Hedge Question

Good Student
Posts: 21
Joined: Fri Aug 17, 2012 3:27 pm

Hedge Question

Postby d2syh » Wed Nov 07, 2012 11:43 am

A fund manager has a portfolio worth $10 million with a beta of 1.0. The manager is concerned about the performance of the market over the next 2 months and plans to use 3-month futures contracts on the Nasdaq to hedge the risk. The current level of index is $800, one contract is on 500 times the index, the risk free rate is 4% per annum, and the dividend yield on the index is 4% per annum. The current 3-month futures price is 750. What is the expected value of the hedger’s position over the next two months?
Choose one answer.
a. $9,980,000
b. $10,860,000
c. $9,085,000
d. $10,475,000
The correct answer is $10,475,000.

Here, value of the futures contracts = 500 * 800 = $400000
So complete hedge requires 1.0 * 10,000,000 / 400000 = 25 contracts need to be shorted thus minimising the risk.
Since the current 3-month future price turns out be 750. The gain in the short futures position is given by,
40 * (800 – 750) * 500 = $1,000,000
But loss on the index is 50/800 = -6.25%.
The index pays a dividend of 4% per annum, or 1% per 3-months. So investor would earn -5.25% in the 3-month period. Also, risk-free interest rate is approximately 1% per 3-months.
So, Expected return on the portfolio during 2-months when the 3-months return on the index is -5.25% is given by,
1 + [1 * (-5.25 – 1)] = -5.25%
Therefore, expected value of the portfolio at the end of 2-months is given by,
10,000,000 * 0.9475 = $9,475,000
So the expected value of the hedger position is given by,
$9,475,000 + $1,000,000 = $10,475,000

Could you explain why we are using "40" for the gain in futures position? How do we get the value 0.9475?



Return to “FRM Part I”


Global Association of Risk Professionals, Inc. (GARP®) does not endorse, promote, review or warrant the accuracy of the products or services offered by EduPristine for FRM® related information, nor does it endorse any pass rates claimed by the provider. Further, GARP® is not responsible for any fees or costs paid by the user to EduPristine nor is GARP® responsible for any fees or costs of any person or entity providing any services to EduPristine Study Program. FRM®, GARP® and Global Association of Risk Professionals®, are trademarks owned by the Global Association of Risk Professionals, Inc

CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by EduPristine. CFA Institute, CFA®, Claritas® and Chartered Financial Analyst® are trademarks owned by CFA Institute.

Utmost care has been taken to ensure that there is no copyright violation or infringement in any of our content. Still, in case you feel that there is any copyright violation of any kind please send a mail to abuse@edupristine.com and we will rectify it.