A client comes to you for help on capital allocation. Their degree of risk aversion $($A$)$ is $2\mathrm{.}2.$ You consider using SPY ETF as the risky asset. The risky asset's expected return is $18\mathrm{.}6\%,$ while the risk$-$free rate is $6\mathrm{.}5\%.$ The risky asset has a volatility of $25\%.$ The client has $$200,000$ to invest.