Question

The spot price for gold is $1,200 and the the 6-month risk-free rate is 3% continuously compounded.

(1) Calculate the 6-month Futures price of gold.

(2) Describe a trading strategy to make arbitrage profits if the quoted futures price is $10 lower than the fair value you calculate in Part (1). Show the cash flows to each element of your trading strategy.

(3) Describe a trading strategy to make arbitrage profits if the quoted futures price is $10 less than the fair value you calculate in Part(1). Show the cash flows to each element of your trading strategy.

Answer 1

Solution of 1

Spot Price (S)= 1200

1200

t= 6months= 6/12=0.5

0.5

r= 0.03

0.03

e^rt= 1.01511497653

e^0.03*0.5

e^0.015

1.015115

F= Se^rt= 1200*1.01511497653 1218.138

1218.138

Note:

To calculate e power rt in normal calculater (other than scientific calculator) following steps are used:

Step 1: Multiply r*t.

step 2: multiply output of step 1 with 0.00024417206 (To compute any continuous componding this number should be used)

step 3: output of step 2 should be "*=" "*=" 12 times

Solution 2 & Solution 3

Step 1

6 months future rate calculated above is "should be" rate. i.e fair value of 6months future rate of Gold

If Actual 6 months Future is $ 10 lessor than fair value, then Future is underpriced. Therefore Buy Futures (i.e. F+)

Therfore Sell Spot (i.e. S-)

This selling Spot and Buy futures is called reverse cash and carry approach.

Arbitrage Profit = $10 (mispricing in Futures)

Step 2

Process of Arbitrage (net settlement of Futures)

Particulars

at T=0

at T=6months

Spot sell Gold @ 1200. getting inflow of 1200

1200

Invest the inflow received @ Risk free rate of 3%. Therfore Outflow of 1200

-1200

Buy Futures @ 1218.138-10

St-1208.138

Getting Inflow of Investment with Risk free Interest (1200*e^0.015)

1218.138

Buy Gold @ T=6 months @ Spot price of that day. Here calls it as St

(St)

Inflow/Outflow/Cashflow

0

10

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