Hedging Stock Exposure Requires a Defined Risk Objective

Summary

The document asks how to hedge a stock modeled as geometric Brownian motion, with a stated price, zero interest rate, and known annual volatility. Its replies show that the problem is underspecified: a hedge depends on what exposure or loss measure is meant and which instruments are available.

One response suggests offsetting the stock position with cash, while another recommends identifying risk factors and using tradable factors and their loadings to construct a hedge. A further reply notes that without a defined objective, doing nothing can minimize trading-related risk. These are brief suggestions rather than a worked hedge design; the document supplies no horizon, target risk measure, hedge instruments, or calculation for selecting hedge ratios.

Key ideas

• A hedge cannot be specified until the desired risk reduction or objective is defined.
• Tradable risk factors can be used to hedge exposure when their relationship to the stock is understood.
• A hedge design depends on available instruments and the chosen risk model.
• Without an objective, taking no position may minimize risk by avoiding exposure altogether.

Tags

# hedging with known volatility


# hedging with known volatility












Suppose we have a stock $X$ at which trades at 100 dollars. We suppose the stock follows a geometric brownian motion. We know that the interest rate is zero and annual volatility is 10 percent. How can we hedge the risk?

## Answer by nicolas (score 1)

https://quant.stackexchange.com/a/10877

You sell your stock $S$ against some cash.

## Answer by Kumar (score 0)

https://quant.stackexchange.com/a/10883

You need a risk model to understand the sources of risk for your stock. If the risk factors can be traded then you can use the factor loadings to hedge your risk.

## Answer by Pam (score 0)

https://quant.stackexchange.com/a/12988

You first need to define "hedge". Or else the question remains undefined, and the minimum risk is achieved not trading at all ;-)

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