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Hedge Ratio
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Simplified Version / Comprehensive Version
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What Is Hedge Ratio?
A hedge ratio calculates the amount of derivatives needed to hedge against the risk of loss in a portfolio of stocks or other derivatives.
The hedge ratio needed to completely hedge against loss in a portfolio is expressed as h=-1 derived from:
Hedge Ratio For Options Trading = Total Delta Equivalent / Total Stock Value
H=-1 means that long puts options or short call options positions (both providing negative deltas)
that are equal in magnitude to the underlying stocks are needed to exactly offset moves in the underlying stocks. In fact,
what we just described here are the Protective Put and
Covered Call option trading strategies!
You can derive the exact number of put options to buy or call options to write
by rearranging the hedge ratio formula to:
Total Delta Equivalent = Total Stock Value x -1
therefore,
Number of contracts = Total Stock Value x -1 / Delta Per Contract
Example : Assuming you own 700 shares of QQQQ at $44. You are trying to hedge with at the money
put options producing delta per contract of -50.
Number Of Contracts = (700 x 44) x -1 / -50 = -30,800 / -50 = 616 contracts
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Now, because delta value changes all the time, Dynamic Hedging is needed to
rebalance the position from time to time so as to maintain the hedge ratio of h=-1.
Hedge Ratio For Stock Options
To completely hedge against downside risk to a portfolio of stock options, the same hedge ratio of h=-1 applies. The hedge ratio formula in this case is
slightly different:
Hedge Ratio = Total Delta Of Hedging Options / Total Delta Of Current Holding
You can also derive the exact number of contracts needed to hedge against current options positions by rearranging the formula as:
Total Delta Of Hedging Options = Total Delta Of Current Holding x -1
therefore,
Number Of Contracts = (Total Delta Of Current Holding x -1) / Delta Per Contract
Example : Assuming you own 10 contracts of QQQQ $42 call options with delta of 80 per contract with QQQQ trading at $44 now.
You are trying to hedge with at the money
put options producing delta per contract of -50.
Number Of Contracts = (10 x 80) x -1 / -50 = -800 / -50 = 16 contracts
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When options positions achieve a hedge ratio of h=-1, it is said to be Delta Neutral.
Hedge Ratio Conclusion
Hedging is not limited to options trading, therefore, hedge ratios are used in the hedging of every kind of financial instruments. No matter what instruments are being hedged against,
the same magic hedge ratio applies:
H = -1
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