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Portfolio of Risk-free and Risky Assets

Portfolio of Risk-free and Risky Assets

By combining a portfolio of risky assets with a risk-free asset, we can improve the return-risk characteristics of the portfolio and realize a better trade-off. This combination is called the capital allocation line (CAL) and the proportion of allocation to risky assets versus allocation to the risk-free asset will be dependent on the risk preferences of the investor.

Capital-Allocation-Line-CAL-given-Investor-Preferences

Combined Portfolios

We can determine the expected return of the composite portfolio of risky assets and risk-free assets as the weighted sum of the expected returns of the underlying assets. The portfolio risk requires us to know the weight or allocation to each underlying asset, the standard deviation or variance of the underlying asset as well as the relationship between the assets measured either by the covariance or the correlation. If the underlying assets are not perfectly correlated, then the variance of the portfolio will be less than the variance of the underlying assets alone.

Each investor will have their own risky portfolio dependent on the assumptions they make on the likely performance of the underlying assets. Since every investor makes their own unique assumptions about the underlying assets, there is no one optimal risk portfolio. We need to make a simplifying assumption that investor expectations are homogenous in order to derive what would be the optimal market portfolio.

Question

If two underlying assets are negatively correlated, combining them to form a portfolio will make the the portfolio risk:

A. Increase

B. Decrease

C. Remain constant

Solution

The correct answer is B.

When uncorrelated assets are combined to form a portfolio, lack of correlation will reduce the overall portfolio volatility.

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