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The presence of a risk-free asset enables the investor to:Group of answer choicesform portfolios having greater Sharpe ratios.invest in the market portfolio and find an interior portfolio using quadratic programming.invest in the market portfolio and borrow or lend at the risk-free rate.borrow or lend at the risk-free rate and form portfolios having greater Sharpe ratios.

Question

The presence of a risk-free asset enables the investor to:Group of answer choicesform portfolios having greater Sharpe ratios.invest in the market portfolio and find an interior portfolio using quadratic programming.invest in the market portfolio and borrow or lend at the risk-free rate.borrow or lend at the risk-free rate and form portfolios having greater Sharpe ratios.

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Solution

The presence of a risk-free asset allows the investor to invest in the market portfolio and borrow or lend at the risk-free rate. Here's why:

  1. Investing in the Market Portfolio: The market portfolio includes all investable assets in the market, each weighted by its market value. This portfolio is considered to be the most diversified and thus carries only systematic risk, which cannot be eliminated through diversification.

  2. Borrowing or Lending at the Risk-Free Rate: The risk-free rate is the theoretical rate of return of an investment with no risk of financial loss. In reality, the risk-free rate does not exist because even the safest investments carry a very small amount of risk. However, government bonds are often used as a proxy for the risk-free rate because the risk of the government defaulting is extremely low.

By combining these two strategies, an investor can adjust the overall risk and return of their portfolio. They can increase their potential returns by borrowing at the risk-free rate and investing more in the market portfolio, or they can reduce their risk by lending at the risk-free rate and investing less in the market portfolio. This strategy is known as the risk-free asset combination strategy.

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