1. Assume these facts as true: Sen. Burr chaired the Senate Intelligence Committee. At a closed confidential hearing in late January, he heard dramatic evidence that the corona virus was likely to heavily impact the United States and its economy (which is what happened). The following day, Sen. Burr called his stockbroker and told him to sell all of his $2 million worth of stock holdings. Two weeks later, the danger of the corona virus became known to the public, and the stock market lost much value. Sen Burr saved $400,000. By selling his stock when he did. Was Sen Burr an “insider”. Did he violate the insider trading laws? Argue one way or the other but support your argument.

Assume these facts as true. Sen Loeffler attended the above described hearing chaired by Sen. Burr. When she returned home that evening, she told her husband about the hearing. Her husband is Chairman of the New York Stock Exchange. The next day, without telling his wife, he sold $3.5 million worth of stock jointly owned with his wife. He saved $600,000.00 in losses by selling his stock then. Was Sen Loeffler or her husband an “insider”? Did either of them violate the insider trading laws? Argue one way or the other.

References

While her husband spent 2½ hours picking out new speakers, a statistician decided to determine whether the percent of men who enjoy shopping for electronic equipment is higher than the percent of women who enjoy shopping for electronic equipment. The population was Saturday afternoon shoppers. Out of 65 men, 25 said they enjoyed the activity. Eight of the 22 women surveyed claimed to enjoy the activity. Interpret the results of the survey. Conduct a hypothesis test at the 5% level. Let the subscript m = men and w = women.
NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

State the distribution to use for the test. (Round your answers to four decimal places.)

P'_m − P'_w ~N : 0, ________ ?

In the following, S0 is the stock price in dollars as of today, K is the strike price in dollars, r is the continuously-compounded risk-free interest (as a decimal), q is the continuous dividend yield (as a decimal), sigma is the volatility (as a decimal) and T is the time to maturity in years. Compute option prices in dollars for the following types of options and the following parameter values with a three step binomial tree.

A. S0 = 100, K = 100, r = 0.07, q = 0.05, sigma = 0.3, T = 1. European call. What is the price in dollars today?

B. S0 = 100, K = 100, r = 0.07, q = 0.05, sigma = 0.3, T = 1. European put. What is the price in dollars today?

C. S0 = 100, K = 100, r = 0.07, q = 0.05, sigma = 0.3, T = 1. American call. What is the price in dollars today?

D. S0 = 100, K = 100, r = 0.07, q = 0.05, sigma = 0.3, T = 1. American put. What is the price in dollars today?

We define the “Early exercise premium” to the difference between the American option price and the corresponding European option price. For the case of call options, and S0 = 100, r = 0.07, q = 0.05, sigma = 0.3, T = 1.

E. What is the Early exercise premium when K = 100?

F. What is the Early exercise premium when K = 125?

G. What is the Early exercise premium when K = 75?

H. What is the Early exercise premium when K = 60?

I. In the case that S0 = 100, r = 0.07, q = 0.05, sigma = 0.3, T = 1, and for an American call option with strike K = 60, what is the price in dollars today?

J. In the case that S0 = 100, r = 0.07, q = 0.05, sigma = 0.3, T = 1, and for an American call option with strike K = 60, at what time would a holder of the option optimally exercise?

All the questions above set the dividend yield to q = 0.05. Change the dividend yield to q = 0.10 and answer the questions corresponding to questions E, F, G and H above.

K. What is the Early exercise premium when the dividend yield q = 0.10 and K = 100?

L. What is the Early exercise premium when the dividend yield q = 0.10 and K = 125?

M. What is the Early exercise premium when the dividend yield q = 0.10 and K = 75?

N. What is the Early exercise premium when the dividend yield q = 0.10 and K = 60?

Now set the dividend yield q = 0.10 and the strike K = 75. . For the case of the European call, q = 0.10 and K = 75, what is the Delta (position in stock to make portfolio of the stock and a short position in one option riskless).

P. For the case of the American call, q = 0.10 and K = 75, what is the Delta (position in stock to make portfolio of the stock and a short position in one option riskless).

Consider the market for butter in Dammam. The demand and supply relations are given as follows:

Demand:             QD = 300 - 2P + 2I             

Supply:               Qs = 3P - 25PM - 25

Where I is the average income and P is the price of butter and PM is the price of milk.

(a)             Assume that I = 25 and PM=2. Calculate:

Equilibrium price of butter (P): ________________                          

Equilibrium quantity of butter (Q):_________________  

(b)             If I = 25, calculate the own-price elasticity of demand of butter at P=100. Is the demand elastic or inelastic?

Eb=.                                       . Demand is ___________________

(c)             If P = 100, calculate the income elasticity of demand of butter at I=25. Is the demand elastic or inelastic?

EI=.                                       . Demand is ___________________

(d)             If P = 100, calculate the cross-price elasticity of supply of butter at PM=5.

EbM=.                                       .

Firm A plans to acquire Firm B. The acquisition would result in incremental cash flows for Firm A of $10 million in each of the first five years. Firm A expects to divest Firm B at the end of the fifth year for $100 million. The beta for Firm A is 1.1, which is expected to remain unchanged after the acquisition. The risk-free rate, Rf, is 7%, and the expected market rate of return, Rm is 15%. Firm A is financed by 80% equity and 20% debt, and this leverage will remain unchanged after the acquisition. Firm A pays interest of 10% on its debt, which will also remain unchanged after the acquisition.
i) Disregarding taxes, what is the maximum price that Firm A should pay for Firm B?



ii) Firm A has a stock price of $30 per share and 10 million shares outstanding. If Firm B shareholders are to be paid the maximum price determined in part (a) via a new stock issue, then how many new shares will be issued and what will be the postmerger stock price?

Use the P-value Approach for all hypothesis tests. Assume that all samples are randomly obtained.

The first significant digit in any number is: 1, 2, 3, 4, 5, 6, 7, 8, and 9. Though we may think that each digit would appear with equal frequency, this is not true. Physicist, Frank Benford, discovered that in many situations where counts accumulate over time that the first digit in the count follows a particular pattern. The probabilities of occurrence to the first digit in a number, known as Benford’s Law, are shown below.

Bloomberg’s web site (www.bloomberg.com) gives information on the stock price and trading volume of the members of the S&P 500 stock index. Suppose a random sample of 100 stocks on a given day were selected from the site, and the first digit of the daily stock volume (total number of shares traded in a given day) was recorded below.

Using a 10% level of significance, test whether the first digits in the stock price follow the distribution of probabilities given by Benford’s Law. Be sure to verify the requirements for the test.