Question 9 (of 10) 9 value: 10.00 points The following is part of the computer o

Question

Question 9 (of 10) 9 value: 10.00 points 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 29 over the coming month. Standard Deviation of Residuals 06 (i.e., 6% monthly) R-sq Beta .75 .65 No suppose that the manager misestimates the beta o ate works stock believing it to be 50 instead o .75. The standard devation o the mon hiy marke rate of retums 5% a. What is the standard deviation of the (now improperty) hedged portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Standard deviation b. what is the probability o incurring a loss over the next month f the monthly market return has an expected lue of 1% and a standard deva on o 5%? Do not round intermediate cal u atons Round your 6.13 % answer to 2 decimal places.) Probability of a negative return References eBook &Resources; Learning Objective: 20-02 Formulate "pure plays on seemingly misaligned security prices, and identify the risks that are hedged in these strategies as well as the risks that remain. Worksheet

Explanation / Answer

Since the manager has miss estimated the beta of Waterworks, the manager will sell four S&P 500 contracts (rather than the six contracts):

($2,000,000*0.50) / ($250*1,000) = 4 contracts

The portfolio is not completely hedged so the expected rate of return is no longer 2.5%. We can determine the expected rate of return by first computing the total dollar value of the stock plus futures position.

The dollar value of the stock portfolio is:

$2,000,000* (1 +r portfolio) = $2,000,000 *[1 +0.005+ 0.75 *( r M- 0.005)+ 0.02+e ]

= $2,042,500+ $1,500,000 * r M +$2,000,000*e

The dollar proceeds from the futures position equal:

4 *$250 (F0-F1) = $1,000* [(S0- 1.005)- S1 ]

= $1,000* S0 * [1.005 -(1+ r M )]

= $5,000+ $1,000,000 * r M

The total value of the stock plus futures position at the end of the month is:

$2,047,500 + ($1,500,000+ $1,000,000)* r M + $2,000,000*e

= $2,047,500+ $500,000* (0.01)* r M + $2,000,000 *e

= $2,052,500+ $2,000,000 *e

The expected rate of return for the (improperly) hedged portfolio is:

= ($,2052,500/ $2,000,000) =-2.625%

Now the z-value for a rate of return of zero is: 2.625%/6.129% = 0.4283

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.