Question

You are a manager looking to hedge a commodity over a 30 day time horizon. In particular you are concerned that prices may rise and you need to purchase in the future. Below is historical data on your spot price and on the futures price

Day	Spot	Futures
0	80	81
1	79.63	80.87
2	77.88	79.09
3	76.4	77.72
4	75.56	77.07
5	77.28	78.84
6	77.59	79.31
7	78.14	80.07
8	77.04	79.21
9	76.85	79.2
10	77.03	79.63

Compute the minimum variance hedge ratio. Make sure you write down any formula that you use so that I can check your computations. Make sure to indicate whether the managers should go long or short the futures contracts.

Answer 1

h* = ρ(σS / σF)

Where,

ρ= Correlation

σ= Standard Deviation

Day  Spot    Futures Correlation     Standard Dev S  Standard Dev F
0       80            81           0.919874431  1.309670326     1.174404298
1       79.63   80.87                   
2       77.88   79.09                   
3       76.4    77.72                   
4       75.56   77.07                   
5       77.28   78.84                   
6       77.59   79.31                   
7       78.14   80.07                   
8       77.04   79.21                   
9       76.85   79.2                    
10      77.03   79.63                   

H=.92*1.31/1.17

=1.01