Final answer:
The Modigliani risk-adjusted performance (M2) for Widget Manufacturing, Inc. can be calculated by taking the risk-free rate and adding the product of the excess return of the investment over the risk-free rate and the ratio of the market's standard deviation to the investment's standard deviation.
Step-by-step explanation:
The question asks for the calculation of M2 (Modigliani risk-adjusted performance) for Widget Manufacturing, Inc. The M2 measure compares the risk-adjusted performance of an investment to that of a market portfolio (such as the S&P 500). It is calculated by taking the risk-free rate and adding the difference between the investment's return and the risk-free rate, multiplied by the ratio of the market's standard deviation to the investment's standard deviation.
Using the given data for Widget Manufacturing, Inc. (average return of 13.4%, beta of 1.1, and standard deviation of 43.8%), the risk-free rate (2.2%), and the market return (8.4%) along with the market standard deviation (25.8%), we can calculate the M2.
The formula for M2 is as follows:
M2 = Risk-free rate + (Investment's return - Risk-free rate) * (Market standard deviation / Investment's standard deviation)
Plugging in the values, we get:
M2 = 2.2 + (13.4 - 2.2) * (25.8 / 43.8)
Calculating the above gives us the M2 value for Widget Manufacturing, Inc.