Lesson 29

    Position Sizing: From Equity to Whole Lots

    Choose a loss basis, calculate the whole-lot limit, then check funding, open exposures and the assumptions behind growth models.

    Maya fits four identical wooden lots into a tray while Mr. Chartist holds up a fifth that does not fit: size is whole lots, rounded down
    A hypothetical NIFTY futures entry at 25,000 with a planned exit at 24,850 and a 65-unit lot risks 150 points, ₹9,750, per lot. A loss allowance of ₹5,000, 1% of a ₹5,00,000 account, divided by ₹9,750 is about 0.51 lots, which rounds down to 0 lots. Round down before checking the funds.

    Does a whole lot fit the allowance?

    ₹5,000allowance÷₹9,750loss per lot=0.51lots, rounded down→0 lotsthe plan does not fit

    Hypothetical NIFTY futures · entry 25,000 · planned exit 24,850 · 65-unit lot · estimates before costs

    Does the account fit the quantity?

    I’m Mr. Chartist. Let’s turn an account allowance into whole lots, then check the loss assumption, the funds and the combined exposure that the first division cannot settle.

    By the end you will be able to answer

    1. What does the number of lots decide?
    2. How do you turn an allowance into whole lots?
    3. Does the account have the money for that many lots?

    You have a view on NIFTY 50, the index of 50 large Indian companies, and you know where you would get out if the view is wrong. The order ticket then asks a different question: how many lots? The smallest quantity the exchange accepts can put more money at risk than you meant to risk on this trade. Being sure about direction does not fix that.

    Position sizing connects three things: your account value, the loss you decided to accept, and the quantity you carry. First decide what the loss number means: a planned exit, the full premium of a bought option, or the worst loss of a finished spread. Then check whole lots, costs, free funds and the positions you already hold. Each check answers a different part of the question.

    We follow a fictional ₹5,00,000 account with a 1% allowance and a NIFTY lot of 65 units. These are teaching numbers, not live contract details and not a recommended risk percentage. Later we look at a run of losses and at a separate model called Kelly, and we mark where their arithmetic stops and real trading begins.

    Updated

    Chapter 1Size and exposure2 min read

    What does the number of lots decide?

    See how the number of lots sets the money at stake.

    Maya

    Mr. Chartist, I know my exit. Why does the order ticket still ask me how many lots?

    Mr. Chartist

    Because the number of lots decides how much money one price move can take from you. Same entry, same exit, three lots lose three times as much.

    Maya

    So how do I pick the lots?

    Mr. Chartist

    Allowance = equity × fraction. Then lots = allowance ÷ loss per lot, rounded down. In our ₹5,00,000 account with a 1% allowance, that is ₹5,000.

    Maya

    One lot could lose ₹9,750. So the answer is zero lots?

    Mr. Chartist

    Yes, and zero is a valid answer. Do not pull the exit closer just to get one lot. That changes the plan to fit the answer.

    Then check the funds, and the risk of all your open positions together.

    Short answer: the number of lots decides how much money one price move can take from you. Picture two learners in the same NIFTY futures contract, with the same entry and the same exit. One holds one lot and the other holds three. Before costs, the second learner wins or loses three times as much. Direction is the same; size is the only thing that changed.

    Start from your account equity: what the account is worth today, with open positions marked at their current value. Money you need for rent, bills or other goals stays outside this number. Then separate three ideas that beginners often mix up. A loss allowance (the Start course calls it a loss budget) is the amount you decide a trade may cost you. Collateral is the money or approved assets the broker holds against your obligations. Buying power is what the broker lets you take on. None of these is a cap on your loss. Margin, leverage and pledging explains the second and third.

    Our account has ₹5,00,000 of equity and a 1% loss allowance, which is ₹5,000. Both are teaching numbers, not advice on what percentage suits you. We assume a NIFTY lot of 65 units. Check the real lot size for your contract and date before you use any calculation here. NIFTY is an index, so nothing is delivered into your demat account. The first lesson on this subject, risk management 101, builds the same idea for shares.

    Chapter 2Whole-lot arithmetic2 min read

    How do you turn an allowance into whole lots?

    Turn an allowance into whole lots.

    Short answer: divide the allowance by the loss on one lot, then round down. Allowance = equity × fraction. Lots = allowance ÷ loss per lot, rounded down to a whole number. If the answer is below one, you take zero lots. Rounding up quietly raises your allowance; it does not solve anything.

    Take a long NIFTY futures lot bought at 25,000 with a planned exit at 24,850. The adverse move is 150 points. At 65 units that is 150 × 65 = ₹9,750 before costs. Your allowance is ₹5,000, and ₹5,000 ÷ ₹9,750 is about 0.513 of a lot. Rounded down, that is zero lots.

    Risk-budget arithmetic only

    Round down before checking the funds

    Same futures trade: entry 25,000, planned exit 24,850, 65-unit lot. One lot loses ₹9,750 before costs.

    Round down before checking the funds: numerical comparison
    Account equityAssumed 1% allowanceWhole lots / planned lossUnused allowance
    ₹2,50,000₹2,5000 lots · ₹0₹2,500
    ₹5,00,000₹5,0000 lots · ₹0₹5,000
    ₹10,00,000₹10,0001 lots · ₹9,750₹250

    The ₹5,00,000 account gives 0 lots. Rounding up would estimate ₹9,750 of loss, or 1.95% of that equity, against its ₹5,000 allowance. At ₹10,00,000, one lot leaves only ₹250 before costs.

    Unused allowance is room on paper, not free cash. Costs are set to zero here, and a stop is not a guaranteed fill. The 1% and the 65 units are teaching assumptions.

    The quotient is not the order quantity

    Use a positive per-lot loss estimate, then take the largest whole number that fits. Do not round upward.

    1. Allowance = ₹5,00,000 × 1% = ₹5,000
    2. Planned loss per lot = 150 futures-price points × 65 units = ₹9,750
    3. Risk-budget lots = floor(5,000 / 9,750) = 0

    A planned exit is an estimate, not a ceiling. If the exit order fills at 24,750 instead of 24,850, the move is 250 points and one lot loses ₹16,250. Fees add to both numbers. The honest sizing question is therefore: what do I lose if the exit is a bit worse than planned? Risk management 101 shows the same point for shares: a stop decides when you sell, not the price you get.

    Chapter 3Funding constraint2 min read

    Does the account have the money for that many lots?

    Pass both the loss test and the funding test.

    Short answer: the lot count must pass two tests. The loss test asks how much you could lose. The funding test asks how much money the position needs. The smaller answer wins.

    Use a second, separate example: ₹10,00,000 of equity and a 2% allowance, which is ₹20,000. Suppose a bought-and-sold Call spread (a credit vertical) has a worst terminal loss of ₹4,550 per lot before costs. The loss test allows four lots, because 20,000 ÷ 4,550 is 4.396, rounded down to 4. Now suppose only ₹1,80,000 is free for this trade and each lot needs ₹1,80,000. The funding test allows one lot. One is the binding answer, and the planned terminal loss is ₹4,550.

    Simplified one-position funding example

    Passing the allowance check does not supply the funds

    A separate ₹10,00,000 account, 2% allowance, ₹4,550 spread loss per lot. Free funds ₹1,80,000; each lot needs ₹1,80,000.

    Passing the allowance check does not supply the funds: numerical comparison
    ConstraintDeclared amountWhole-lot limit
    Loss allowance₹20,000 / ₹4,550 per lot4 lots
    Usable funding₹1,80,000 / ₹1,80,000 per lot1 lot
    Smaller whole-lot limitBoth constraints must hold1 lot

    One lot uses ₹4,550 of the loss allowance and all ₹1,80,000 of the assumed usable funding. The remaining ₹15,450 allowance cannot fund another lot.

    Every funding number is made up. Real margin can change with your other positions and is not a fee or a maximum loss. Costs, premium cash and delivery need their own checks.

    Take the smaller of two integer limits

    The example calculator treats loss allowance and funding as separate constraints, using the declared inputs without inferring a live margin.

    1. Risk lots = floor(20,000 / 4,550) = 4
    2. Funding lots = floor(1,80,000 / 1,80,000) = 1
    3. Permitted by these inputs = min(4, 1) = 1 lot

    Real margin does not behave like this tidy division. It changes with your other positions, the hedges you hold, market conditions and broker rules, and the requirement for two lots is not always twice the requirement for one. This example does not calculate live SPAN or exposure margin. Check the actual requirement for the whole position you intend to hold, and remember that a margin figure is collateral, not a measure of loss.

    Chapter 4Zero is an output2 min read

    What does a result of zero lots tell you?

    Accept zero lots as a valid answer.

    Short answer: for this account and this trade, the position is too big. Zero is a valid answer, not an error. In our example, one lot would put ₹9,750 at risk, which is 1.95% of a ₹5,00,000 account, against a 1% allowance.

    You can change the trade. A different contract, a smaller structure or a different exit makes a different calculation. What you should not do is move your exit closer just to make the arithmetic return one lot. That changes the plan to fit the answer, and a tighter exit is more likely to be hit by ordinary movement.

    A smaller structure such as a spread can fit the allowance, but check it as carefully as the first idea. A quoted credit is not a filled credit. A partly filled order can leave you with one leg only. The protective leg must match in underlying, expiry and quantity. If the limits still say zero, keep zero.

    Chapter 5Constructed loss runs2 min read

    What happens to the allowance as the account shrinks?

    Compare a percentage allowance with a fixed one.

    Short answer: a percentage allowance gets smaller after every loss, and a fixed rupee allowance does not. To see this cleanly, allow any position size and assume every trade loses its full allowance. Start with ₹5,00,000. If each loss is 1% of the equity left, twenty losses leave about ₹4,08,953.47. If each loss is a fixed ₹5,000, twenty losses leave ₹4,00,000.

    The next loss allowance changes with the account

    Start with ₹5,00,000. Every trade loses its full allowance: 1% of the latest equity, or a fixed ₹5,000.

    • Recalculated 1% loss allowance
    • Constant ₹5,000 loss allowance
    • Fixed rule risks more than 1%
    ₹4,000₹4,500₹5,00005101520₹5,000₹4,089.53

    ₹910.47Fixed rule risks more than 1%: widest after 20 full losses, ₹4,089.53 against ₹5,000.

    Axis cropped to ₹4,000–₹5,000 so the gap shows; it does not start at ₹0. The recalculated line is 1% of the equity left after that many full losses. Any position size, no costs, no gaps, no lot floors.

    Complete plotted values: Loss allowance for the next trade · ₹ against Number of assumed full-loss trades already taken
    SeriesNumber of assumed full-loss trades already takenLoss allowance for the next trade · ₹
    Recalculated 1% loss allowance05,000
    Recalculated 1% loss allowance14,950
    Recalculated 1% loss allowance24,900.5
    Recalculated 1% loss allowance34,851.49
    Recalculated 1% loss allowance44,802.98
    Recalculated 1% loss allowance54,754.95
    Recalculated 1% loss allowance64,707.4
    Recalculated 1% loss allowance74,660.33
    Recalculated 1% loss allowance84,613.72
    Recalculated 1% loss allowance94,567.59
    Recalculated 1% loss allowance104,521.91
    Recalculated 1% loss allowance114,476.69
    Recalculated 1% loss allowance124,431.92
    Recalculated 1% loss allowance134,387.61
    Recalculated 1% loss allowance144,343.73
    Recalculated 1% loss allowance154,300.29
    Recalculated 1% loss allowance164,257.29
    Recalculated 1% loss allowance174,214.72
    Recalculated 1% loss allowance184,172.57
    Recalculated 1% loss allowance194,130.84
    Recalculated 1% loss allowance204,089.53
    Constant ₹5,000 loss allowance05,000
    Constant ₹5,000 loss allowance15,000
    Constant ₹5,000 loss allowance25,000
    Constant ₹5,000 loss allowance35,000
    Constant ₹5,000 loss allowance45,000
    Constant ₹5,000 loss allowance55,000
    Constant ₹5,000 loss allowance65,000
    Constant ₹5,000 loss allowance75,000
    Constant ₹5,000 loss allowance85,000
    Constant ₹5,000 loss allowance95,000
    Constant ₹5,000 loss allowance105,000
    Constant ₹5,000 loss allowance115,000
    Constant ₹5,000 loss allowance125,000
    Constant ₹5,000 loss allowance135,000
    Constant ₹5,000 loss allowance145,000
    Constant ₹5,000 loss allowance155,000
    Constant ₹5,000 loss allowance165,000
    Constant ₹5,000 loss allowance175,000
    Constant ₹5,000 loss allowance185,000
    Constant ₹5,000 loss allowance195,000
    Constant ₹5,000 loss allowance205,000
    The next loss allowance changes with the account: numerical comparison
    Case after 20 lossesRemaining equityDrawdown from startGain needed on remainder
    Recalculated 1%₹4,08,953.4718.21%22.26%
    Fixed ₹5,000₹4,00,000.0020.00%25.00%
    Separate case: recalculated 2%₹3,33,803.9933.24%49.79%
    Separate case: fixed ₹10,000₹3,00,000.0040.00%66.67%

    The 1% allowance shrinks after each loss. A fixed ₹5,000 takes a growing share of a shrinking account. The 2% rows are a separate comparison.

    A made-up loss run with no probability. Positions can be any size, and costs, lots, gaps and deposits are left out. Neither percentage is a recommendation.

    Inspect the two equity rules

    Recalculate from full-precision equity; round money only for display.

    1. Fixed fraction: E_n = E_0 × (1 − f)^n
    2. Fixed cash: E_n = E_0 − n × L, where L stays constant
    3. At 20 losses: 500000 × 0.99^20 = ₹4,08,953.47
    4. At 20 losses: 500000 − 20 × 5000 = ₹4,00,000.00

    At a 2% fraction the same twenty losses leave about ₹3,33,803.99, against ₹3,00,000 for a fixed ₹10,000 loss. This is arithmetic, not a forecast. It is not a typical losing run, and it does not show that any sizing method will keep an account alive. Both paths lose money.

    The smooth curve ignores whole lots. With real lots the allowed quantity moves in steps, so the risk on one trade rarely equals the chosen percentage exactly, and it can fall to zero. Costs, gaps, deposits and withdrawals also change the path.

    Chapter 6Recovery arithmetic2 min read

    Why does a loss need a bigger gain to recover?

    See why recovery is measured on a smaller account.

    Short answer: the gain is measured on a smaller account. A drawdown is the fall from the highest value your account reached to a later, lower value. Start with ₹5 lakh and lose 20%, and you hold ₹4 lakh. To get the ₹1 lakh back, you must gain 25% on ₹4 lakh. The two percentages use different bases.

    Recovery uses the smaller remaining balance

    A fall is measured from the peak. The gain to recover is measured on what remains. No deposits or withdrawals.

    • Required arithmetic recovery gainSolid line

    Gain needed on remaining equity · %

    Gain needed on remaining equity · % against Drawdown from reference equity · %Exact supplied series. Legend identifies solid and dashed lines. All plotted values are available in the following accessible table. Both axes start at 0%. The curve stops at an 80% fall (400% gain); a 100% fall cannot be recovered.

    Drawdown from reference equity · %

    Drag the slider to read each line at that point.

    Both axes start at 0%. The curve stops at an 80% fall (400% gain); a 100% fall cannot be recovered.

    Complete plotted values: Gain needed on remaining equity · % against Drawdown from reference equity · %
    SeriesDrawdown from reference equity · %Gain needed on remaining equity · %
    Required arithmetic recovery gain00
    Required arithmetic recovery gain11.0101010101
    Required arithmetic recovery gain22.0408163265
    Required arithmetic recovery gain33.0927835052
    Required arithmetic recovery gain44.1666666667
    Required arithmetic recovery gain55.2631578947
    Required arithmetic recovery gain66.3829787234
    Required arithmetic recovery gain77.5268817204
    Required arithmetic recovery gain88.6956521739
    Required arithmetic recovery gain99.8901098901
    Required arithmetic recovery gain1011.1111111111
    Required arithmetic recovery gain1112.3595505618
    Required arithmetic recovery gain1213.6363636364
    Required arithmetic recovery gain1314.9425287356
    Required arithmetic recovery gain1416.2790697674
    Required arithmetic recovery gain1517.6470588235
    Required arithmetic recovery gain1619.0476190476
    Required arithmetic recovery gain1720.4819277108
    Required arithmetic recovery gain1821.9512195122
    Required arithmetic recovery gain1923.4567901235
    Required arithmetic recovery gain2025
    Required arithmetic recovery gain2126.582278481
    Required arithmetic recovery gain2228.2051282051
    Required arithmetic recovery gain2329.8701298701
    Required arithmetic recovery gain2431.5789473684
    Required arithmetic recovery gain2533.3333333333
    Required arithmetic recovery gain2635.1351351351
    Required arithmetic recovery gain2736.9863013699
    Required arithmetic recovery gain2838.8888888889
    Required arithmetic recovery gain2940.8450704225
    Required arithmetic recovery gain3042.8571428571
    Required arithmetic recovery gain3144.9275362319
    Required arithmetic recovery gain3247.0588235294
    Required arithmetic recovery gain3349.2537313433
    Required arithmetic recovery gain3451.5151515152
    Required arithmetic recovery gain3553.8461538462
    Required arithmetic recovery gain3656.25
    Required arithmetic recovery gain3758.7301587302
    Required arithmetic recovery gain3861.2903225806
    Required arithmetic recovery gain3963.9344262295
    Required arithmetic recovery gain4066.6666666667
    Required arithmetic recovery gain4169.4915254237
    Required arithmetic recovery gain4272.4137931034
    Required arithmetic recovery gain4375.4385964912
    Required arithmetic recovery gain4478.5714285714
    Required arithmetic recovery gain4581.8181818182
    Required arithmetic recovery gain4685.1851851852
    Required arithmetic recovery gain4788.679245283
    Required arithmetic recovery gain4892.3076923077
    Required arithmetic recovery gain4996.0784313725
    Required arithmetic recovery gain50100
    Required arithmetic recovery gain51104.0816326531
    Required arithmetic recovery gain52108.3333333333
    Required arithmetic recovery gain53112.7659574468
    Required arithmetic recovery gain54117.3913043478
    Required arithmetic recovery gain55122.2222222222
    Required arithmetic recovery gain56127.2727272727
    Required arithmetic recovery gain57132.5581395349
    Required arithmetic recovery gain58138.0952380952
    Required arithmetic recovery gain59143.9024390244
    Required arithmetic recovery gain60150
    Required arithmetic recovery gain61156.4102564103
    Required arithmetic recovery gain62163.1578947368
    Required arithmetic recovery gain63170.2702702703
    Required arithmetic recovery gain64177.7777777778
    Required arithmetic recovery gain65185.7142857143
    Required arithmetic recovery gain66194.1176470588
    Required arithmetic recovery gain67203.0303030303
    Required arithmetic recovery gain68212.5
    Required arithmetic recovery gain69222.5806451613
    Required arithmetic recovery gain70233.3333333333
    Required arithmetic recovery gain71244.8275862069
    Required arithmetic recovery gain72257.1428571429
    Required arithmetic recovery gain73270.3703703704
    Required arithmetic recovery gain74284.6153846154
    Required arithmetic recovery gain75300
    Required arithmetic recovery gain76316.6666666667
    Required arithmetic recovery gain77334.7826086957
    Required arithmetic recovery gain78354.5454545455
    Required arithmetic recovery gain79376.1904761905
    Required arithmetic recovery gain80400
    Recovery uses the smaller remaining balance: numerical comparison
    Drawdown from ₹5,00,000Remaining equityGain needed on remainder
    10.00%₹4,50,000.0011.11%
    20.00%₹4,00,000.0025.00%
    50.00%₹2,50,000.00100.00%
    80.00%₹1,00,000.00400.00%

    After a 20% loss, ₹4,00,000 remains. The missing ₹1,00,000 is 25% of that. A 50% loss needs a 100% gain.

    This is arithmetic, not a forecast. Costs would add to the gain needed. A zero balance cannot be recovered by any percentage.

    Inspect the recovery denominator

    H is the reference equity, E is remaining equity and D is decimal drawdown.

    1. D = (H − E) / H
    2. Required gain = H / E − 1 = D / (1 − D)
    3. 20% drawdown: 0.20 / 0.80 = 0.25 = 25%

    If the drawdown is D, the gain needed to recover is D ÷ (1 − D). A 50% fall needs a 100% gain. An 80% fall needs a 400% gain. This assumes no deposits, withdrawals or costs on the way back, and it says nothing about whether or how soon you will recover. Risk management 101 draws the same climb for share investors; the next lesson in this series, risk per trade, handles account limits.

    Chapter 7Loss definitions2 min read

    Which loss number belongs to which position?

    Match each position to its own loss measure.

    Short answer: each position has its own loss measure, and you must use the right one. A bought NIFTY Call at ₹100 per unit, paid for in full, costs 65 × ₹100 = ₹6,500. That is the most it can lose before costs, so on a full-premium basis it fits zero lots against a ₹5,000 allowance. If you plan to sell at ₹40, the estimated loss is ₹3,900, but that is a plan, not the ₹6,500 limit, and nobody guarantees a fill at ₹40. Index points and option premium rupees are different things, so a stop on the index cannot be dropped into an option loss formula.

    A matched Call credit spread has a 100-point strike width and a filled net credit of ₹30 per unit. Its worst loss at expiry, before costs, is (100 − 30) × 65 = ₹4,550. One lot fits the ₹5,000 allowance. A debit spread uses its net debit as its worst loss. These limits only hold if you keep both legs and the legs match. They do not guarantee an exit price or cover delivery funds for stock options.

    Four different loss measures

    Name the loss basis before dividing

    Four separate NIFTY positions, 65 assumed units each, before costs. An exit estimate, a payoff bound and a stress case mean different things.

    Name the loss basis before dividing: numerical comparison
    PositionDeclared loss basisOne-lot amountBoundary / funding check
    Long futuresPlanned exit 25,000 → 24,850: 150 futures-price points.₹9,750Exit at 24,750 instead loses ₹16,250 before costs. Check collateral and MTM cash separately.
    Bought cash-settled Call · C / CEStandalone index option; ₹100 premium per unit can be lost in full.₹6,500Gross terminal maximum option loss before costs. 0 lots fit ₹5,000 on this basis. Pay premium upfront.
    Call credit vertical · C / CESame expiry; 100-point strike width less ₹30 net credit per unit.₹4,550Gross expiry loss bound for both matched legs retained. 1 lot fits before costs; collateral remains separate.
    Uncovered short Call · C / CEStrike 25,000, premium ₹100; assumed final reference 25,300.₹13,000 stress lossOne constructed adverse outcome, not maximum loss. The model permits unbounded upside loss. Margin is not a loss cap.

    Only the bought option and the finished spread have a stated worst loss. The futures exit and the short Call stress case are estimates, not maximums.

    Blue marks the Call contract, not profit. A spread bound needs both legs, the same underlying, expiry and quantity. Stock options can need delivery cash or shares, so a premium limit does not cap settlement funding.

    Keep the units consistent

    Futures-price distance and option-premium loss are different inputs. An underlying move is not an interchangeable option-premium move.

    1. Bought Call full premium = 100 × 65 = ₹6,500
    2. Matched credit vertical = (100 − 30) × 65 = ₹4,550
    3. Short Call stress loss = (max(25,300 − 25,000, 0) − 100) × 65 = ₹13,000

    A naked short Call has no upper limit on loss, because the index can keep rising. A naked short Put can lose a very large but finite amount, since the index cannot fall below zero. A stress loss at one chosen level is only that scenario, and margin is neither of these. A stock option that settles by delivery can ask for strike money or shares, so its premium limit does not cap the delivery funds or later losses on shares.

    Chapter 8Binary growth model2 min read

    What does the Kelly formula answer, and what does it not?

    Learn what the Kelly formula answers and its limits.

    Short answer: Kelly finds the bet size that grows money fastest in a simple repeated game whose odds you already know. It does not tell you how much to risk in real options trading. Our game has two outcomes. You lose a fraction f of your equity, or you win b times that fraction, and the chance of winning is p.

    For p between 0 and 1 and f below 1, expected log growth is p × ln(1 + bf) + (1 − p) × ln(1 − f). The best f is p − (1 − p) ÷ b. If that comes out negative, the best bet in this game is zero. If you do not know p, you cannot run the calculation, and the right input is not 50%.

    A different assumed win probability moves the optimum

    A two-outcome game: lose f of equity, or win 2 × f. Compare win chances of 50% and 40%.

    • Win chance p = 50% · win pays 2×Solid line
    • Win chance p = 40% · win pays 2×Dashed line

    Expected log growth per trial · natural log, dimensionless

    Expected log growth per trial · natural log, dimensionless against Fraction of equity lost on failure · %Exact supplied series. Legend identifies solid and dashed lines. All plotted values are available in the following accessible table. Plotted from 0% to 60% in steps of 0.5 points. Growth falls without limit as the bet nears 100%, so that end is left off.

    Fraction of equity lost on failure · %

    Drag the slider to read each line at that point.
    • p = 50%: model maximum at 25.00%
    • p = 40%: model maximum at 10.00%

    Plotted from 0% to 60% in steps of 0.5 points. Growth falls without limit as the bet nears 100%, so that end is left off.

    Complete plotted values: Expected log growth per trial · natural log, dimensionless against Fraction of equity lost on failure · %
    SeriesFraction of equity lost on failure · %Expected log growth per trial · natural log, dimensionless
    Win chance p = 50% · win pays 2×00
    Win chance p = 50% · win pays 2×0.50.0024688945
    Win chance p = 50% · win pays 2×10.0048761457
    Win chance p = 50% · win pays 2×1.50.0072225822
    Win chance p = 50% · win pays 2×20.0095090029
    Win chance p = 50% · win pays 2×2.50.0117361781
    Win chance p = 50% · win pays 2×30.0139048503
    Win chance p = 50% · win pays 2×3.50.0160157354
    Win chance p = 50% · win pays 2×40.0180695233
    Win chance p = 50% · win pays 2×4.50.0200668789
    Win chance p = 50% · win pays 2×50.0220084427
    Win chance p = 50% · win pays 2×5.50.0238948319
    Win chance p = 50% · win pays 2×60.0257266408
    Win chance p = 50% · win pays 2×6.50.0275044415
    Win chance p = 50% · win pays 2×70.0292287848
    Win chance p = 50% · win pays 2×7.50.0309002005
    Win chance p = 50% · win pays 2×80.0325191981
    Win chance p = 50% · win pays 2×8.50.0340862676
    Win chance p = 50% · win pays 2×90.0356018795
    Win chance p = 50% · win pays 2×9.50.0370664859
    Win chance p = 50% · win pays 2×100.0384805206
    Win chance p = 50% · win pays 2×10.50.0398443995
    Win chance p = 50% · win pays 2×110.0411585212
    Win chance p = 50% · win pays 2×11.50.0424232677
    Win chance p = 50% · win pays 2×120.0436390041
    Win chance p = 50% · win pays 2×12.50.0448060793
    Win chance p = 50% · win pays 2×130.0459248268
    Win chance p = 50% · win pays 2×13.50.0469955642
    Win chance p = 50% · win pays 2×140.0480185941
    Win chance p = 50% · win pays 2×14.50.0489942042
    Win chance p = 50% · win pays 2×150.0499226675
    Win chance p = 50% · win pays 2×15.50.0508042428
    Win chance p = 50% · win pays 2×160.0516391747
    Win chance p = 50% · win pays 2×16.50.0524276941
    Win chance p = 50% · win pays 2×170.0531700179
    Win chance p = 50% · win pays 2×17.50.0538663499
    Win chance p = 50% · win pays 2×180.0545168805
    Win chance p = 50% · win pays 2×18.50.055121787
    Win chance p = 50% · win pays 2×190.0556812339
    Win chance p = 50% · win pays 2×19.50.0561953728
    Win chance p = 50% · win pays 2×200.0566643427
    Win chance p = 50% · win pays 2×20.50.05708827
    Win chance p = 50% · win pays 2×210.057467269
    Win chance p = 50% · win pays 2×21.50.0578014415
    Win chance p = 50% · win pays 2×220.0580908771
    Win chance p = 50% · win pays 2×22.50.0583356534
    Win chance p = 50% · win pays 2×230.0585358358
    Win chance p = 50% · win pays 2×23.50.0586914778
    Win chance p = 50% · win pays 2×240.058802621
    Win chance p = 50% · win pays 2×24.50.0588692951
    Win chance p = 50% · win pays 2×250.0588915178
    Win chance p = 50% · win pays 2×25.50.0588692951
    Win chance p = 50% · win pays 2×260.058802621
    Win chance p = 50% · win pays 2×26.50.0586914778
    Win chance p = 50% · win pays 2×270.0585358358
    Win chance p = 50% · win pays 2×27.50.0583356534
    Win chance p = 50% · win pays 2×280.0580908771
    Win chance p = 50% · win pays 2×28.50.0578014415
    Win chance p = 50% · win pays 2×290.057467269
    Win chance p = 50% · win pays 2×29.50.05708827
    Win chance p = 50% · win pays 2×300.0566643427
    Win chance p = 50% · win pays 2×30.50.0561953728
    Win chance p = 50% · win pays 2×310.0556812339
    Win chance p = 50% · win pays 2×31.50.055121787
    Win chance p = 50% · win pays 2×320.0545168805
    Win chance p = 50% · win pays 2×32.50.0538663499
    Win chance p = 50% · win pays 2×330.0531700179
    Win chance p = 50% · win pays 2×33.50.0524276941
    Win chance p = 50% · win pays 2×340.0516391747
    Win chance p = 50% · win pays 2×34.50.0508042428
    Win chance p = 50% · win pays 2×350.0499226675
    Win chance p = 50% · win pays 2×35.50.0489942042
    Win chance p = 50% · win pays 2×360.0480185941
    Win chance p = 50% · win pays 2×36.50.0469955642
    Win chance p = 50% · win pays 2×370.0459248268
    Win chance p = 50% · win pays 2×37.50.0448060793
    Win chance p = 50% · win pays 2×380.0436390041
    Win chance p = 50% · win pays 2×38.50.0424232677
    Win chance p = 50% · win pays 2×390.0411585212
    Win chance p = 50% · win pays 2×39.50.0398443995
    Win chance p = 50% · win pays 2×400.0384805206
    Win chance p = 50% · win pays 2×40.50.0370664859
    Win chance p = 50% · win pays 2×410.0356018795
    Win chance p = 50% · win pays 2×41.50.0340862676
    Win chance p = 50% · win pays 2×420.0325191981
    Win chance p = 50% · win pays 2×42.50.0309002005
    Win chance p = 50% · win pays 2×430.0292287848
    Win chance p = 50% · win pays 2×43.50.0275044415
    Win chance p = 50% · win pays 2×440.0257266408
    Win chance p = 50% · win pays 2×44.50.0238948319
    Win chance p = 50% · win pays 2×450.0220084427
    Win chance p = 50% · win pays 2×45.50.0200668789
    Win chance p = 50% · win pays 2×460.0180695233
    Win chance p = 50% · win pays 2×46.50.0160157354
    Win chance p = 50% · win pays 2×470.0139048503
    Win chance p = 50% · win pays 2×47.50.0117361781
    Win chance p = 50% · win pays 2×480.0095090029
    Win chance p = 50% · win pays 2×48.50.0072225822
    Win chance p = 50% · win pays 2×490.0048761457
    Win chance p = 50% · win pays 2×49.50.0024688945
    Win chance p = 50% · win pays 2×500
    Win chance p = 50% · win pays 2×50.5−0.0025313972
    Win chance p = 50% · win pays 2×51−0.0051261882
    Win chance p = 50% · win pays 2×51.5−0.0077852975
    Win chance p = 50% · win pays 2×52−0.0105096836
    Win chance p = 50% · win pays 2×52.5−0.0133003409
    Win chance p = 50% · win pays 2×53−0.0161583007
    Win chance p = 50% · win pays 2×53.5−0.0190846331
    Win chance p = 50% · win pays 2×54−0.0220804479
    Win chance p = 50% · win pays 2×54.5−0.025146897
    Win chance p = 50% · win pays 2×55−0.0282851757
    Win chance p = 50% · win pays 2×55.5−0.0314965247
    Win chance p = 50% · win pays 2×56−0.0347822317
    Win chance p = 50% · win pays 2×56.5−0.0381436341
    Win chance p = 50% · win pays 2×57−0.0415821206
    Win chance p = 50% · win pays 2×57.5−0.045099134
    Win chance p = 50% · win pays 2×58−0.048696173
    Win chance p = 50% · win pays 2×58.5−0.0523747956
    Win chance p = 50% · win pays 2×59−0.0561366212
    Win chance p = 50% · win pays 2×59.5−0.059983334
    Win chance p = 50% · win pays 2×60−0.0639166858
    Win chance p = 40% · win pays 2×00
    Win chance p = 40% · win pays 2×0.50.0009726072
    Win chance p = 40% · win pays 2×10.0018908494
    Win chance p = 40% · win pays 2×1.50.0027553382
    Win chance p = 40% · win pays 2×20.0035666609
    Win chance p = 40% · win pays 2×2.50.0043253809
    Win chance p = 40% · win pays 2×30.0050320388
    Win chance p = 40% · win pays 2×3.50.0056871528
    Win chance p = 40% · win pays 2×40.0062912197
    Win chance p = 40% · win pays 2×4.50.0068447154
    Win chance p = 40% · win pays 2×50.0073480953
    Win chance p = 40% · win pays 2×5.50.0078017952
    Win chance p = 40% · win pays 2×60.0082062319
    Win chance p = 40% · win pays 2×6.50.0085618033
    Win chance p = 40% · win pays 2×70.0088688893
    Win chance p = 40% · win pays 2×7.50.0091278521
    Win chance p = 40% · win pays 2×80.0093390367
    Win chance p = 40% · win pays 2×8.50.0095027713
    Win chance p = 40% · win pays 2×90.0096193677
    Win chance p = 40% · win pays 2×9.50.0096891217
    Win chance p = 40% · win pays 2×100.0097123133
    Win chance p = 40% · win pays 2×10.50.0096892074
    Win chance p = 40% · win pays 2×110.0096200537
    Win chance p = 40% · win pays 2×11.50.0095050874
    Win chance p = 40% · win pays 2×120.0093445289
    Win chance p = 40% · win pays 2×12.50.009138585
    Win chance p = 40% · win pays 2×130.008887448
    Win chance p = 40% · win pays 2×13.50.008591297
    Win chance p = 40% · win pays 2×140.0082502973
    Win chance p = 40% · win pays 2×14.50.0078646013
    Win chance p = 40% · win pays 2×150.0074343481
    Win chance p = 40% · win pays 2×15.50.0069596639
    Win chance p = 40% · win pays 2×160.0064406624
    Win chance p = 40% · win pays 2×16.50.0058774444
    Win chance p = 40% · win pays 2×170.0052700987
    Win chance p = 40% · win pays 2×17.50.0046187014
    Win chance p = 40% · win pays 2×180.0039233167
    Win chance p = 40% · win pays 2×18.50.0031839965
    Win chance p = 40% · win pays 2×190.0024007809
    Win chance p = 40% · win pays 2×19.50.0015736979
    Win chance p = 40% · win pays 2×200.0007027639
    Win chance p = 40% · win pays 2×20.5−0.0002120168
    Win chance p = 40% · win pays 2×21−0.0011706515
    Win chance p = 40% · win pays 2×21.5−0.002173159
    Win chance p = 40% · win pays 2×22−0.0032195701
    Win chance p = 40% · win pays 2×22.5−0.0043099272
    Win chance p = 40% · win pays 2×23−0.0054442842
    Win chance p = 40% · win pays 2×23.5−0.0066227068
    Win chance p = 40% · win pays 2×24−0.0078452723
    Win chance p = 40% · win pays 2×24.5−0.0091120699
    Win chance p = 40% · win pays 2×25−0.0104232002
    Win chance p = 40% · win pays 2×25.5−0.011778776
    Win chance p = 40% · win pays 2×26−0.0131789217
    Win chance p = 40% · win pays 2×26.5−0.0146237737
    Win chance p = 40% · win pays 2×27−0.0161134803
    Win chance p = 40% · win pays 2×27.5−0.0176482021
    Win chance p = 40% · win pays 2×28−0.0192281117
    Win chance p = 40% · win pays 2×28.5−0.020853394
    Win chance p = 40% · win pays 2×29−0.0225242466
    Win chance p = 40% · win pays 2×29.5−0.0242408792
    Win chance p = 40% · win pays 2×30−0.0260035147
    Win chance p = 40% · win pays 2×30.5−0.0278123885
    Win chance p = 40% · win pays 2×31−0.0296677491
    Win chance p = 40% · win pays 2×31.5−0.0315698585
    Win chance p = 40% · win pays 2×32−0.0335189918
    Win chance p = 40% · win pays 2×32.5−0.0355154377
    Win chance p = 40% · win pays 2×33−0.037559499
    Win chance p = 40% · win pays 2×33.5−0.0396514924
    Win chance p = 40% · win pays 2×34−0.041791749
    Win chance p = 40% · win pays 2×34.5−0.0439806144
    Win chance p = 40% · win pays 2×35−0.0462184492
    Win chance p = 40% · win pays 2×35.5−0.0485056291
    Win chance p = 40% · win pays 2×36−0.0508425452
    Win chance p = 40% · win pays 2×36.5−0.0532296046
    Win chance p = 40% · win pays 2×37−0.0556672305
    Win chance p = 40% · win pays 2×37.5−0.0581558624
    Win chance p = 40% · win pays 2×38−0.0606959569
    Win chance p = 40% · win pays 2×38.5−0.0632879881
    Win chance p = 40% · win pays 2×39−0.0659324474
    Win chance p = 40% · win pays 2×39.5−0.0686298446
    Win chance p = 40% · win pays 2×40−0.0713807083
    Win chance p = 40% · win pays 2×40.5−0.074185586
    Win chance p = 40% · win pays 2×41−0.0770450448
    Win chance p = 40% · win pays 2×41.5−0.0799596723
    Win chance p = 40% · win pays 2×42−0.0829300766
    Win chance p = 40% · win pays 2×42.5−0.0859568873
    Win chance p = 40% · win pays 2×43−0.0890407558
    Win chance p = 40% · win pays 2×43.5−0.0921823564
    Win chance p = 40% · win pays 2×44−0.0953823864
    Win chance p = 40% · win pays 2×44.5−0.0986415675
    Win chance p = 40% · win pays 2×45−0.101960646
    Win chance p = 40% · win pays 2×45.5−0.1053403938
    Win chance p = 40% · win pays 2×46−0.1087816092
    Win chance p = 40% · win pays 2×46.5−0.1122851181
    Win chance p = 40% · win pays 2×47−0.1158517742
    Win chance p = 40% · win pays 2×47.5−0.1194824608
    Win chance p = 40% · win pays 2×48−0.1231780911
    Win chance p = 40% · win pays 2×48.5−0.1269396099
    Win chance p = 40% · win pays 2×49−0.1307679941
    Win chance p = 40% · win pays 2×49.5−0.1346642543
    Win chance p = 40% · win pays 2×50−0.1386294361
    Win chance p = 40% · win pays 2×50.5−0.142664621
    Win chance p = 40% · win pays 2×51−0.1467709282
    Win chance p = 40% · win pays 2×51.5−0.1509495156
    Win chance p = 40% · win pays 2×52−0.1552015819
    Win chance p = 40% · win pays 2×52.5−0.1595283677
    Win chance p = 40% · win pays 2×53−0.1639311574
    Win chance p = 40% · win pays 2×53.5−0.1684112811
    Win chance p = 40% · win pays 2×54−0.1729701162
    Win chance p = 40% · win pays 2×54.5−0.1776090896
    Win chance p = 40% · win pays 2×55−0.1823296798
    Win chance p = 40% · win pays 2×55.5−0.1871334191
    Win chance p = 40% · win pays 2×56−0.1920218958
    Win chance p = 40% · win pays 2×56.5−0.1969967568
    Win chance p = 40% · win pays 2×57−0.2020597106
    Win chance p = 40% · win pays 2×57.5−0.2072125292
    Win chance p = 40% · win pays 2×58−0.2124570519
    Win chance p = 40% · win pays 2×58.5−0.2177951882
    Win chance p = 40% · win pays 2×59−0.2232289208
    Win chance p = 40% · win pays 2×59.5−0.2287603096
    Win chance p = 40% · win pays 2×60−0.234391495
    A different assumed win probability moves the optimum: numerical comparison
    Fraction lost on failureWin / loss wealth multipliersLog growth: p = 50%Log growth: p = 40%
    0.00%1.00 / 1.000.0000000.000000
    10.00%1.20 / 0.90+0.038481+0.009712
    25.00%1.50 / 0.75+0.058892−0.010423
    40.00%1.80 / 0.60+0.038481−0.071381
    60.00%2.20 / 0.40−0.063917−0.234391

    The best size falls from 25% to 10% when the win chance falls from 50% to 40%. At 25%, the second case already shrinks wealth.

    Two fixed outcomes, known odds, any bet size, no costs. The odds are invented. Log growth is not a rupee or percentage return, and this does not show an options edge or an allocation.

    Inspect the binary log-growth model

    Natural logarithms act on the two wealth multipliers; b denotes net win divided by the amount lost.

    1. g(f) = p × ln(1 + b × f) + (1 − p) × ln(1 − f)
    2. For 0 < p < 1 and b > 0: constrained optimum = max(0, p − (1 − p) / b)
    3. p = 0.50, b = 2: f* = 0.25; p = 0.40, b = 2: f* = 0.10
    4. A non-positive edge gives a zero non-negative-wager optimum; missing probability inputs give no calculation.

    With p = 50% and b = 2, the best fraction is 25%. Expected log growth there is about 0.05889 per trial. At 10% or 40% it is about 0.03848, and at 60% it turns negative. These are log numbers for this toy game. They are not percentage returns and not advice to risk 25%.

    Now change p to 40%, with b still 2. The best fraction drops to 10%, and the old 25% bet gives negative growth. A small error in the odds can turn a good size into a bad one. Real trades have costs, jumps and positions that move together. Full Kelly is not a safe ceiling, and betting less than Kelly does not guarantee survival. The curve offers no measured NIFTY edge.

    Chapter 9Shared exposure2 min read

    How much do all your open positions risk together?

    Add up the risk of all open positions together.

    Short answer: add the allowances, then test one shared market move. Four positions that each carry a ₹5,000 allowance on a ₹5 lakh account carry ₹20,000 together, or 4%. That sum holds whether the positions are related or not. Relatedness matters for how they move together, not for the addition.

    Add the allowances, then test a joint outcome

    A ₹5,00,000 account, four positions, ₹5,000 allowance each. Two stress cases give every position the same loss.

    Planned allowance ledger

    Four allowances of ₹5,000
    ₹20,000.00

    4.00% of starting equity; the sum is unchanged by dependence between positions.

    Funds and clearing margin
    Separate check

    No margin, premium availability or delivery-funding requirement is computed here.

    Separate assumed stress case 1

    Loss on each of four positions
    −₹3,500.00
    Combined account P&L
    −₹14,000.00

    2.80% loss of starting equity; this is a scenario assumption, not a probability estimate.

    Separate assumed stress case 2

    Loss on each of four positions
    −₹7,500.00
    Combined account P&L
    −₹30,000.00

    6.00% loss of starting equity; this is a scenario assumption, not a probability estimate.

    Add the allowances, then test a joint outcome: numerical comparison
    PositionPlanned allowanceStress 1: assumed P&LStress 2: assumed P&L
    Position 1₹5,000.00−₹3,500.00−₹7,500.00
    Position 2₹5,000.00−₹3,500.00−₹7,500.00
    Position 3₹5,000.00−₹3,500.00−₹7,500.00
    Position 4₹5,000.00−₹3,500.00−₹7,500.00
    Account total₹20,000.00−₹14,000.00−₹30,000.00

    Allowances add to ₹20,000, or 4%. The first stress loses ₹14,000 (2.80%); the second loses ₹30,000 (6.00%), more than the plan. Different names can share one driver.

    Each case adds four losses from one assumed market state. These are made-up amounts, not forecasts or maximum losses. Real gaps, costs and fills can differ.

    Inspect the account-wide addition

    Allowances are positive planning amounts; scenario P&Ls carry their actual signs.

    1. Planned sum = 4 × 5000 = ₹20,000.00 = 4.00% of starting equity
    2. Stress 1 P&L = 4 × (−3500) = −₹14,000.00
    3. Stress 2 P&L = 4 × (−7500) = −₹30,000.00

    A single NIFTY move can hit your Calls, your futures and your bank stocks at once. Pick one move, work out each position's own result, and add the signed rupees. In the separate example below, four scenario losses of ₹3,500 total ₹14,000, and four stress losses of ₹7,500 total ₹30,000, which is more than the combined allowance. Neither case claims a probability, or that everything always falls together.

    Events, thin liquidity, costs and limited funds can all be reasons to trade smaller than the formula allows. A written account rule for what you do at a drawdown boundary helps, but it has costs too, and it does not promise a recovery. India VIX does not set your stop width. Keep your inputs, contracts, whole quantities and real fills on record. The next lesson separates a planned risk from a loss that actually happened.

    Before you go

    Check yourself

    5 questions from this lesson. Pick an answer to see why, then slide on to the next.

    Question 1 of 5

    The fictional ₹5,00,000 account uses a 1% allowance. A futures exit estimate is 150 points away, with 65 assumed units per lot. What quantity fits before costs and funding checks?

    Questions readers ask

    Common questions

    How do I calculate whole lots for a hypothetical NIFTY futures position?

    Multiply equity by your loss fraction to get the allowance. Divide it by the planned loss on one lot (points × units), then round down. In the example, ₹5,00,000 × 1% = ₹5,000, and 150 points × 65 units = ₹9,750 per lot. ₹5,000 ÷ ₹9,750 is about 0.513, so the answer is 0 lots. The 65-unit lot is an assumption; use the dated lot size of the contract you trade.

    What does zero lots mean in a position-sizing calculation?

    It means this position does not fit this allowance. One lot would put 1.95% of the account at risk against a 1% allowance. Zero is a valid answer, not an error. Moving your exit closer only to force one lot changes the plan to fit the answer; it does not make the trade safer.

    Does a stop-loss order cap the loss at the amount used for sizing?

    No. A stop triggers an order, but it does not fix the fill price. In the example, a fill at 24,750 after entry at 25,000 loses 250 × 65 = ₹16,250, not the ₹9,750 planned at 24,850. For an option, measure the loss in premium rupees, not index points.

    Is a bought option sized from its premium, and what changes for stock options?

    Yes, for a standalone bought index Call the most you can lose is the premium: ₹100 × 65 = ₹6,500 before costs, which gives 0 lots against ₹5,000. A planned earlier sale can use a smaller estimate, but label it a plan, not the maximum. Stock options settle by delivery, so an exercised Call needs strike money and an exercised Put needs shares. The premium limit does not cap that funding or later losses on the shares.

    How does fixed-fraction sizing differ from fixed cash or fixed lots after a loss?

    Fixed-fraction sizing recalculates the allowance from current equity: after a ₹5,000 loss, 1% of ₹4,95,000 is ₹4,950. Fixed cash keeps ₹5,000, a larger share of a smaller account. Fixed lots keep the quantity, and the rupee loss stays constant only if the per-unit loss does. None of these guarantees survival. Recovery is measured on what is left: a 20% loss needs a 25% gain.

    How do spread loss and available margin constrain the final lot count?

    Take the smaller of two whole-lot limits. The Call spread loses at most (100 − 30) × 65 = ₹4,550 per lot, so a ₹20,000 allowance on ₹10,00,000 permits four lots. If only ₹1,80,000 is free and each lot needs ₹1,80,000, funding permits one. The answer is one. Real margin changes with your other positions and is collateral, not a loss cap.

    Can Kelly determine a suitable risk percentage for live options trading?

    No. Kelly solves a simple repeated game with known odds. With a 50% win chance and a win twice the size of a loss, the best size is 25%; at a 40% chance it is 10%. Real trades have costs, jumps and unknown odds, and an unknown chance is not 50%. Treat Kelly as a way to see how sensitive size is to the odds, not as an allocation.

    Do separate positions each get an independent account risk allowance?

    No. Look at the whole account. Two ₹5,000 allowances add to ₹10,000. Under a ₹12,000 account limit only ₹2,000 remains, so a third ₹5,000 fails. Positions with different names can share one driver, so test them together under one market move and check cash and collateral for all of them.

    Sources for further reading

    17 sources

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