive skew has a long right tail); kurtosis measures tail heaviness, with excess kurtosis above 3 indicating fat tails.

An ETF is a listed fund whose shares trade intraday on an exchange; creation and redemption in kind by authorised participants keeps price close to NAV.

NAV per share = (total assets − liabilities) / shares outstanding; premium or discount = (market price − NAV) / NAV.

Physical ETFs hold the underlying securities; synthetic ETFs gain exposure via swaps and carry counterparty risk.

Tracking difference is the realised return gap versus the index; tracking error is the volatility of that gap.

Total expense ratio covers management and administrative costs but excludes brokerage and bid-offer costs of trading the ETF itself.

Leveraged and inverse ETFs rebalance daily, so returns over longer periods deviate from a simple multiple of the index return.

Distributing ETFs pay out dividends; accumulating ETFs reinvest income inside the fund, raising NAV instead.

ETF liquidity depends on both secondary-market volume and the liquidity of underlying holdings; the creation mechanism supports arbitrage.

Bond price = Σ coupon / (1 + y)^t + face / (1 + y)^n; price and yield move inversely, with longer duration amplifying the move.

Macaulay duration is the weighted average time to cash flows; modified duration = Macaulay duration / (1 + y/m) approximates percentage price change per 1% yield change.

Convexity captures curvature: ΔP/P ≈ −D_mod × Δy + ½ × convexity × (Δy)²; positive convexity benefits the holder for large yield moves.

Clean price excludes accrued interest; dirty (full) price = clean price + accrued interest, where accrued = coupon × days since last coupon / days in period.

Yield to maturity assumes all coupons reinvested at the YTM; realised return differs if reinvestment rates change.

Duration of a zero-coupon bond equals its maturity; a par bond's duration is below maturity and a premium bond's is lower still.

Credit spread = yield on corporate bond − yield on comparable government bond; it compensates for default and liquidity risk.

Floating rate notes reset coupons to a reference rate plus spread, so their price sensitivity to rates is low between reset dates.

Price-weighted index (e.g. Dow method) weights by share price; a high-priced stock dominates regardless of company size, and a divisor adjusts for splits.

Capitalisation-weighted index weights by market cap; larger companies dominate and the index automatically reflects share issuance.

Equal-weighted indices rebalance to equal weights, giving small caps more influence and requiring periodic rebalancing trades.

Float-adjusted weighting uses only shares available to outside investors, avoiding distortion from strategic holdings.

Index divisor adjustment keeps the index level continuous when constituents change, shares are issued, or splits occur.

Total return index reinvests dividends; price index excludes them, so total return exceeds price return over time.

Rebalancing effect: additions to a major index often see buying pressure before inclusion and partial reversal afterwards.

Index futures fair value = spot × (1 + r − q)^T, where q is the dividend yield; the basis converges to zero at expiry.

Order types: market orders execute immediately at best available price; limit orders execute only at the specified price or better.

Stop orders become market orders once the trigger price is reached, so slippage is possible in fast or thin markets.

Settlement cycles vary by market (commonly T+1 or T+2); trade date and settlement date differ, affecting cash timing.

Bid-offer spread plus commission and taxes form total transaction cost; quoted spread alone understates cost for large orders.

Short selling involves borrowing securities and selling them, with a later repurchase to close; losses are theoretically unlimited.

Margin trading uses borrowed funds with a maintenance margin; a margin call forces deposit or liquidation when equity falls below the threshold.

Liquidity measures include average daily volume, quoted depth, and the price impact of a standard-sized trade.

Corporate actions (splits, dividends, mergers) adjust open orders and positions; contract specifications define the adjustment method.

A warrant is issued by the company (or a bank for covered warrants) and gives the right, not obligation, to buy or sell shares at a strike price before expiry.

Warrant premium = (warrant price + strike) − share price for a call warrant, expressed as a percentage of share price to compare issues.

Gearing (leverage) = share price / warrant price; effective gearing = gearing × delta, measuring sensitivity to the underlying.

Warrant value = intrinsic value + time value; intrinsic value of a call = max(0, share price − strike) and of a put = max(0, strike − share price).

Issuers may adjust the exercise ratio and strike for dividends, splits, and rights issues so warrant holders are not disadvantaged.

Implied volatility rises with demand and time to expiry; warrant prices fall through time decay as expiry approaches.

Covered (bank-issued) warrants are cash-settled and do not dilute share capital, unlike company-issued warrants.

Exercise style may be American (any time before expiry) or European (only at expiry); confirm before valuing.

Commodity futures price = spot × (1 + r + storage − convenience yield)^T; the cost-of-carry model links spot and futures.

Contango: futures price above spot, typical when storage costs exceed convenience yield; the futures curve slopes upward.

Backwardation: futures price below spot, often when supply is tight and convenience yield is high; the curve slopes downward.

Roll yield is positive in backwardation (sell higher near contract, buy lower far contract) and negative in contango for long positions.

Commodity indices use roll rules (e.g. monthly roll) that determine exposure to roll yield; the choice materially affects returns.

Commodities are usually traded via futures or ETFs, not physical delivery, and are priced in USD, adding currency exposure.

Gold is often treated as a store of value and safe-haven asset, with demand from jewellery, investment, and central bank reserves.

Supply is inelastic in the short run because of long production cycles, so demand shocks drive large price swings.