BA 443
In-class solution
02/04/09
1. Beta of an equal-weighted portfolio:
1.2 * 0.25 + 1 * 0.25 + 1.69 * 0.25 + 2.46 * 0.25 = 1.59
2. With a long-only portfolio, the best we can do is to eliminate our positions in AT&T
and Sprint and double up our positions in Verizon and Quest.
Beta: 1.2 * 0.5 + 1.69 * 0.5 = 1.45
3. Without the short-selling constraint, we would go long Verizon and Quest and short-
sell AT&T and Sprint. The weights would be 0.5, 0.5, -0.5, -0.5.
Beta: 1.2 * 0.5 + 1.69 * 0.5 + 1 * (-0.5) + 2.46 * (-0.5) = -0.29
4. Returns for each of the portfolios:
Portfolio 1: Invested $250,000 in each of the four stocks. Verizon and
Quest increase by 2%, which means that the values of those investments increase
to 255,000. AT&T and Sprint decrease by 2% which means that the value of those
investments decrease to 245,000. At the end of the month, the portfolio value
would be:
255,000 + 255,000 + 245,000 + 245,000 = 1 million
Return = 0%
Portfolio 2: The $500,000 positions in Verizon and Quest would increase to
$510,000 each. Our portfolio value at the end of the month would be 1.02 million.
Return = 2%
Portfolio 3: Our long positions would increase to 1.02 million (as in portfolio 2).
Our short positions would also increase by 20,000. So our portfolio value would
be 1.04 million, with a return of 4%.
