Question

Salina is evaluating the possible movements of the price of gold. She believes that, at the end of 2020, there is a 18% chance that the price per ounce will go up to $2200, a 36% chance that it will go up to $ 2000, and a 12% chance that the price per ounce will go down to $1600. Otherwise, the price will stay at the today’s level of $1800 at the end of 2020. In anticipation, Salina is buying 60 ounces of gold at $1800 today. (please try to avoid using complicated formula, preferably an easy calculation in the last few questions)

Q: What could Salina expect to make on her purchase of 60 ounces of gold at the end of 2020? Please provide an interpretation of the result.

Answer 1

First we compute the probability distribution of the profit made on one ounce of gold buy here as:

P(X = 2200 - 1800 = 400) = 0.18,
P(X = 2000 - 1800 = 200) = 0.36,
P(X = 1600 - 1800 = -200) = 0.12,
P(X = 0) = P(price remains the same) = 1 - 0.12 - 0.18 - 0.36 = 0.34

Using this the expected profit per ounce in absolute terms here is computed as:
= 0*0.34 + 400*0.18 + 200*0.36 - 200*0.12

= 120

Therefore the expected profit that Salina would make on 60 ounces of gold now is computed here as:

= 60*120

= $7200

Therefore $7200 is the required expected value here.

Note that the interpretation of this is that if we repeatedly buy 60 ounces of gold and invest with the similar probability distribution, then in long run the average we expected to make is $7200 per investment.