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Unformatted text preview: University of California, Los Angeles Department of Statistics Statistics C183/C283 Instructor: Nicolas Christou The efficient frontier with short sales allowed and risk free lending and borrowing Suppose riskless lending and borrowing exists. Let R f be the return of the riskless asset (savings account, treasury bills, government bonds, etc.). We will examine the geometric pattern of combi- nations of the riskless asset and a risky portfolio. Consider the portfolio possibilities curve below constructed using different combinations of two stocks. The efficient frontier is the concave part of the curve that begins with the minimum risk portfolio and extends to the maximum expected return portfolio. Risk (standard deviation) Expected return Suppose now that the investor wants to invest a portion of her wealth on portfolio A (a point on the efficient frontier) and her remaining wealth on the riskless asset. Let x be the portion invested in portfolio A and 1- x the portion invested in the riskeless asset. This combination is a new portfolio. It has the following expected return and standard deviation: 1...
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This note was uploaded on 06/02/2011 for the course STATS 183 taught by Professor Nicolas during the Spring '11 term at UCLA.
- Spring '11