363LecNote-Part3

# 363LecNote-Part3 - 5 Risk and Rates of Return 5.1 Portfolio...

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5 Risk and Rates of Return 5.1 Portfolio Basics Portfolio Weights Example: A portfolio consists of \$1 million in IBM stock and \$3 million in AT&T stock. What are the portfolio weights of the two stocks? (portfolio weights) Short-Selling Investors can sell short certain securities — they can sell investments that they do not currently own. When/Why might you want to sell securities that you do not own?

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(short-selling) To sell short securities, the investor must borrow the securities from someone who owns them. This is known as taking a short position in a security. To close out the short position, the investor buys the investment back and returns it to the original owner. Selling short an investment is equivalent to plac- ing a negative portfolio weight on it. In contrast, a long position , achieved by buying an investment, has a positive portfolio weight. Many-Stock Portfolio Example: Describe the weights of a \$40 , 000 portfolio invested in four stocks. The dollar amounts invested in each stock are as follows: Stock :1 2 3 4 Amount : \$20 , 000 \$5 , 0 0 0\$ 2 5 , 000 (many stock portfolio weights)
Portfolio Returns Example: A \$4 million portfolio is composed of \$1 million of IBM stock and \$3 million of AT&T stock. If IBM s tockha sar e tu rno f10%andAT&Ts sa return of 5%, what is the portfolio return? (Portfolio Returns) (Portfolio Returns) In general, for N securities, indexed 1 through N , the portfolio return ( R p )isg ivenby R p = w 1 r 1 + w 2 r 2 + ... + w N r N = N X i =1 w i r i where r i is the return on the i -th security, and w i is its portfolio weight. This is nothing but an weighted average of re- turns.

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5.2 Expected Return No one has the luck of invest with perfect fore- sight. We focus on the anticipated (expected) future returns of investments. A variety of future return outcomes are likely to exist for a given risky investment, each occurring with a speci f c probability. To compute the expected return (also called the mean return), weight each of the return outcomes by the probability of the outcome and sum the probability weighted returns over all outcomes. Example: Suppose that the return on Dell Computer depends on the future economic growth. Compute the expected return on the Dell stock using the following table. Growth Probability Return Outcome High 25% +30% Medium 40% +10% Low 35% 20% In practice, one often estimates the expected re- turn by computing the historical average returns. Example: Historical Average Returns (source: Datastream) Year S&P500 NASDAQ T-bills 1996 25 . 7% 26 . 7% 5 . 2% 1997 36 . 9% 19 . 5% 5 . 3% 1998 32 . 2% 47 . 5% 4 . 9% 1999 24 . 3% 95 . 6% 4 . 7% 2000 5 . 7% 34 . 3% 5 . 9% 2001 10 . 8% 21 . 2% 3 . 8% 2002 21 . 4% 30 . 6% 1 . 6% 2003 28 . 5% 52 . 3% 1 . 0% 2004 10 . 5% 8 . 4% 1 . 2% 2005 5 . 1% 3 . 6% 3 . 0% average 12 . 5% 16 . 8% 3 . 7% Std. Dev. 20 . 1% 40 . 9% 1 . 8% Properties of Expected Returns The expected value of a constant times a return is the constant times the expected return: E ( w × ˜ r )= w × E r ) where the notation ˜ r emphasizes that the future return r is uncertain (risky).
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## This note was uploaded on 11/05/2011 for the course FINA 363 taught by Professor Masoudie during the Spring '10 term at South Carolina.

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363LecNote-Part3 - 5 Risk and Rates of Return 5.1 Portfolio...

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