Fnd the optimal hedge ratio, Econometrics

Hedging ?nancial risk is a very important practical issue in economics.  In this exercise, you will derive your optimal hedge ratio, assuming that you are an expected utility maximizer with quadratic tastes over rates of return who has a spot position in a single risky asset.

Here's the notation.  The random return on a portfolio that consists of a spot position in a single risky asset is


If you hedge your risk by selling a fraction h of your asset forward then your return becomes

Rp = Rs - h ⋅ Rf

where Rf is the payoff on the forward contract.  Your utility function, where  γ  is a risk preference parameter, is

u (Rp) = E ( Rp) - γ var (Rp)

Here's the story.  Say that all of your wealth is invested in a single asset whose uncertain return is Rs over t.  Now suppose that you want to reduce the riskiness of your spot position (is risk aversion reason enough?) as measured by its variance.  One way to hedge the risk is to sell the asset forward in a forward or futures market.  For example, you might be a manufacturer of electric guitars who exports to the United States.  Chances are, you will be paid in US dollars, say, a month later.  Your spot position then is the one-month rate of return on manufacturing guitars.  As an exporter, you face a number of risks: one is default risk, the risk of not being paid; another is unexpected changes in the rate of in?ation; and still another is foreign exchange risk.  Let's ignore default risk by assuming that you're dealing with a longtime and ?nancially stable customer.  Let's also ignore in?ation risk because, after all, this is Canada - eh? - and it's only one month.  That leaves foreign exchange risk.  A naive currency hedge would be one-for-one or dollar-for dollar (h =1); so, if you're owed US $1,000 at the end of the month, you'd sell US $1,000 forward one month.  If spot and futures prices on the dollar are highly correlated, then any change in the spot price at month's end will be largely offset by changes in the futures price.  Since we're talking in terms of rates of return rather than dollars, that simple hedge ratio would be 1, which is the same as saying that 100% of your spot position is hedged.  But is a hedge ratio of 1 optimal?

Posted Date: 3/15/2013 3:42:46 AM | Location : United States

Related Discussions:- Fnd the optimal hedge ratio, Assignment Help, Ask Question on Fnd the optimal hedge ratio, Get Answer, Expert's Help, Fnd the optimal hedge ratio Discussions

Write discussion on Fnd the optimal hedge ratio
Your posts are moderated
Related Questions
Probelm: (a) Differentiate between homoscedasticity and heteroscedasticity. (b) Outline the reasons why the variances of disturbance term may vary. (c) Given the 3 observ

What''s the relationship between economic efficiency and technical efficiency

write a term paper on modelling and multicollinearity

Define McKinsey & Company's present "core competence" in terms used by Hamel & Prahalad and state how it fits with McKinsey's longer term vision. Answer) McKinsey an

Factor that affect the volume of production

Greenstone Coffee is experiencing financial pressures due to increased competition for its numerous urban coffee shops. Total sales revenue has dropped by 15% and the company wishe

a. If 10,000 two-liter bottles of Pepsi are currently being demanded in your community each month, and the price increases from $1.90 to $2.10 per bottle, what will happen to quant

what is the mathematical origin of durbin watson test for autocorrelation

Assume that Jane spends her entire income of $100 on two goods,  x  and  y.  Moreover, these goods are perfect complements for her.  Let the price of good  x  go up while the price