Question

A Japanese pension plan has invested a portion of the entrusted money into a well diversified U.S. mutual fund that focuses on large capitalization stocks.  The managers' of the pension plan want to protect their investment into the fund.  They are concerned about two risks that could diminish the value of the plan's investment: 1) falling stock prices in the U.S. and 2) depreciation of the USD against the Japanese Yen.

Based on the following information and the example given in class, set up the hedge on February 3.  What is the net value in JPY of the pension plan's investment on May 27?  Note that the CME specifies for the S&P 500 futures 0.1 index points = USD 25,- and for the foreign exchange contract 12,500,000 Japanese yen per contract.  Was the hedge effective?

	Mutual Fund (JPY)	Spot (=cash) USD/JPY	June S&P 500 futures (points)	June USD/JPY futures
Feb 3 May 27	98,758,624 82,465,462	0.010802 0.011211	868.60 739.62	0.010887 0.011256

Date	Cash Market	Futures Market
	Portfolio value JPY ………….
	Portfolio value JPY ………….

Answer 1

Short Sell June S&P 500 future (To eliminate risk of US stock price decrease)

AT Feb 3, Portfolio Value=98,758,624 JPY=98,758,624*0.010802=$1,066,790.66

So, number of contract need to sell= 1066790.66/(250*868.60)=4.91 contract or 5 contract approximately

As 0.1 index point=$25, so contract size=25/0.1=250

Long USD/JPY June Future (To eliminate the risk of US dollar depreciating against JPY)

Number of contract need to buy=98,758,624/12500000=7.9 contract or 8 contract approximately

3. On May 27

Loss on Spot Market= ((739.62-868.6)/868.8)*1,066,790.66= -$1,58,373

Gain on S&P Future Market= 5*250*(868.6-739.62)=161225

Overall gain on S&P Future Market & on US stocks=(161225-158373)=$2852=2852*1/0.011211=254393 JPY

Loss on FX spot market=(98,758,624-1,066,790.66/0.011211)=3,602,914 JPY

Gain on FX Future Market= 8*12500000*(0.011256-0.010887)=36900 USD=36900/0.011211=3,291,410 JPY

Total Gain/Loss on FX market=(3291410-3602914)=-311504 JPY

Total Loss/Gain= 254393-311504=-57111 JPY

Net Value of Mutual Fund in JPY= (98,758,624-57111)=98,701,513 JPY

As there is a loss of only 0.0578%, the hedge was effective.