The risk free asset is important to the capital asset pricing model. When a risk-free asset is combined with a risky portfolio (assume the proportion of the portfolio the investor places in the tangency portfolio T is wT):
A graph of possible portfolio risks-return combinations becomes a straight line between the two assets.
The introduction of a risk-free asset changes the efficient frontier into a straight line. This straight efficient frontier line is called the Capital Market Line (CML) for all investors, and Capital Allocation Line (CAL) for one investor. Since the line is straight, the math implies that any two assets falling on this line will be perfectly positively correlated with each other. Note: When p(a,b) = 1 then the equation for risk changes to σportfolio = WAσA + WBσB.
Now, the line Rf-M dominates all portfolios on the original efficient frontier. Thus, the CML becomes the new efficient frontier.
Portfolio M is a completely diversified portfolio that includes all risky assets in proportion to their market value. It is referred to as the market portfolio. It includes all risky assets.
The CML represents all the possible portfolio combinations by investing in the risk-free asset and the market portfolio.
Note for CAL, the portfolio used in the equation does not necessarily need to be a fully diversified portfolio. It is the best portfolio available to one single investor.
The CML leads all investors to invest in the same risky portfolio, the market portfolio. That is, all investors make the same investment decision. They can, however, attain their desirable risk preferences by adjusting the weight of the market portfolio in their portfolios.
Therefore, investors make different financing decisions based on their risk preferences. The separation of the investment decision from the financing decision is called the separation theorem.
A. (E(RP) - RF) / σP.
B. (E(RP) - RF) / σC.
C. (E(RP) - RF) / σM.
Note this is CAL and it has nothing to do with the market portfolio.
I. After adding the risk-free asset to a risky portfolio, the shape of efficient frontier changes from a curve to a line.
II. CML assumes all investors have the same risk aversion level.
III. An investor's CAL is a straight line.
The CAL intersects the y-axis at the risk free rate and lies tangent to the efficient frontier.
I. the expected return is 8.5%
II. the standard deviation is 12%.
III. the standard deviation is 20%.
E(Rp) = (0.6)(0.12) + (0.4)(0.05) = 0.092 or 9.2%. wp σ 2X = (0.6)(0.20) = 0.12 or 12%.
A. I will generate a rate of return equal to X's
B. I will create a portfolio with less risk than X
C. I will create a portfolio with more risk than X
D. my new portfolio will have an expected return less than X's
The portfolio's risk is equal to the weight in X times X's standard deviation. Borrowing at the risk-free rate allows us to establish a weight in X that is greater than 100%. Therefore, the risk level will exceed that of X alone.
I. contains all risky assets
II. is efficient
III. is the preferred combination of risky assets for all investors
Investors will agree on M but will disagree on how much M to combine with the risk-free asset.
A. M is not efficient by itself, but must be combined with the risk-free asset
B. Portfolios formed by borrowing at the risk-free rate and investing in M are less risky than M alone
C. The Capital Market Line connects the zero risk, zero expected return point with M
D. A portfolio with 50% M and 50% risk-free asset will have 1/2 the risk of M
M is efficient - it lies on the EF. Borrowing portfolios are more risky because they have added financial risk (leverage). The CML goes to the RF, which dominates holding currency (zero risk, zero return).
A. it is the most efficient of all portfolios.
B. it is the one portfolio that all investors will choose to get the highest CML.
C. it dominates all portfolios on the CML.
The other answers are untrue.
A. capital allocation line.
B. efficient frontier.
C. capital market line.
I. When combined with the risk-free asset, no other portfolio along the efficient frontier provides a higher expected reward-to-risk ratio than the tangency portfolio.
II. Investors can have different CALs.
III. When combined with the risk-free asset, the optimal risky portfolio should always be the tangency portfolio.
II: The intercept and slope of the CAL depends on the asset expectations (mean returns, variance of returns, and correlations) of an individual investor.
III: This is because the portfolio maximizes the investor's reward-to-risk ratio.
I. The risk-free asset has a variance of 0
II. Any portfolio containing the risk-free asset has zero risk
III. The risk-free asset has a correlation of 0 with any risky asset
By definition, the risk-free asset has a variance and a standard deviation of 0. Portfolios containing the risk-free asset will have risk proportionate to their exposure in risky assets. Since its return does not vary, the risk-free asset is uncorrelated with any risky asset.
A. consisting of risky assets moves down parallel to itself.
In the presence of a risky asset, the efficient frontier of risky assets is dominated by a new efficient frontier consisting of the risk-free security and the tangent portfolio found by joining the risk-free security with a point on the efficient frontier of risky securities where the line has the highest slope.
The CML is the line that is tangent to the efficient frontier and has the intercept equal to the risk-free rate. It is plotted on the expected return versus the standard deviation plane.