Question

In: Finance

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

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.

Solutions

Expert Solution

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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