Computing hedge ratio: the modified duration method, Financial Management

Let us consider a situation wherein a position in an interest rate dependent asset such as a bond portfolio or a money market security is hedged by using an interest rate futures contract.

Let us assume that the change in the yield ?y, will be same for all maturities, i.e., only parallel shifts in the yield curve can occur. From the modified duration definition, we have,

         1187_hedge ratio.png

We can also say that to a reasonable approximation, it is also true that,

         1584_hedge ratio1.png

In the first equation, S0 represents value (decimal form) of the asset that is being hedged and MDrepresents modified duration of the asset. In the second equation, F0,T represents quoted price in decimals for the interest rate futures contract and MDrepresents modified duration of the asset underlying the futures contract (i.e., modified  duration of the cheapest to deliver bond).

As ?y is assumed to be the same for all maturities, we have ρΔSΔF = 1.  By combining first and second equation, we get,

         10_hedge ratio2.png

This can be written as,

         1520_hedge ratio3.png

Thus, we get,  

         1239_hedge ratio4.png

Finally, the optimal Hedge Ratio (HR) is used for hedging 

         1593_hedge ratio5.png

By using this equation we can equate the duration of the combined position equal to zero.

However, the hedge obtained using the above equation is not perfect because of following reasons:

  • It assumes that ?y is same for all yields. But, in reality short-term yields are generally more volatile and also have low correlation with long-term yields. Consequently, the performance of the hedge will not be appreciable, particularly when there is large variation between MDS and MDF.

  • It does not consider convexity. In case the convexity of the asset underlying the futures contract is remarkably different from the convexity of the asset being hedged, and at the same time if there is large difference in interest rates, then the performance hedge will be worse than is expected.

  • An assumption with regard to cheapest-to-deliver bond is essential to compute MDF. If the cheapest-to-deliver bond changes, then MDF   as well as optimal number of contracts also changes.

Now, as we know the hedge ratio, let us see the number of futures contracts to be purchased. We have earlier studied that the number of futures contracts required is given as

         651_hedge ratio6.png

In the above equation, NS indicates the number of units of spot asset to be hedged and k indicates the contract size.

We can estimate hedge ratio by using regression also. It can be interpreted as follows:

         1552_hedge ratio7.png

We have earlier studied that,  210_hedge ratio8.png   Here  2120_hedge ratio9.png   represents conversion factor of the cheapest to deliver bond at time 0 and SCTD,0  represents its price. If we replace F0,T in the above formula, we get,

         569_hedge ratio10.png

This can be interpreted as follows:

1461_hedge ratio11.png

Posted Date: 9/11/2012 2:42:36 AM | Location : United States







Related Discussions:- Computing hedge ratio: the modified duration method, Assignment Help, Ask Question on Computing hedge ratio: the modified duration method, Get Answer, Expert's Help, Computing hedge ratio: the modified duration method Discussions

Write discussion on Computing hedge ratio: the modified duration method
Your posts are moderated
Related Questions
Par tnership A legally authorized business form in which two or more partners are co-owners, sharing profits, losses, and liabilities related with the business they own.

Bonds pay interest periodically at a pre-specified rate of interest. The annual rate at which this interest is paid is known as the coupon rate or simply the coup

The assets and liabilities of S Harrison as at 30 June 2012 are: On 1 July 2011 when the business commenced, Harrison owed $58,000 on the land and buildings and $1,200 on

In the case of dual currency bonds, the interest is paid in one currency, while the principal repayment is made in another currency. Deep Di

Wing Yin Tsui, CEO of Lian Huang & Wong Bin Dean Hwang Manufacturing Limited is considering a four year project. The project requires an initial investment of $10,000,000 to buy ne

Cross-Sector Analysis: The growth of a country depends upon how fast a country can adapt to deregulation and internationalization. Deregulation and internationalization put com

Purchasing and discounting of bills is the most important, from in which a bank lends without any collateral security. Present day commerce is build upon credit. The seller draws a

Peak Inc. needs to order Canadian raw materials to use in its production process. The Canadian exporter typically invoices Peak in Canadian dollars. Assume that the current exchang

Auction Technique Auction is the most common method to sell Government Securities. Other methods include tap sales, syndication and book building process. Presently many countr

State about the investigate of Competition Directorate Competition Directorate will generally investigate the below areas: (i)  Mergers and takeovers This is when larg