Question

Tyre Inc. Portfolio Return	Tyre Inc Standard Deviation	Risk Free Rate	Borrowing Rate	Market Index Return	Market Index Std. Deviation
10%	27%	2%	5%	7%	22%

Evaluate the investment performance of Tyre Inc compared to a passive investment with the same exact risk. Calculate the under or over (% return) of Tyre relating to this passive benchmark.

Answer 1

We observe that market has given a return of 7% and Tyre In has given a return of 10% so we may conclude Tyre Inc has performed better. However, that interpretation is wrong as all the parameters of risk and return should be considered which is not done in the given case.

Sharpe Ratio is helpful in determining the risk return impact on the portfolio. It helps in determining return earned above risk free rate for given level of risk

i.e Sharpe Ratio = (Portfolio Return - Risk Free Rate) / Standard Deviation

For Tyre Inc, SR = (10 - 2) / 27 = 0.2962

For Market Index: SR = (7-2)/ 22 = 0.2272

Hence as the Sharpe Ratio of Tyre Inc is higher than Market Index, the portfolio has performed better than passive investment.