Question

The price of oil is currently at $24 but you expect it to either increase by 18 percent or decrease by 7 percent over the next 6 months. The 6-month risk-free rate of interest is 1.98 percent. What is the probability that the price will increase?

Answer 1

If investors are indifferent to risk, the expected rate of return on oil for next 6 months should be same as the next 6 months risk free rate of return viz. 1.98%.
We know that price of oil can either go up by 18% or fall by 7% over the next 6 months.
Therefore ,
Expected Return=	[Probability of rise x 18%] + [(1 – Probability of rise) x (-7%)]
Let Probability of rise= P
Expected Return=	[Probability of rise x 18%] + [(1 – Probability of rise) x (-7%)]
1.98%=	[ P x 18%] + [ (1-P)x (-7%)
0.0198=	0.18P-0.07+0.07P
0.0198+ 0.07=	0.18P+ 0.07P
0.0898=	0.25P
P=	0.0898/0.25
P=	0.3592
P=	36%
Probabilty of price increase will be 36%.