Problem 1: You receive $1,500 as part of your work compensation, which you will not spend over the next year. You evaluate the following options:

. Invest $1,500 through your bank in a Certificate of Deposit (CD), which

promises an APR of 6% compounded monthly;

.  Divide the $1,500 in two parts: 80% is deposited in your savings account,

which pays an APR of 3% compounded annually; 20% is invested in shares of a new startup IMBAD. The advisor expects the shares to either grow in value by 50%, or drop in value by 20% over the next year.  The two scenarios are equally likely.

Answer the following questions, detailing all the information required:

1. What is the net  expected  return of each of the three aforementioned in- vestment vehicles (that is, the CD, the savings account and the shares)?

2. What is the net expected return of each of the two investment strategies? Which strategy would you pick to maximize expected return?

3. You are interested in comparing IMBAD to other assets:

(a) From Yahoo Finance, download monthly price data for the following comparables: Apple (tracker ID: AAPL) and Microsoft (tracker ID: MSFT). For each series, generate the realized net returns, the annu- alized sample average net returns, and the annualized standard devi- ation of these returns. You are interested in recent periods, therefore you disregard all data prior to January 2013. How do these estimates compare with IMBAD’s?

(b) Repeat the same exercise using the time series of the S&P500 index (tracker ID: GSPC). Comment on your findings.

(c) Would you ever invest in IMBAD if you could choose Apple or Mi- crosoft instead? Discuss.

Problem 2: The NY State has studied the frequency with which individuals and businesses make mistakes on their tax forms, which consist in documents of two pages.  Specifically, it has established that the probability of a mistake being in the first page is 0.08. Given that the first page features a mistake, the probability that the second page also has a mistake rises to 0.25; given that the first page does not have a mistake, then the probability that the second page does drops to 0.05.  Let  denote the number of pages with errors on a randomly selected form, which itself is a random variable.  Find the expected value of the random variable , which is E[X], and its volatility σ[X].