Question

No 3. Consider three securities: Asset I with expected return of 14% and standard deviation of return of 6%, Asset 2 with average return of 8% and standard deviation of returns of 3%, and Asset 3 with mean return of 20% and standard deviation of return of 15%. Further, assume that the correlation coefficient between Asset 1 and Asset 2 is 0.5, between Asset 1 and Asset 3 is 0.2, and between Asset 2 and Asset 3 is 0.4. Finally, assume that the riskless lending and borrowing rate is 5%. a) Derive the expected return and standard deviation of the tangency portfolio b) Explain to which extent is the presented data consistent with the Capital Asset Pricing Model (CAPM) and whether there is any arbitrage strategy. Stock Beta Expected Return (%) А 0,9 14% в 1,2 16,6% 0.6 11% D 19,5% 1.S c) With reference to empirical evidence, critically assess the validity of CAPM

Answer 1

A)

Sharpe ratio for Asset 1 = (14%-5%)/6% = 1.5

Sharpe ratio for Asset 2 = (8%-5%)/3% = 1.0

Sharpe ratio for Asset 3 = (20%-5%)/15% = 1.0

Since sharpe ratio of asset 1 is highest it provides the highest return for 1 unit of risk.

B)

As per CAPM expected return = Rf + b*(Rm-Rf)

Stock A : Rm = 15%

Stock B : Rm = 14.67%

Stock C : Rm = 15%

Stock D : Rm = 14.67%

Since the market return are lower for Stock B and Stock D, hence there is an arbitrage opportunity.