Question

5.         Question 5                                                                                                [Total: 20 marks]

1. The spot price of silver is $50 per ounce. The storage costs are $ 0.52 per ounce to be paid at the end of the year. The futures contract on silver has 1 year and 6 months to maturity and the risk-free rate of interest is 0.9% per year with continuous compounding. What is the futures price (per ounce) if silver is considered to be an investment asset?  (Please display all computations.)                                                                   

[10 marks]                                                                                       

                

2. Please define the concept of “convenience yield” in relation to a consumption asset and discuss what happens to the size of the convenience yield, when there is excess demand for that consumption commodity.                                                      

[10 marks]  

Answer 1

Solution:

Given is

Spot rate(S) = $ 50 pe ounce, Risk free rate(r) = 0.9% p.a continuosly compounded, Storage cost (T) = $0.52 per ounce

a) The period of the futures contract is 1 year & 6 months & storage costs are to be paid at the end of month, therefore only one storage cost will be paid at the end of one year.

We have to first calculate the present value of storage cost = $ 0.52 / ert

= 0.52 / e(.009 * 1)

= 0.52 / 1.0090

= $ 0.51 per ounce

Then,

we can calculate the futures price using the cost of carry model.

F = (S+T) * ert

= (50 + 0.51) * e(0.009 * 18/12)

= 50.51 * 1.0136

= $ 51.20 per ounce

b) Convenience yeild is the advantage or benifit associated with holding an underlying consumption asset rather than having a derivative contract on that asset.

The convenience yield tends to exist when storage costs such as insurance, warehousing, etc is relatively low or storage for the commodity is scarce and demand is high.

When there is an excessive demand for that commodity, the price will rise and which will increase the convenience yield.

For eg: if someone is holding inventory of rice and after weeks there is a flood then the demand will be more which will increase the price. So the difference between the price paid for purchases before the flood and after flood is convenience yield.