Question

In: Finance

A trader owns silver as part of a long-term investment portfolio. The trader can buy silver...

A trader owns silver as part of a long-term investment portfolio. The trader can buy silver today for $34 per ounce and sell silver today for $33 per ounce. The trader has indicated that there is no arbitrage opportunity if the lending rate is 8% p.a. (or less) and the borrowing rate is 9% p.a. (or more) with continuous compounding frequency. Assume that there is no bid-offer spread for forward prices, and that there is no storage cost and no convenience yield.

Required: Calculate the range within which the one-year silver forward prices must fall so that there is no arbitrage opportunity. Assume the trader can short sell silver if required.

Expert Solution

To calculate the range within which one year silver forward rate should fall so that there is no arbitrage oppurtunity, we should first evaluate the option a trader has today to earn an arbitrage profit

1)Borrow today to buy silver and short sell silver after one year

Purchase price of silver-$34(S1)

Borrow-$34

r1(Borrowing Rate)-9%

Amount Payable after one year(With continous compounding)=S1*e^(r1*t)

34*e^(0.09*1)=34*2.7183^(0.09)=36.468

2)Sell stock today at spot price, invest the proceeds and buy after one year

Proceeds from sale of one ounce of silver-$33(S2)

Rate of return(Lending)-8%(R2)

Period of investment-t

Proceeds after one year-S2*e^(R2*t)

33*2.7183^0.08=$35.12

Comment on option 1-In order to have no arbitrage profit, the forward price should be $36.468

Option 2-In 2nd scenario, in order to have no arbitrage profit, forward price of one ounce of silver should be $35.12

Therefore in order to have no arbitrage position , one year silver forward price should fall in range of $35.12-$36.47

jeff jeffy answered 2 years ago

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