Final answer:
To achieve a portfolio with a 25% standard deviation, you would invest your $1,000 and borrow an additional $250 to invest in the market portfolio, giving you a total market investment of $1,250, which is 125% of your own money. This leveraged position allows you to reach the preferred level of risk.
Step-by-step explanation:
To achieve a portfolio standard deviation of 25% when you prefer a portfolio with an expected standard deviation of 25%, can invest in the market with an expected return of 15% and a standard deviation of 20%, and can borrow or invest money at the risk-free rate of 5%, we can use the concept of combining a risk-free asset with a risky asset to find the appropriate portfolio weights.
Let's denote the percentage of your portfolio to be invested in the market as y and the rest, 1 - y, would be the percentage either borrowed or invested at the risk-free rate.
According to the Capital Asset Pricing Model (CAPM), the expected standard deviation of a portfolio that combines the market and a risk-free asset is y times the market's standard deviation.
To solve for y, we set up the equation:
0.25 = y * 0.20
This implies that:
y = 0.25 / 0.20 = 1.25
Since y exceeds 1, it means you need to borrow funds such that your total investment in the market is $1,250 (125% of your own money). The amount borrowed would be $1,250 - $1,000 = $250. Yo
u will invest $1,000 of your own money and borrow $250 to invest at the market rate to achieve the desired portfolio standard deviation of 25%.