Lesson 1.2: Stocks, futures, options and FX
Learn what traders trade: shares and corporate actions, futures and margin, option payoffs and currency pairs, with the arithmetic of each worked by hand.
By the end of this lesson you will be able to describe the four main instruments traders use and what each one obliges the holder to do, price a future from the spot price with the cost-of-carry formula, calculate how leverage turns a small price move into a large return on margin, draw the profit and loss of a call and a put at expiry, read a currency quote and compute a forward rate from two interest rates, and adjust a share price history for splits and dividends. You will find that a 6 per cent fall on a futures contract wipes out half of its margin, that a call bought for ₹4 only breaks even at 104, and that a naive price series shows a 50 per cent "crash" on the day a share simply split two for one. You should have read Lesson 1.1, since the instruments here trade in the order books described there. The mathematics is percentages, one exponential and the maximum of two numbers. This course is education about how markets work, not investment advice.
A trading idea is always expressed through an instrument. "The market will rise" can be acted on by buying shares, buying a future, buying a call option or selling a put, and each has a different cost, a different risk and a different shape of profit and loss. A quant has to know the instruments well enough to pick the right one, and to know what is hidden in their price histories. This lesson takes the four main families in turn.
Shares
A share, or stock, is a unit of ownership in a company. The holder is entitled to a part of the profits, usually paid as dividends, and a vote at shareholder meetings. The price changes as people revise their view of the company's future earnings and as demand and supply shift. A share has no expiry and carries limited liability: the most a buyer can lose is the money paid.
You can also sell short: borrow shares, sell them, and buy them back later. The short seller gains if the price falls and loses if it rises, and because a price can rise without limit, the possible loss is in principle unlimited. Short selling needs a lender, a cost to borrow and strict rules, and regulators in many countries restrict or monitor it. In India, rules limit who may short sell in the cash market, so a lot of bearish positions are taken in the derivatives market instead.
Corporate actions and why price histories lie
A raw price history is not a record of returns, because companies do things that change the price without changing anyone's wealth. These corporate actions are a common source of silent errors in quant research.
A stock split divides each share into several. In a 2-for-1 split, a holder of one share at ₹1,000 becomes the holder of two shares at ₹500. The company is worth the same. A raw price series shows a fall from 1,000 to 500, a "return" of −50 per cent, that never happened.
A bonus issue gives extra shares free, and has the same effect on the price.
A dividend moves cash from the company to the shareholder. On the ex-dividend date the price drops by about the dividend. If a share closes at ₹1,000 and pays a dividend of ₹20, it opens at around ₹980 the next day. Looking at prices alone suggests a loss of 2 per cent, though the holder received ₹20 in cash and is no worse off.
Rights issues and mergers change the share count or the company itself.
The cure is to use adjusted prices, which are back-corrected so that returns are right. For the split, multiply every price before the split date by 0.5. The pre-split 1,000 becomes 500, and the return across the split date is 500 ÷ 500 − 1 = 0. For a dividend, multiply earlier prices by one minus the dividend divided by the previous close, here 1 − 20 ÷ 1,000 = 0.98. The pre-dividend 1,000 becomes 980, so the return across the ex-date is zero, which correctly shows that the holder lost nothing. This adjusted series gives the total return, with the dividend counted. Lesson 3.1 treats adjustment in detail. For now the point is that a backtest on unadjusted prices will find a spectacular "crash" every time a stock splits, and a strategy that profits from it.
Futures
A future is a contract to buy or sell an asset at an agreed price on a set future date. Both sides are obliged to complete: the buyer, who is long, must buy and the seller, who is short, must sell, at the agreed futures price. No one pays the full value upfront. Instead each side posts a deposit called margin, typically a modest share of the contract's value, to show good faith.
Futures are marked to market every day. At the end of each day, the exchange compares the settlement price with the previous day's, and the gain or loss is moved from one side's account to the other's in cash. If a loss eats into the margin below a required level, the broker issues a margin call, demanding more money, and if it is not paid the position is closed. This daily settlement is what makes futures safe for the exchange and dangerous for the unprepared trader.
Most futures contracts on indices, such as the Nifty, are cash settled: at expiry the difference between the futures price and the final index value is paid in cash, and no shares change hands. Single-stock futures in India are settled by physical delivery of shares, as many regulators prefer, and the rules differ by product, so check the exchange's contract specifications for the details.
Leverage
Margin makes futures leveraged: a small deposit controls a large position. Suppose a futures contract has a value of ₹10 lakh and the margin is ₹1.2 lakh, 12 per cent. A rise of 2 per cent in the price makes ₹20,000, which on the ₹1.2 lakh of margin is a return of 20,000 ÷ 120,000 = 16.7 per cent. The leverage is 10 ÷ 1.2 = 8.3 times. But it works equally on losses.
Predict first: you hold that futures contract, worth ₹10 lakh with ₹1.2 lakh of margin. The price falls 6 per cent. Will you lose about 6 per cent of the margin, about 12 per cent, or about half of it? Decide before reading on.
About half. The loss is 6 per cent of the ₹10 lakh contract value, ₹60,000, and that is 60,000 ÷ 120,000 = 50 per cent of the margin. A fall of 12 per cent would wipe the margin out entirely, and in practice the broker would have closed the position well before, after a margin call. Leverage multiplies returns in both directions, and the trader's job is to size positions so that a bad day does not end the game, a subject of Lesson 11.1.
The price of a future: cost of carry
The futures price is not a forecast of the spot price. It is tied to the spot price by a no-arbitrage argument. Suppose the spot price of an index is 100, you can borrow or lend at a yearly rate r, and the index pays a dividend yield q. To own the asset in three months you could either buy a future now, or buy the asset today with borrowed money and hold it. The second route costs interest on the borrowing, and earns the dividends. If the future were priced differently from the cost of the second route, an arbitrageur could buy the cheaper one, sell the dearer one and lock in a risk-free profit, and the trading would push the price back. So the fair futures price is
F = S × e^((r − q) × T)
where T is the time to expiry in years and e is the exponential constant 2.718. With S = 100, r = 7 per cent, q = 0 and T = 0.25, the fair price is 100 × e^(0.07 × 0.25) = 100 × e^0.0175 = 101.77. The future trades at a premium to spot of 1.77, which is the cost of carrying the asset for three months. If the dividend yield rose to 3 per cent, the exponent would fall to 0.01 and the fair price to 101.01. At expiry the future must equal the spot price, so the premium, called the basis, shrinks to zero as expiry nears.
Options
An option gives the buyer the right, but not the obligation, to buy or sell an asset at a fixed price. A call option gives the right to buy and a put gives the right to sell. The fixed price is the strike, the last date to use the right is the expiry, and the price paid for the option is the premium. The seller, called the writer, receives the premium and takes on the obligation if the buyer exercises.
The asymmetry is the whole point. The buyer's loss is limited to the premium, while the gain can be large. The writer's gain is limited to the premium, while the loss can be large. Exchange-traded index options in India are European style, meaning they can be exercised only at expiry, and they are cash settled. Other options can be American style, exercisable any time. The difference matters for pricing in Lesson 7.4.
Payoffs at expiry
At expiry, the value of an option depends only on the price of the asset, the spot price S, and the strike K.
A call is worth max(S − K, 0): it is worth something only if the price is above the strike.
A put is worth max(K − S, 0): it is worth something only if the price is below the strike.
The buyer's profit is the payoff minus the premium paid. Take a call with strike 100 bought for a premium of 4. If at expiry the price is 90, the option expires worthless and the buyer loses the premium, −4. At 100 it is also worthless: −4. At 104 the payoff is 4, just paying back the premium, so the profit is 0. This price, strike plus premium, is the breakeven. At 110 the payoff is 10 and the profit is 6. A put with strike 100 bought for 3 loses 3 at any price above 100, breaks even at 97, and at 90 pays 10, a profit of 7.
Options also have time value. Before expiry, an option is worth more than its payoff at that moment, the intrinsic value, because there is still time for the price to move. The extra is the time value, which shrinks to zero at expiry, a decay that works against the buyer and for the writer. Lesson 6.2 and Lesson 7.2 explain how it is priced.
Currencies
A foreign exchange, or FX, quote gives the price of one currency in terms of another. The quote USD/INR = 80.00 means one US dollar costs 80 rupees, with the first currency the base and the second the quote currency. A move to 80.50 means the dollar became dearer, up 0.5 ÷ 80 = 0.625 per cent, and the rupee weaker. Seen from the other side, one rupee used to buy 1 ÷ 80 = 0.012500 dollars and now buys 1 ÷ 80.5 = 0.012422, a fall of 0.62 per cent. The two percentages are nearly equal for small moves but not identical, a small trap when computing returns on a currency.
FX is quoted with a bid and an ask like any other market, and the smallest price step is called a pip, usually the fourth decimal place for major pairs. Most FX trading is OTC, between banks, though exchanges also list currency futures and options, such as those on the NSE.
The forward rate
A forward is an agreement made now to exchange currencies on a future date at a rate fixed today. Like a future, its price follows from no-arbitrage, here called covered interest parity. Suppose the spot rate is 80.00 rupees per dollar, the one-year interest rate in rupees is 7 per cent and in dollars 4 per cent. Starting with 80 rupees, you can either invest at home and have 80 × 1.07 = 85.60 rupees in a year, or convert to one dollar, invest at 4 per cent to have 1.04 dollars, and sell them forward. For both routes to give the same result, the forward rate must satisfy 1.04 × F = 85.60, so F = 82.31 rupees per dollar. The currency with the higher interest rate trades at a forward discount: the rupee is forecast to be weaker, 82.31 against 80.00 spot. The forward points are 2.31, an annual rate of about 2.9 per cent, close to the interest rate gap of 3 percentage points. This is not a forecast of where the rupee will be. It is the cost of money in each currency, and the real exchange rate in a year could be anywhere.
Choosing an instrument
The same view can be expressed in different instruments, each with a different cost and risk.
· Shares · Futures · Options (buyer) · Options (writer)Obligation · None · Both sides must settle · None, a right · Must perform if exercised
Upfront cost · Full price · Margin only · Premium · Margin, receives premium
Worst loss · The price paid · Larger than the margin · The premium · Very large, sometimes unlimited
Leverage · None, unless borrowed · High · High, in percentage terms · High
Expiry · None · Yes · Yes · Yes
Shape of profit · Straight line · Straight line · Bent: limited loss · Bent: limited gain
Main extra cost · Brokerage, taxes · Margin and daily settlement · Time decay · Tail risk
Quants choose among them for reasons beyond the view. Futures give cheap, liquid exposure to an index, shares allow a portfolio of individual names, options let you trade the size and direction of a move separately, and currency instruments carry a rate on top of the price. An idea that works in shares may be too costly in options, and one that requires shorting may be possible only through futures. The choice of instrument is part of the strategy.
python
import numpy as np
def futuresfair(spot, r, q, years):
"""Cost-of-carry price with continuous compounding."""
return spot np.exp((r - q) years)
def callpnl(price, strike, premium):
return np.maximum(price - strike, 0) - premium
def putpnl(price, strike, premium):
return np.maximum(strike - price, 0) - premium
def fxforward(spot, rquote, rbase, years=1.0):
"""Covered interest parity: forward = spot (1 + rquoteT) / (1 + rbaseT)."""
return spot (1 + rquote years) / (1 + rbase years)
print(round(futuresfair(100, 0.07, 0.0, 0.25), 2), round(futuresfair(100, 0.07, 0.03, 0.25), 2))
print(callpnl(np.array([90, 100, 104, 110]), 100, 4), putpnl(np.array([90, 97, 100]), 100, 3))
print(round(fxforward(80, 0.07, 0.04), 2))
leverage on a futures contract
contract, margin = 1000000, 120000
for move in (0.02, -0.06, -0.12):
pnl = contract move
print(f"move {move:+.0%}: pnl Rs {pnl:,.0f}, return on margin {pnl / margin:+.1%}")
adjusting a price history for a 2-for-1 split and a Rs 20 dividend
import pandas as pd
raw = pd.Series([1000.0, 1010.0, 505.0, 510.0, 490.0],
index=pd.todatetime(["2026-01-01", "2026-01-02", "2026-01-05", "2026-01-06", "2026-01-07"]))
adj = raw.copy()
adj[:"2026-01-02"] = 0.5 # split on 5 Jan: earlier prices halved
adj[:"2026-01-06"] = 1 - 20 / 510 # Rs 20 dividend, ex-date 7 Jan: earlier prices scaled down
print(raw.pctchange().round(3).tolist())
print(adj.pctchange().round(3).tolist()) # the fake -50% return on the split date disappears
Common mistakes
Backtesting on unadjusted prices. Splits and bonuses create fake crashes, and dividends create fake losses.
Reading the futures price as a forecast. It is spot plus the cost of carry. The premium says nothing about where the market is going.
Ignoring daily settlement. A futures position with a floating loss must be funded in cash every day, and a margin call can force you out at the worst moment.
Confusing a small margin with a small risk. Leverage makes the loss on the contract, not on the margin, your exposure.
Forgetting time decay. An option buyer can be right about direction and still lose, if the move is too slow.
Judging an option by its premium alone. Look at the breakeven. A call with strike 100 and premium 4 needs a rise to 104 just to break even.
Mixing up the two sides of a currency quote. A rise in USD/INR means the dollar is stronger and the rupee weaker.
Assuming a forward is a forecast. It is the cost of money in two currencies.
Assuming short selling is free or always allowed. It needs a lender, a borrowing cost and compliance with the rules.
Key takeaways
A share is ownership with limited loss. Splits, bonuses and dividends change the price without changing anyone's wealth, so research must use adjusted prices.
A future is a binding agreement with daily settlement and margin. A fall of 6 per cent on a contract with 12 per cent margin costs half of the margin.
The fair futures price is S × e^((r − q) × T), which is 101.77 for S = 100, r = 7 per cent, q = 0 and three months. It is a cost-of-carry price, not a forecast.
An option is a right, not an obligation. A call pays max(S − K, 0) and a put pays max(K − S, 0), and the buyer's loss is limited to the premium. A call with strike 100 and premium 4 breaks even at 104.
A currency quote gives the price of the base currency in the quote currency. The forward rate follows from interest rates: 80 × 1.07 ÷ 1.04 = 82.31.
The choice of instrument sets the cost, the risk and the shape of the profit, and is part of the strategy.
Check yourself
1. A stock closes at ₹800 and splits 4-for-1 the next day, opening at ₹200. What is the true return, and what does the raw series show?
The true return is 0 (800 ÷ 4 = 200, so nothing changed). The raw series shows 200 ÷ 800 − 1 = −75 per cent.
2. A futures contract worth ₹5 lakh has margin of 10 per cent. The price rises 3 per cent. What is the return on the margin?
The gain is 3 per cent of ₹5 lakh, ₹15,000, on a margin of ₹50,000, so the return is 30 per cent.
3. Spot is 200, the interest rate is 6 per cent a year, there are no dividends, and the future expires in six months. What is the fair futures price?
200 × e^(0.06 × 0.5) = 200 × e^0.03 = 206.09.
4. You buy a put with strike 50 for a premium of 2. What is the breakeven, and what is the most you can lose?
Breakeven is 50 − 2 = 48. The most you can lose is the premium of 2.
5. The spot rate for USD/INR is 83 and the one-year rates are 6.5 per cent for INR and 3.5 per cent for USD. What is the one-year forward rate?
83 × 1.065 ÷ 1.035 = 85.41.
Try this
Set aside forty-five minutes and use a spreadsheet or the Python functions above.
1. Take the price history of a share that has split or paid a bonus, and compute daily returns from the raw and the adjusted prices. Find the date where they differ.
2. Compute the fair price of a one-month and a three-month index future from today's rate and a dividend yield you assume, and compare them with the traded prices. Note the gap.
3. For a futures position of your choice, write down the margin, the contract value and the leverage, and use the leverage simulator to find the price move that would trigger a margin call at 50 per cent loss of margin.
4. Draw the profit and loss at expiry of a call, a put, and a call and put with the same strike bought together, over a wide range of prices.
5. Find the breakeven of three options of your choice and say how far the price must move.
6. Take a currency pair and compute the forward rate from two interest rates, then compare it with a quoted forward if you can.
7. Write a short note: for the view that a stock will rise over the next month, list three ways to express it, with the cost, the worst loss and the breakeven of each.
A good result is a table of three ways to express one view, with the cost, the breakeven and the worst loss of each, and one chart of an option's profit at expiry. The next lesson turns from instruments to returns: how to measure gains correctly, compound them and describe risk.
Read more
Options, Futures and Other Derivatives by John Hull is the standard introduction to the instruments and their pricing, and Option Volatility and Pricing by Sheldon Natenberg is a practical guide to options from a trader's side. For contract specifications, margins and lot sizes, use the exchange's own website, since they are revised from time to time.
Tags: Quant Trader Futures Options Foreign exchange Leverage