In a recent 5-year period mutual fund manager Diana Sauros produced the following percentage rates of return for the Mesozoic Fund

a) Average Fund return = (-1.3%+23.5%+41.4%+10.4%+0.4%)/5 = 14.88%

Average Market Index return = (-0.9%+16%+30.9%+11.7%-0.7%)/5 = 11.40%

Variance of the Fund Returns

= ((-1.3%-14.88%)^2+(23.5%-14.88%)^2+(41.4%-14.88%)^2+(10.4%-14.88%)^2+(0.4%-14.88%)^2)/4

=0.0317287

Standard deviation of Fund returns = square root of variance = 0.1781 = 17.81%

Variance of the Market Index Returns

= ((-0.9%-11.4%)^2+(16%-11.4%)^2+(30.9%-11.4%)^2+(11.7%-11.4%)^2+(-0.7%-11.4%)^2)/4

=0.01748

Standard deviation of Market Index returns = square root of variance = 0.1322 = 13.22%

The above information is presented in tabular forms as given below

b) The Mesozoic fund has given a higher return than market but its standard deviation (risk) is also higher

To measure the risk adjusted performance,

Coefficient of Variation (CV)= Standard deviation/ Average Return

  can be calculated which gives the risk per unit return,

CV of Fund returns = 17.81%/14.88% =1.197

CV of Market Index returns = 13.22%/11.40% =1.15975

As the CV of market index returns is lesser than CV of Fund returns,

Ms. Sauros of Mesozoic fund has not performed better than market index on a risk adjusted basis