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
What is the expected value and variance of y = 3x+2 knowing that E(X) = 8 and var(X) = 4.

Problem: a) In what circumstances would you apply switching models? b) Using dummy variables for seasonality show how you would test for January effects in financial data?

In a year, weather can impose storm damage to a home. From year to year the damage is random. Let Y be the dollar value of damage in a given year. Assume that 95% of the year's Y=$

if there is multicollinearity so why we can not estimate the value of parameters?

A city government wants to raise $3 million by issuing bonds. By ballot proposition, the bond's coupon interest rate was set at 8% per year with semiannual payments. However, marke

Process of least cost method and how to do a minimisation problem

ear Sir/Madam, I need somebody to implement the followintg models and test: Plot the variables studied Test for a unit root of all my variables using the ADF (p) tests for the le