The following is part of the computer output from a regression of monthly returns on Waterworks stock against the S&P 500 index. A hedge fund manager believes that Waterworks is underpriced, with an alpha of 2% over the coming month.
Beta = 0.75
R-square = 0.65
Standard Deviation of Residuals = 0.06 (i.e., 6% monthly)
Assuming that monthly returns are approximately normally distributed, what is theprobability that this market-neutral strategy will lose money over the next month?
Assume the risk-free rate is .5% per month.
Answer:
0.33853
Explanation:
Given that, the expected rate of return of the market-neutral position is equal to the risk-free rate plus the alpha:
0.5%+ 2.0% = 2.5%
Hence, since we assume that monthly returns are approximately normally distributed.
The z-value for a rate of return of zero is
−2.5%/6.0% = −0.4167
Therefore, the probability of a negative return is N(−0.4167) = 0.33853
<em>Break-even point is the level of activity that achieves no profit or loss. At this level profit is zero because the the total revenue is equal to total cost.</em>
<em>The break-even point is calculated as </em>
<em>Units to achieve target profit = (Total general fixed cost for the period + target profit)/ contribution per unit</em>
Contribution per unit = Selling Price - Variable cost
Contribution per unit = 15- (1+3+0.50) = 10.5
Fixed cost = 500 +( 50× 4) = 700
So the units requited to achieve break-even point:
