Question

Question

1. You conduct a poll comparing two candidates. In a poll of 400 people,

210 prefer candida4te A, and 190 prefer B.

1. 1. What is the point estimate for the probability that a voter will choose candidate A?
   2. What is the stdev for that point estimate?
   3. What is the 95% Confidence interval?
   4. What is the probability that candidate B loses in the actual election?
   5. If you want to shrink one STDEV error to 1%. How many people do you need to survey
2. You are considering two investment choices:

A -> 1 year CD that pays 2% for sure;

       B -> investing in SP500 with 8% expected and 20% stdev.

1. 1. If you put 50% in each of the two, what in the mean and stdev for your portfolio return?
2. 2. You want to maximize your expected return for the portfolio, as long as the stdev risk is no more than 10% per year. What is the allocation to CD and to socks? What is the mean return of the portfolio?
   3. You want to reach 17% mean return per year as a minimum. What is the least amount you need to allocate to stocks? What is the stdev of the portfolio?

3. In addition to two instruments in question 5, you also can invest in a long-term bond with 4% meanreturn and 10% stdev annually. Stock and bonds funds have a correlation of -0.4(negative 0.4).
4. 1. What is the mean return and stdev for a portfolio that is 50% in stock and 55% in bond
   2. What is the mean return and stdev for a portfolio that is 25% in stock and 25% in bond and 50% in 1 year CD?
5. 3. What is the mean return and stdev for a portfolio that is 75% in stock and 75% in bond and -50%(negative 50%, ie borrow money) in 1 year CD?

Answer 1

a)

In a poll of 400 people , 210 prefer Candidate A.

So, point estimate for the probability that a voter will choose candidate A, = 210 / 400 = 0.525

b)

Standard deviation of point estimate, SE ( ) = = =.025

c)

95% Confidence interval-

- Z/2=0.025 * SE ( ) < p < + Z/2=0.025 * SE ( )

=0.525 - 1.96 * 0.025 < p < 0.525 + 1.96 * 0.025

=0.476 < p < 0.574

d)

The probability that candidate B loses in the actual election = The probability that candidate A wins in the actual election = P ( > .5 )

= P ( ( - p) / SE ( ​​​​​​​) > (.5-p) / SE ( ​​​​​​​) )

= P( Z> (.5 - .525)/.025) = P( Z> -1)

= 1- P ( Z<-1)

= 1-  

= 1- 0.15866

= 0.84134

The probability that candidate B loses in the actual election is 0.84134.

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