Hydra Capital offers a range of 1-year investment products for customers. The details for two such investment products are as follows:

Investment A is a security tied to market performance. For an initial investment of $100, the security, one year from today, will be worth:

• $145 if the market is good,
• $108 if the market is moderate, and
• $85 if the market is bad.

Investment B is a security also tied to the performance of the market. However, it performs better the worse the market is doing. For an initial investment of $100, the second security, one year from today, will be worth:

• $75 if the market is good
• $87 if the market is moderate, and
• $165 if the market is bad.

Bob is a prospective investor looking at Hydra Capitals investment products. He has studied the market and concludes that over the coming year, there is a 25% chance the economy will be good, a 45% chance the market will be moderate, and a 30% chance the market will be bad.

a) If Bob spends $100 on Investment A, what is his expected return for the year, assuming he is correct about the economy over the coming year?

b) What is the variance and standard deviation for the return on Investment A?

c) If Bob spends $100 on Investment B, what is his expected return for the year?

Bob considers both products, and ultimately decides to spend $600 on Investment A and $400 on Investment B to construct his investment portfolio.

d) Determine the value of Bobs portfolio after one year under each of the three possibilities for the market. Clearly label each case.

e) What is the expected return on Bobs portfolio?

f) Calculate the variance and standard deviation of the return on Bobs portfolio.