Suppose you have $5 million and you are interested in investing in a high risk hedge fund. You get data about the performance of this hedge fund in the last five years and you know that this fund has generated an average return of 31% per year (with a t-stat of 2.18) with a standard deviation of 39%.

You are interested in analyzing the risk-adjusted returns of this hedge fund. You have data on the following two investment opportunities from which to construct a replicating portfolio:

1. Risk-free asset earning 3% per year;
2. A broad market index, with a Beta of 1, earning 19% per year and with a standard deviation of 21%.

Should you invest in the hedge fund you are interested based on the performance analysis you can conduct using the data above?