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 theworsethe 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 Capital's 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 Bob's portfolio after one year under each of the three possibilities for the market. Clearly label each case.

e) What is the expected return on Bob's portfolio?

f) Calculate the variance and standard deviation of the return on Bob's portfolio.