Question

(a) Suppose that silver currently sells for $1,200 an ounce. If the risk-free rate is 1% per year, what should be the price of a one-year maturity futures contract?

(b) Suppose the price of one-year futures contract is $1,220 instead in the previous problem, please construct an arbitrage strategy so that investors can make riskless profits. (c) Suppose the price of one-year futures contract is $1,205 instead in the previous problem, please construct an arbitrage strategy so that investors can make riskless profits.

Answer 1

a.Spot price of the stock=S=1200/ ounce

Risk free rate (Rf)= 1% p.a.

Theoretical price of futures contract= S+ interest saved

Thus,

Theoretical price of 1 year maturity futures contract = 1200 + (1200*1%) = 1212/ounce

b. Actual price of 1 year maturity futures contract= 1220

Since should be price is less than actual price, it is over priced. So, we can conduct cash & carry arbitrage as below:

Activity	Cash flow
F- sell future	0
S+ buy stock	-1200
Borrow at Rf	1200
Net cash flow	0

Irrespective of the price on maturity (say St), arbitrage profit will be equal to the amount of mispricing ie. 8 (1220-1212). This can be seen as below:

Particulars	Amount
Interest expense	1200*1%=12
F- at 1220	1220-St
S+ at 1200	St-1200
Arbitrage profit	8

c. Actual price of 1 year maturity futures contract= 1205

Since should be price is greater than actual price, it is under priced. So, we can conduct reverse cash & carry arbitrage as below:

Activity	Cash flow
F+ buy futures	0
S- sell stock	1200
Invest at Rf	-1200
Net cash flow	0

Irrespective of the price on maturity (say St), arbitrage profit will be equal to the amount of mispricing ie. 7 (1212-1205). This can be seen as below:

Particulars	Amount
Interest income	1200*1%=12
F+ at 1205	St-1205
S- at 1200	1200-St
Arbitrage profit	7