Question

Consider an oil drilling venture. The price of a share of this venture is $875. It is expected to yield the equivalent of $1,000 after 1 year, but due to high uncertainty about how much oil is at the drilling site, the standard deviation of the return is σ = 40%. Currently, the risk-free rate is 10%. The expected rate of return on the market portfolio is 17%, and the standard deviation of this rate is 12%. Compare this venture with the capital market line.

Show work eg not excel.

Answer 1

Expected Rate of Return as per Capital Market Line (CML)
= Rf + σp*[(Rm-Rf)/σm]
Where,
Rf = Risk Free Rate = 10% = 0.10
σp = Standard Deviation of Return = 40% = 0.40
Rm = Return on market Portfolio = 17% = 0.17
σm = Standard Deviation of market = 12% = 0.12
So,
Expected Rate of Return as per Capital Market Line (CML)
= Rf + σp*[(Rm-Rf)/σm]
= 0.10 + 0.40*[(0.17-0.10) / 0.12]
= 0.10 + 0.40*[(0.07 / 0.12]
= 0.10 + 0.40*0.5833
= 0.10 + 0.2333
= 0.3333
i.e. 33.33%
Now, Actual Expected Rate of Return = (Expected Yield / Price of Share) - 1
				= ($1000 / $875) -1
				= 0.1429
				i.e. 14.29%
As the actual expected rate of return (14.29%) is well below the expected rate
of return as per CML (33.33%), So this venture does not constitute an efficient
portfolio.