Delta
The change in an option's value for a small change in the underlying price: between 0 and 1 for a call, between −1 and 0 for a put. It is also the hedge ratio, the units of the underlying that offset one option.
Where you will meet it
Delta appears in 12 learning outcomes on the CFA syllabus. A few of them:
- Explain sensitivity and scenario risk measures and weigh them against VaR
“Sensitivity measures show how value changes for a small move in one risk factor: beta for equity markets, duration and convexity for interest rates, delta, gamma and vega for options.”
- Discuss relative value hedge fund strategies: their investment features, how they are put into practice and the role they play in a portfolio
“Convertible bond arbitrage buys convertibles whose embedded options look cheap and shorts the issuer's shares in proportion to the option's delta, earning coupon income and trading gains around the hedge.”
- Explain how the Black–Scholes–Merton call formula can be read as a leveraged holding of the underlying
“In symbols, where nS is the call's delta, B the present value of the strike and nB its weight N(d2), the risk-neutral chance of exercise, the call is c = nS × S − nB × B.”
- Contrast the deltas of a covered call and a protective put with that of an asset held long and hedged by a short forward
“Long asset plus short forward has delta 1 − 1 = 0: fully hedged, with neither upside nor downside.”
See also
Practise it
Practise delta until it is automatic: questions that explain every wrong option.
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