2. You are a producer of gold, and have expenses of 800 per ounce of gold produc

Question

2. You are a producer of gold, and have expenses of 800 per ounce of gold produced Assume that the cost of all other production-related expenses is negligible, and that you will be able to sell all gold produced at the market price. In 1 year, the market price of gold will be 1 of 3 possible prices, corresponding to the following probability table Gold Price in 1-year 750 per ounce 850 per ounce 950 per ounce Probability 0.2 0.3 0.5 You hedge the price of gold by buying a 1-year put option with an exercise price of 900 per ounce. The option costs 100 per ounce now, and the continuously compounded interest rate is 6%. Calculate your expected 1-year profit of your total position

Explanation / Answer

SOLUTION =

BASIC INFORMATION -

1)COST OF GOLD = 800 PER OUNCE

2) EXERCISE PRICE = 900 PER OUNCE

3) OPTION COST = 100 PER OUNCE

4) COMPOUNDED INTEREST RATE = 6%

5) EXPECTED ONE YEAR PRICE PER OUNCE AND PROBABILITY

A) 750 0.2

B) 850 0.3

C) 950 0.5

CALCULATION OF COST WITH COMPOUNDED INTEREST FOR THE YEAR

COMPOUNDED COST = P(1+R/N)^NT

P= 100

R= RATE OF INTEREST

N= NUMBER OF TIMES COMPOUNDING

T= YEAR

COST = 100(1+.06/12)^12*1=106.18

CALCULATION OF 1 YEAR PROFIT FOR THREE PROBABLE PRICES

1) (750-800)+ (900-750)- 106.18=-6.18

2)(850-800)+(900-850)-106.18=-6.18

3)(950-800)+(900-950)#+-106.18=43.82

# IGNORED AS OUR EXCERCISE PRICE IS 900 PER OUNCE

CALCULATION OF EXEPECTED ONE YEAR PROFIT WITH RESPECTIVE PROBABILITIES

EXPECTED PROFIT=-6.18*0.2+-6018*0.3+43.82*0.5=18.82

ANSWER = EXPECTED ONE YEAR PROFIT AS PER MY POSITION IS 18.82 PER OUNCE.

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