Question

Table 1: ABC Managed Fund Performance

Table 1: ABC Managed Fund Performance

	ABC	S&P Index	T-bills
Mean	13.0%	12.0%	7.6%
Standard deviation	12.4%	9.4%	0.5%
Cov(ABC, S&P I)	0.0107

Calculate the Sharpe ratio for the fund and the market portfolio.

Calculate the Treynor ratio for the fund and the market portfolio. show working out

Answer 1

Sharpe ratio = (Expected return- Risk free rate)/(Standard deviation of stock-standard deviation of risk free return)

So, Sharpe ratio of ABC = (13% - 7.6%)/(12.4%-0.5%)

0.4537815126

Sharpe ratio of S&p index( Matket) = (12%-7.6%)/(9.4%-0.5%)

0.4943820225

So, Sharpe ratio of ABC is 0.45% and market is 0.49%

To Calculate trenyor ratio, beta is required

Market beta is always 1. so beta of S&P index is 1

Beta of ABC foumula = Covariance/(standard deviation of matket)^2

0.0107/(9.4%)^2

1.210955183

Trenyor ratio formula = (Expected return of security-Risk free rate)/Beta of security

Trenyor of ABC = (13%-7.6%)/1.210955183

4.46%

Trenyor of Market index = (12%-7.6%)/1

4.40%

So, trenyor of ABC is 4.46% and of Market is 4.40%