A global equity manager is assigned to select stocks from a universe of large stocks throughout the world. The manager will be evaluated by comparing her returns to the return on the MSCI World Market Portfolio, but she is free to hold stocks from various countries in whatever proportions she finds desirable. Results for a given month are contained in the following table:

a. Calculate the total value added of all the manager’s decisions this period. (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

b. Calculate the value added (or subtracted) by her country allocation decisions. (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

c. Calculate the value added from her stock selection ability within countries. (Do not round intermediate calculations. Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.)

5. This problem illustrates an interesting variation of simple random sampling.

a. Open a blank spreadsheet and use the RAND() 
function to create a column of 1000 random numbers. Don’t freeze them. This is actually
a simple random sample from the uniform distribution between 0 and 1. Use the COUNTIF function to count the number of values between
0 and 0.1, between 0.1 and 0.2, and so on. Each such interval should contain about 1/10 of all values. Do they? (Keep pressing the F9 key to see how the results change.) 


b.Repeat part a, generating a second column of random numbers, but now generate the first 100
as uniform between 0 and 0.1, the next 100 as uniform between 0.1 and 0.2, and so on, up to
0.9 to 1. (Hint: For example, to create a random number uniformly distributed between 0.5 and 0.6, use the formula =0.5+0.1*RAND(). Do you see why?) Again, use COUNTIF to find the number of the 1000 values in each of the intervals, although there shouldn’t be any surprises this time. Why might this type of random sampling be preferable to the random sampling in part a? (Note: The sampling in part a is called Monte Carlo sampling, whereas the sampling in part b is basically Latin Hypercube sampling, the form of sampling we advocate in Chapters 15 and 16 on simulation.)

The following table lists the weight of individuals before and after taking a diet prescribed by a weight-loss company for a month:

You may find this Student's t distribution table useful in answering the following questions. You may assume that the differences in weight are normally distributed.

a)Calculate the sample variance (s_d²) of the changes in individual weights. Give your answer to 2 decimal places.

s_d² =

b)A disgruntled customer states:

"This weight-loss company is a complete farce. All the people I know who signed up experienced no changes in their weight at all. I seriously doubt this diet has any effect whatsoever. I want my money back!"

You plan to do a hypothesis test on this claim where the hypotheses are:

H₀: the customer's claim is true and the program has no effect on weight
H_A: the customer's claim is not true and the program does have an effect on weight, whether it increases or decreases

According to the data given, you should accept, reject, not reject the null hypothesis at a confidence level of 90%.

1. IDM purchases one model of computer at a wholesale cost of $300 per unit and resells it to end consumers. The annual demand for the company’s product is 600,000 units. Ordering costs are $1,200 per order and carrying costs are $75 per computer, including $30 in the opportunity cost of holding inventory. It currently takes 2 weeks to supply an order to the store. assume that demand can vary during the 2-week purchase-order lead time. The following table shows the probability distribution of various demand levels: Total Demand for computers for 2 Weeks Probability of Demand (sums to 1) 21,670 0.05 22,450 0.2 23,078 0.5 24,820 0.2 25,820 0.05 If IDM runs out of stock, no safety stock is kept. It would have to rush order the computers at an additional cost of $3 per computer. How much could IDM spend in stock out cost?

2.

IDM purchases one model of computer at a wholesale cost of $300 per unit and resells it to end consumers. The annual demand for the company’s product is 600,000 units. Ordering costs are $1,200 per order and carrying costs are $75 per computer, including $30 in the opportunity cost of holding inventory. It currently takes 2 weeks to supply an order to the store.

(Please round all numbers to the next digit).

What is the annual relevant total cost of ordering and carrying inventory with the EOQ?

A financial analyst has recently argued that portfolio managers who rely on asset allocation techniques
spend too much time trying to estimate expected returns on different classes of securities and not enough
time on estimating the correlations between their returns. The correlations are important, he argues,
because a change in correlation, even with no change in expected returns, can lead to changes in the
optimal portfolio. In particular, he argues that as the correlation between stock and bond returns ranges
from 0.2 to 0.6, “the allocation to stocks remains fairly constant…but there are major asset shifts between
cash and bonds”.
See if you can illustrate this point with the following example: A portfolio manager is considering three
categories assets: stocks, bonds and cash. The expected returns, E(r), and standard deviations of returns
for these assets are as follows:
E(r) Std. Dev.
Stock 0.14 0.17
Bonds 0.10 0.09
Cash 0.08
The average degree of risk aversion of the portfolio’s clients is A= 4.
(a) What is the optimal complete portfolio composition if the correlation between stock and bond returns
is 0.2? (10 points)
(b) What is the optimal complete portfolio composition if the correlation between stock and bond returns
is 0.6? (10 points)
(c) Are your answers to (a) and (b) consistent with the analyst’s point? How would you explain what is
happening as we move from the conditions in part (a) to those of part (b)? (10 points)

The demand for electrical components is fixed at a rate of 2400 units/month.Each time the store makes an order ot costs 320$.The item costs $3.the annual inventory holding cost rate is 20%. Q*=5543 units, T8=2.3 months.

Explanation: Periodic rderis calculated on the annual demand basis. Annual demand D=2400 *12units/year. The order cost K is $320 and now we need ‘h’ which is holding cost per unit. As we have $3 per unit cost the annual holding rate is 0.2 of it, which is 0.2*3= $0.6 /per unit holding cost in $. Then we have the EOQ= sqrt(2*2400*12*320 /0.6)=5543 units/order. With K=320, h=$0.6 we have Toptimal (in years) = sqrt(2*320/(0.6*2400*12))=0.19yr=2.3 months- every 2.3 months the inventory is to be replenished by 5543 units.

So, components are stored in inventory for 2.3 months before they are fully sold. The inventory turns ( annually) in such case is1/ 0.19 ( year)=5.26

Let’s increase the inventory annual holding cost rate from 20% to 30%, all else being the same How would that reflect on the EOQ value, optimal period and inventory turns#?

Note for help: consistency matters- if the inventory holding cost rate is given as annual, the demand D also has to be given as annual.

A particular variable measured on the US population is approximately normally distributed with a mean of 126 and a standard deviation of 20. Consider the sampling distribution of the sample mean for samples of size 36. Enter answers rounded to three decimal places.

According to the empirical rule, in 95 percent of samples the SAMPLE MEAN will be between the lower-bound of ____and the upper-bound of_____

For a particular large group of people, blood types are distributed as shown below. (Note that each person is classified as having exactly one of these blood types.)

(a) If one person is selected at random, what is the probability that the selected person's blood type will be either AB or O?

A. 0.45
B. 0.4
C. 0.05
D. None of the above.

(b) A person who has type B blood can safely receive blood transfusions from people whose blood type is either O or B. If a person is selected at random, what is the probability that the selected person will be able to safely donate blood to a person with type B blood?

A. 0.55
B. 0.31
C. 0.11
D. None of the above.

(c) If two people are independently selected at random, what is the probability that both will have type O blood?

A. 0.04
B. 0.4
C. 0.2
D. None of the above.

Let the difference be defined as Before – After.