Risk Free Asset

correct, regarding, following, statements, capital

Which of the following statements regarding the risk-free asset is least accurate?

A) Markowitz portfolio theory develops into capital market theory with the inclusion of a risk-free asset.

B) The covariance of the risk-free asset with other assets is +1.

C) The variance of the risk-free asset is zero.

Your answer: B was correct!

The risk-free rate is constant so it does not co-vary with other assets. Thus the covariance is zero.

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Two Questions on the explanation:
1) Is the risk free rate really constant--doesn't the treasury rate move daily?
2) Why is the covariance zero--can't the covariance be higher for assets that have high correlation with macroeconomic factors and lower for assets that have low correlation with macro econoimc factors?

RMontgomery

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发表于 2011-7-11 19:44 | 只看该作者

got it thanks. rfr doesnt move once you invest in it, so its correlation with anything else is zero sicne it does not ever change. just came across another relatively simply PM question...can you help me to reason out why B is incorrect here?

Portfolio Management Associates (PMA) provides asset allocation advice for pensions. PMA recommends that all their pension clients select an appropriate weighting of the risk-free asset and the market portfolio. PMA should explain to its clients that the market portfolio is selected because the market portfolio:

A) maximizes the Sharpe ratio.

B) maximizes return and minimizes risk.

C) maximizes return.

Your answer: B was incorrect. The correct answer was A) maximizes the Sharpe ratio.

The risk and return coordinate for the market portfolio is the tangency point for the capital market line (CML). The CML has the steepest slope of any possible portfolio combination. The slope of the CML is the Sharpe ratio. Therefore, the Sharpe ratio is highest for the market portfolio.

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Pegasus2008

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发表于 2011-7-11 19:44 | 只看该作者

If you calculate the slope of the CML from the graph at Rm, you will see that at the market return of Rm, you have the highest point on the curve. The slope is simply rise over run, so it is (Rm-Rf) / (std deviation of market - std deviation of risk-free asset), which is (Rm-Rf) / (std deviation of market - 0), which is (Rm-Rf) / std deviation of market. So, you should invest by including some Rm in your portfolio to get the best return per unit of risk..something like that!

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President1988