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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 An investor can often sell a security that he does not own. This process is called “short selling”. So far we have assumed that short sales are not allowed which means x i ≥ , i = 1 , ··· ,n . When short sales are allowed some of the x i can be negative but as before always ∑ n i =1 x i = 1. With short sales allowed the investor can achieved larger expected returns but as we will see below this large increase in the expected return is associated with a very large increase in risk. Consider the following example with 2 stocks. A B ¯ R 0.14 0.08 σ 0.06 0.03 In addition ρ AB = 0 . 5. If short sales are not allowed the largest expected return the investor can have is 14% (invest all his wealth in stock A ). However, with short sales allowed higher expected returns can be achieved by short selling stock B (borrow B and sell it). The proceeds are used to buy more shares of stock A . For example, suppose the investor initially has $100 to invest. The investor can short $1000 worth of stock B and invest now $1100 in stock A . Therefore, x A = 11 and x B =- 10. The expected return and standard deviation of this combination are: ¯ R p = x A ¯ R A + x B ¯ R B = 11(0 . 14)- 10(0 . 06) = 0 . 74 ....
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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