Portfolio Composition
an Investment Firm Has Classified Its Clients According

question 11

Essay

Portfolio Composition
An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds,primarily stocks,or a balanced mix of bonds and stocks).The proportions of clients falling into the various categories are shown in the following table:
$$\begin{array}{l}\quad \quad \quad \quad \text { Partfolin Compasition }\\\begin{array} { | l | c | c | c | } \hline \text { Cender } & \text { Ennds } & \text { Stacks } & \text { Galanced } \\\hline \text { Mala } & 0.18 & 0.20 & 0.25 \\\hline \text { Female } & 0.12 & 0.05 & 0.20 \\\hline\end{array}\end{array}$$ One client is selected at random,and two events A and B are defined as follows:
A: The client selected is male.
B: The client selected has a balanced portfolio.
-Are A and B independent events? Explain.

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Definitions:

Risk-Free Asset

A risk-free asset refers to an investment that theoretically provides a certain return with no risk of financial loss.

Risky Asset

An asset that has a significant degree of uncertainty in its returns, often leading to higher potential rewards and higher potential losses.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, indicating how much the individual data points differ from the mean.

Expected Rate

The anticipated return on an investment, factoring in the probability of various outcomes, including risks and rewards.