In: Finance
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.
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 | ||||||||||||||
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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