The following data is reported for a fund and an appropriate benchmark as well as the risk$-$free rate each year:

Fund Return Benchmark Return Risk$-$free rate

Year $111\%8\%2\%$

Year $212\%9\%2\%$

Year $327\%24\%2\%$

Year $430\%25\%2\%$

Year $530\%24\%2\%$

Year $631\%24\%2\%$

Year $722\%20\%2\%$

Year $820\%18\%2\%$

Year $917\%15\%2\%$

Year $1015\%14\%2\%$

Required:

a$.$ What is the Sharpe ratio for the fund and the benchmark?

b$.$ What is the Treynor ratio for the fund and the benchmark?

c$.$ What is the fund tracking error?

d$.$ What is the beta for the fund?

e$.$ What is Jensen$$s alpha for the fund?