Question

The six-month forward price of 1g gold is $2255.69. if the risk free rate is 5% per annum and no other holding cost is involved the current price of this gold should be $2000. (True/False)

Answer 1

Solution :

The forward price of 1g gold is calculated using the formula

Forward Price = S₀ * e ^{( r * t )}

Where

S₀ = Current price ;    r = Risk free rate ;   t = Term of the contract expressed in years ; e = 2.17828 ;

As per the information available in the question we have

Forward Price = $ 2,255.69 ; r = 5 % = 0.05 ; t = 6 months = 0.5 year ; e = 2.17828 ; S₀ = To find ;

Applying the above information in the formula we have the forward price as

$ 2,255.69 = S₀ * ( 2.71828 ) ^{( 0.05 * 0.5 )}

$ 2,255.69 = S₀ * ( 2.71828 ) ^{( 0.025 )}

$ 2,255.69 = S₀ * 1.025315

$ 2,255.69 / 1.025315 = S₀

S₀ = $ 2,255.69 / 1.025315

S₀ = 2,199.996852

S₀ = 2,200 ( when rounded off to the nearest dollar )

Thus the current price of the gold should be 2,200 and not $ 2,000

Hence, the given statement is false.

The solution is False.

Note : The value of ( 2.71828 ) ^0.025   has been calculated using the excel function =POWER(Number,Power). Thus =POWER(2.71828,0.025) = 1.025315