@@ Line 1: / Line 1: @@
-'''[[Texas hedge]]''' is an investment strategy in which an investor takes an offsetting position in a related security or financial instrument to reduce exposure to an existing position. The term is commonly used in [[Financial markets|financial markets]] and [[Risk management|risk management]].
+'''[[Texas hedge]]''' is an investment strategy in which an investor attempts to offset the risk of an existing position by taking another position in a related asset, security, or financial instrument. The second position is intended to provide gains when the original position experiences losses, but unlike a conventional hedge, the offsetting position may itself carry substantial market risk.
-Unlike a conventional hedge that is designed primarily to reduce risk, a Texas hedge generally involves taking a position that can increase the potential for both gains and losses. The expression is sometimes described as a strategy in which an investor attempts to hedge one risky position with another risky position.
+The term is commonly associated with situations in which an investor uses one risky investment to hedge another rather than using a relatively direct hedging instrument such as a [[Futures contract|futures contract]], [[Option (finance)|option]], or other derivative.
 ==Concept==
-A simplified representation of a Texas hedge is:
+A simplified Texas hedge consists of two related positions:
 <math>
@@ Line 12: / Line 12: @@
 \text{Original Position}
 +
-\text{Offsetting Position}
+\text{Hedging Position}
 </math>
-The two positions are typically related but may not move perfectly in opposite directions.
+If the two positions respond differently to changes in market conditions, gains in one position may partially or fully offset losses in the other.
-If the positions have imperfect correlation, the hedge can reduce some risks while leaving the investor exposed to additional risks.
+The effectiveness of the hedge depends on the relationship between the two positions.
+A simplified portfolio return can be represented as:
+<math>
+R_p
+=
+w_1R_1
++
+w_2R_2
+</math>
+where:
+* <math>R_p</math> = portfolio return;
+* <math>w_1</math> = weight of the original position;
+* <math>w_2</math> = weight of the hedging position;
+* <math>R_1</math> = return of the original position;
+* <math>R_2</math> = return of the hedging position.
+==Relationship between the positions==
+The two positions in a Texas hedge generally have some economic, market, or statistical relationship.
+For example, the positions may be:
+* securities issued by companies in the same industry;
+* assets whose prices respond to a common economic factor;
+* securities with opposing exposures to a particular market development;
+* positions in related commodities;
+* positions in related equity or debt instruments.
+The hedge does not require the two assets to move in exactly opposite directions.
+If the returns have a negative correlation, the second position may provide an offset when the first position declines.
+The correlation coefficient can be represented as:
+<math>
+\rho_{12}
+=
+\frac{\operatorname{Cov}(R_1,R_2)}
+{\sigma_1\sigma_2}
+</math>
+where:
+* <math>\rho_{12}</math> = correlation between the two positions;
+* <math>\operatorname{Cov}(R_1,R_2)</math> = covariance of their returns;
+* <math>\sigma_1</math> and <math>\sigma_2</math> = standard deviations of their returns.
+A negative correlation can provide an offsetting effect, although correlation alone does not guarantee an effective hedge.
+==Difference from a conventional hedge==
+A conventional hedge generally seeks to reduce exposure to a particular risk by taking an offsetting position whose value is expected to move in the opposite direction.
+For example, a producer exposed to falling commodity prices may use a futures contract to lock in a selling price.
+A Texas hedge instead uses another potentially risky investment as the offsetting position.
+The distinction can be represented as:
+<math>
+\text{Conventional Hedge}
+\rightarrow
+\text{Risk Exposure}
++
+\text{Purpose-Built Offset}
+</math>
+<math>
+\text{Texas Hedge}
+\rightarrow
+\text{Risky Position}
++
+\text{Another Risky Position}
+</math>
+The second structure may reduce one source of risk while introducing or retaining other risks.
 ==Example==
-Suppose an investor holds a security that is expected to decline if a particular market factor deteriorates. Instead of using a conventional derivative hedge, the investor takes a position in another security whose value is expected to increase under some of the same conditions.
+Suppose an investor owns shares of Company A and is concerned about weakness in the technology sector.
+Instead of selling the shares or using a sector derivative, the investor takes a position in Company B, whose business is expected to benefit from the same market development that could negatively affect Company A.
+If Company A falls while Company B rises, the gain in Company B can partially offset the loss in Company A.
+For example:
+<math>
+\text{Loss on Company A}
+=
+-\$10,000
+</math>
+and:
+<math>
+\text{Gain on Company B}
+=
++\$7,000
+</math>
+then:
+<math>
+\text{Combined Result}
+=
+-\$10,000+\$7,000
+=
+-\$3,000
+</math>
+The second position has reduced the overall loss, but it has not eliminated the risk.
+==Hedge ratio==
+The relative size of the hedging position can affect the effectiveness of the strategy.
+A simplified hedge ratio is:
+<math>
+h
+=
+\frac{\text{Value of Hedging Position}}
+{\text{Value of Original Position}}
+</math>
+For example, if an investor holds $100,000 of an asset and establishes a $50,000 offsetting position:
+<math>
+h
+=
+\frac{50,000}{100,000}
+=
+.5
+</math>
+A hedge ratio of 0.5 means that the nominal value of the hedging position is 50% of the original position.
+The appropriate hedge ratio depends on the relationship between the assets, their volatility, and the investor's risk objective.
+==Basis risk==
+A Texas hedge can involve substantial [[Basis risk|basis risk]], which arises when the hedging position and the original position do not move sufficiently closely.
+If:
+<math>
+\Delta R_1
+\neq
+-\Delta R_2
+</math>
+the hedge will not completely offset changes in the original position.
-If the second position offsets losses from the first, the combined portfolio may experience a smaller loss.
+For example, the original position may decline by 15% while the hedging position rises by only 5%.
-However, if the second position also declines, the investor can suffer losses from both positions.
+The hedge therefore reduces the loss but does not eliminate it.
-==Risk==
+==Correlation risk==
-The principal characteristic of a Texas hedge is that the offsetting position is itself risky.
+The effectiveness of a Texas hedge can also depend on the stability of the relationship between the two positions.
-A simplified portfolio-return relationship is:
+Historical correlation does not necessarily remain constant.
+A simplified portfolio variance relationship is:
 <math>
-R_p
+\sigma_p^2
 =
-w_1R_1
+w_1^2\sigma_1^2
++
+w_2^2\sigma_2^2
 +
-w_2R_2
+w_1w_2\rho_{12}\sigma_1\sigma_2
 </math>
 where:
-* <math>R_p</math> = portfolio return;
+* <math>\sigma_p^2</math> = portfolio variance;
+* <math>\sigma_1^2</math> and <math>\sigma_2^2</math> = variances of the two positions;
 * <math>w_1</math> and <math>w_2</math> = portfolio weights;
-* <math>R_1</math> and <math>R_2</math> = returns of the two positions.
+* <math>\rho_{12}</math> = correlation between the two positions.
+This relationship illustrates why the correlation between the positions can materially affect the overall risk of the combined portfolio.
+==Double-loss risk==
+One of the principal risks of a Texas hedge is that both positions can lose value at the same time.
+If the assumed relationship between the two investments fails, the investor may experience losses on the original position and the purported hedge simultaneously.
+A simplified combined loss is:
+<math>
+L_p
+=
+L_1+L_2
+</math>
+where:
+* <math>L_p</math> = total portfolio loss;
+* <math>L_1</math> = loss on the original position;
+* <math>L_2</math> = loss on the hedging position.
+This distinguishes a Texas hedge from a hedge designed specifically to provide a contractual or derivative-based offset.
+==Market risk==
+Because the hedging position remains exposed to market movements, a Texas hedge does not eliminate market risk.
+The investor may remain exposed to:
+* equity-market risk;
+* interest-rate risk;
+* commodity-price risk;
+* currency risk;
+* credit risk;
+* liquidity risk;
+* volatility risk;
+* correlation risk.
+The strategy may therefore transform the portfolio's risk rather than simply eliminate it.
+==Liquidity risk==
+The ability to establish or exit the offsetting position can be affected by [[Liquidity risk|liquidity risk]].
+If the hedging asset becomes difficult to sell during a market disruption, the investor may be unable to adjust the hedge at the desired price.
+This can increase losses or prevent the investor from maintaining the intended hedge ratio.
+==Leverage==
+A Texas hedge can involve [[Leverage (finance)|leverage]], particularly when derivatives, margin accounts, or borrowed funds are used.
+Leverage can increase both the gains and losses associated with the hedging position.
+If the hedging position requires margin, adverse price movements can also generate [[Margin call|margin calls]].
+==Texas hedge and speculation==
+A Texas hedge can blur the distinction between [[Hedging|hedging]] and [[Speculation|speculation]].
+A conventional hedge is generally established primarily to reduce an existing exposure.
+A Texas hedge may involve taking a new market position that is itself based on an expectation about future prices or market relationships.
+Consequently, the investor may be attempting to offset one risk while simultaneously making another investment bet.
+==Texas hedge and derivatives==
+A Texas hedge can be contrasted with derivative-based hedging.
+For example, an investor with exposure to an asset may use:
+* a futures contract;
+* a forward contract;
+* a put option;
+* a swap;
+* another derivative.
+Such instruments can be designed to provide a more direct offset to a particular exposure.
+A Texas hedge instead relies on the behavior of another investment.
+The distinction is therefore based primarily on the nature of the offsetting position rather than simply on whether a financial instrument is used.
+==Advantages==
+Potential advantages of a Texas hedge include:
+* reduction of some portfolio exposures;
+* diversification across related securities;
+* flexibility in selecting the offsetting investment;
+* potential for the hedging position to generate independent returns;
+* use of market relationships when direct hedging instruments are unavailable or costly.
+However, these potential benefits depend on the quality and stability of the relationship between the positions.
+==Disadvantages==
+Potential disadvantages include:
+* imperfect hedging;
+* basis risk;
+* correlation risk;
+* double-loss risk;
+* additional transaction costs;
+* liquidity risk;
+* leverage risk;
+* model risk;
+* unintended factor exposures.
+The strategy can therefore produce a more complex risk profile than a direct hedge.
+==Risk management==
+Investors using a Texas hedge may evaluate the strategy using measures such as:
+<math>
+\text{Hedge Effectiveness}
+=
+-
+\frac{\operatorname{Var}(R_p)}
+{\operatorname{Var}(R_1)}
+</math>
-The effectiveness of the hedge depends on the relationship between <math>R_1</math> and <math>R_2</math>.
+where:
+* <math>R_p</math> = return of the hedged portfolio;
+* <math>R_1</math> = return of the unhedged original position.
+A higher value indicates a greater reduction in variance under this simplified measure.
+The measure is only one possible way of assessing hedge effectiveness and does not capture every form of investment risk.
+==Importance==
+A Texas hedge illustrates the distinction between reducing a particular exposure and eliminating investment risk. An offsetting investment can reduce losses from an existing position when the two investments behave in the expected manner, but the offsetting investment remains subject to its own market risks.
+The strategy therefore requires analysis of correlation, volatility, hedge ratio, liquidity, leverage, and the underlying economic relationship between the positions.
 ==See also==
@@ Line 55: / Line 350: @@
 * [[Risk management]]
 * [[Financial risk]]
-* [[Derivative (finance)]]
+* [[Basis risk]]
 * [[Correlation]]
 * [[Portfolio management]]
-* [[Long (finance)]]
+* [[Diversification (finance)]]
-* [[Short (finance)]]
+* [[Derivative (finance)]]
+* [[Futures contract]]
+* [[Option (finance)]]
+* [[Speculation]]
+* [[Leverage (finance)]]
+* [[Liquidity risk]]
+* [[Market risk]]
 [[Category:Financial markets]]
+[[Category:Investment]]
 [[Category:Risk management]]
-[[Category:Investment]]
+[[Category:Hedging]]
 [[Category:Portfolio management]]
+[[Category:Financial risk]]

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