Optimal Hedge Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Optimal Hedge Ratio = (Standard Deviation of Changes in Spot Price/Standard Deviation of Changes in Futures Price)*Correlation of Changes in Spot and Futures Prices
Δoptimal = (σs/σf)*ρs/f
This formula uses 4 Variables
Variables Used
Optimal Hedge Ratio - Optimal Hedge Ratio is the proportion of a position in a hedging asset relative to the position being hedged, aiming to minimize risk exposure while maximizing effectiveness in hedging.
Standard Deviation of Changes in Spot Price - Standard Deviation of Changes in Spot Price measures the volatility or variability of price movements over time for a financial asset or security.
Standard Deviation of Changes in Futures Price - Standard Deviation of Changes in Futures Price measures the variability or dispersion of price movements over time for a futures contract, reflecting the degree of market volatility.
Correlation of Changes in Spot and Futures Prices - Correlation of Changes in Spot and Futures Prices is the linear relationship between the movements of spot prices and corresponding futures prices.
STEP 1: Convert Input(s) to Base Unit
Standard Deviation of Changes in Spot Price: 0.05 --> No Conversion Required
Standard Deviation of Changes in Futures Price: 0.09 --> No Conversion Required
Correlation of Changes in Spot and Futures Prices: 0.3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Δoptimal = (σsf)*ρs/f --> (0.05/0.09)*0.3
Evaluating ... ...
Δoptimal = 0.166666666666667
STEP 3: Convert Result to Output's Unit
0.166666666666667 --> No Conversion Required
FINAL ANSWER
0.166666666666667 0.166667 <-- Optimal Hedge Ratio
(Calculation completed in 00.018 seconds)

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Indian Institute of Technology, Indian School of mines, Dhanbad (IIT ISM Dhanbad), Dhanbad
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20 International Finance Calculators

FRA Payoff ( Long Position )
​ Go FRA Payoff = Notional Principal*(((Underlying Rate at Expiration-Forward Contract Rate)*(Number of Days in Underlying Rate/360))/(1+(Underlying Rate at Expiration*(Number of Days in Underlying Rate/360))))
Put-Call Parity
​ Go Call Option Price = Spot Price of Underlying Asset+Put Option Price-((Strike Price)/((1+(Risk-Free Rate of Return/100))^(No. of Months/12)))
Optimal Hedge Ratio
​ Go Optimal Hedge Ratio = (Standard Deviation of Changes in Spot Price/Standard Deviation of Changes in Futures Price)*Correlation of Changes in Spot and Futures Prices
Option Premium
​ Go Option Premium = ((Share Option Warrant/Number of Securities Per Option Warrant)+(Purchase Price*100/Price Security-100))
Balance of Financial Account
​ Go Balance of Financial Account = Net Direct Investment+Net Portfolio Investment+Asset Funding+Errors and Omissions
Annualised Forward Premium
​ Go Annualised Forward Premium = (((Forward Rate-Spot Rate)/Spot Rate)*(360/No. of Days))*100
Balance of Capital Account
​ Go Balance of Capital Account = Surpluses or Deficits of Net Non-Produced+Non-Financial Assets+Net Capital Transfers
Current Account Balance
​ Go Current Account Balance = Exports-Imports+Net Income Abroad+Net Current Transfers
Uncovered Interest Rate Parity
​ Go Expected Future Spot Rate = Current Spot Exchange Rate*((1+Domestic Interest Rate)/(1+Foreign Interest Rate))
Covered Interest Rate Parity
​ Go Forward Exchange Rate = (Current Spot Exchange Rate)*((1+Foreign Interest Rate)/(1+Domestic Interest Rate))
International Fisher Effect using Interest Rates
​ Go Change in Exchange Rate = ((Domestic Interest Rate-Foreign Interest Rate)/(1+Foreign Interest Rate))
Optimal Number of Contracts
​ Go Optimal Number of Contracts = (Optimal Hedge Ratio*Number of Positions Hedged)/Futures Contract Size
Relative Strength Index
​ Go Relative Strength Index = 100-(100/(1+(Average Gain during Up Period/Average Loss during Down Period)))
Bid Ask Spread
​ Go Bid Ask Spread = ((Ask Price-Bid Price)/Ask Price)*100
International Fischer Effect using Spot Rates
​ Go Change in Exchange Rate = (Current Spot Exchange Rate/Spot Rate in Future)-1
Vega (Options Greek)
​ Go Vega = Change in Option Premium/Change in Volatility of Underlying Asset
Theta
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Gamma
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Rho (Options Greek)
​ Go Rho = Change in Option Premium/Change in Rate of Interest
Hedge Ratio
​ Go Hedge Ratio = Hedge Value/Total Position Value

Optimal Hedge Ratio Formula

Optimal Hedge Ratio = (Standard Deviation of Changes in Spot Price/Standard Deviation of Changes in Futures Price)*Correlation of Changes in Spot and Futures Prices
Δoptimal = (σs/σf)*ρs/f

What is Optimal Hedge Ratio ?

The optimal hedge ratio refers to the ideal proportion of a hedging asset that an investor should hold relative to the position being hedged. It is determined through statistical analysis, taking into account factors such as the volatility of the asset being hedged, the correlation between the hedging asset and the asset being hedged, and the investor's risk tolerance. By using the optimal hedge ratio, investors aim to minimize the overall risk exposure of their portfolio while still benefiting from potential gains. For example, in commodities trading, a producer might use futures contracts to hedge against price fluctuations. The optimal hedge ratio in this context would be the quantity of futures contracts that provides the most effective hedge against adverse price movements in the underlying commodity.Finding the optimal hedge ratio involves complex calculations and modeling techniques, often utilizing statistical methods such as regression analysis.

How to Calculate Optimal Hedge Ratio?

Optimal Hedge Ratio calculator uses Optimal Hedge Ratio = (Standard Deviation of Changes in Spot Price/Standard Deviation of Changes in Futures Price)*Correlation of Changes in Spot and Futures Prices to calculate the Optimal Hedge Ratio, The Optimal Hedge Ratio is the proportion of a position in a hedging asset relative to the position being hedged, aiming to minimize risk exposure while maximizing effectiveness in hedging. Optimal Hedge Ratio is denoted by Δoptimal symbol.

How to calculate Optimal Hedge Ratio using this online calculator? To use this online calculator for Optimal Hedge Ratio, enter Standard Deviation of Changes in Spot Price s), Standard Deviation of Changes in Futures Price f) & Correlation of Changes in Spot and Futures Prices s/f) and hit the calculate button. Here is how the Optimal Hedge Ratio calculation can be explained with given input values -> 0.166667 = (0.05/0.09)*0.3.

FAQ

What is Optimal Hedge Ratio?
The Optimal Hedge Ratio is the proportion of a position in a hedging asset relative to the position being hedged, aiming to minimize risk exposure while maximizing effectiveness in hedging and is represented as Δoptimal = (σsf)*ρs/f or Optimal Hedge Ratio = (Standard Deviation of Changes in Spot Price/Standard Deviation of Changes in Futures Price)*Correlation of Changes in Spot and Futures Prices. Standard Deviation of Changes in Spot Price measures the volatility or variability of price movements over time for a financial asset or security, Standard Deviation of Changes in Futures Price measures the variability or dispersion of price movements over time for a futures contract, reflecting the degree of market volatility & Correlation of Changes in Spot and Futures Prices is the linear relationship between the movements of spot prices and corresponding futures prices.
How to calculate Optimal Hedge Ratio?
The Optimal Hedge Ratio is the proportion of a position in a hedging asset relative to the position being hedged, aiming to minimize risk exposure while maximizing effectiveness in hedging is calculated using Optimal Hedge Ratio = (Standard Deviation of Changes in Spot Price/Standard Deviation of Changes in Futures Price)*Correlation of Changes in Spot and Futures Prices. To calculate Optimal Hedge Ratio, you need Standard Deviation of Changes in Spot Price s), Standard Deviation of Changes in Futures Price f) & Correlation of Changes in Spot and Futures Prices s/f). With our tool, you need to enter the respective value for Standard Deviation of Changes in Spot Price, Standard Deviation of Changes in Futures Price & Correlation of Changes in Spot and Futures Prices and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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