# Midterm

Midterm Econ 171, instructor: Tyler Hull

Name______________________________________________

Give the best answer for each question, showing formulas used can only help your grade.

Show you work!

Good Luck, you will do great!

1. Alex always dreamed of owning 100 Dalmatians, not 101 but 100. He currently has the opportunity to invest at an 8% risk free rate. Each Dalmatian currently costs $45.

A) Assuming prices do not change, how much must he invest today to be able to buy the dogs in 4 years time? (use annual compounding)

B) What was Alex’s exact annual real rate of return if at the end of 4 years if the money he has can only buy 89 Dalmatians?

C) Not taking in account inflation, if Alex is in the 30% tax bracket and is deciding between a 8% risk free return and a 5% municipal bond (also risk free), which should he choose and why(show math)?

2. You would like to short a stock called OWZA, currently priced at $46. Your broker requires a 50% initial margin requirement and a 30% maintenance margin, assume there is no interest on the margin account.

A) If you have 30,000 dollars today, how many shares can you short? (Assume this answer can have decimals)

B) What percent change in price of OWZA will lead to a margin call (assume no time has elapsed)?

C) If the price falls 9 dollars over a one year period, what is your holding period return (HPR)?

3. You would like to borrow $50,000 for a period of two years. You are deciding between a loan for $50,000, in which you pay an 8.25% interest rate compounded annually or a loan of $50,000, in which you pay an 8% interest rate compounded quarterly? On either loan you do not need to make any payments until 2 years time.

A) Calculate the final payment you will have to make in either case and state which loan you would prefer to use to borrow $50,000.

B) Construct a Market Weighted index, using these three stocks, use them to find the market weighted index return:

Stop inc. P0=40 Q0=200 P1=44 Q1=200

Drop Co. P0=20 Q0=500 P1=8 Q1=1000

Roll Tech. P0=5 Q0=1000 P1=3 Q1=3000

C. Explain what R- squared is, when used for a particular stock in contrast to the market? What relationship does R-squared have with firm specific risk for a particular security?

4. Use the following information for stock Hip and stock Cool:

E(rHip)=.09 SDhip=.15

E(rcool)=.12 SDcool=.2

rf=.03 Correlation coefficient= .25

A) Find the expected return and standard deviation of a portfolio with 30% allocated to stock Cool and 70% allocated to stock Hip.

B) Draw a graph that shows and labels the following:

X and Y axis (names), POS, Optimal risky portfolio, CAL, Optimal complete portfolio, risk free asset, and a tangent indifference curve

C) Explain why each item is drawn as it is and what this means, for:

POS, Optimal risky portfolio, CAL, Optimal complete portfolio, risk free asset and a tangent indifference curve(use the back of the paper if needed)

5. Worth 30 Points

A. if the optimal risky portfolio has an expected return of 15% and a standard deviation of 20%, write down your utility function you will need to maximize to determine the optimal complete portfolio using a risk free rate of .04. Take the derivative of this to maximize utility, show each step. Use this to come up with a formula for the optimal allocation to the optimal risky portfolio.

B. Solve for the Y value (as defined in class), if A=2 or 5 and give a thorough explanation what these optimal Y values mean and what your portfolio looks like.

C. Solve for the Sharpe ratio for when A=2 and A=5 in part C.

5. (Continued)

D. What if you can borrow at a 6% rate, now what is the optimal Y if A=2 or 5. What do these Y values mean and what would your portfolio look like.

E. Solve for the Sharpe ratio for when A=2 and A=5 in part D.

6. Assuming the assumptions of the CAPM, with E(rm)=.12 SDm=.2 and the rf=.03

A) If you have a stock, Aim High stock with beta=1.8. If e(raim high)=.20 what is Aim High’s Alpha?

B) Create a tracking portfolio to capture this gain. What is its expected return and Beta? Explain what your tracking portfolio is made up of.

C) Explain step by step how you will make a profit (initial and final selling and buying). What will your portfolio look like? Is the gain risk free, why or why not?

Name______________________________________________

Give the best answer for each question, showing formulas used can only help your grade.

Show you work!

Good Luck, you will do great!

1. Alex always dreamed of owning 100 Dalmatians, not 101 but 100. He currently has the opportunity to invest at an 8% risk free rate. Each Dalmatian currently costs $45.

A) Assuming prices do not change, how much must he invest today to be able to buy the dogs in 4 years time? (use annual compounding)

B) What was Alex’s exact annual real rate of return if at the end of 4 years if the money he has can only buy 89 Dalmatians?

C) Not taking in account inflation, if Alex is in the 30% tax bracket and is deciding between a 8% risk free return and a 5% municipal bond (also risk free), which should he choose and why(show math)?

2. You would like to short a stock called OWZA, currently priced at $46. Your broker requires a 50% initial margin requirement and a 30% maintenance margin, assume there is no interest on the margin account.

A) If you have 30,000 dollars today, how many shares can you short? (Assume this answer can have decimals)

B) What percent change in price of OWZA will lead to a margin call (assume no time has elapsed)?

C) If the price falls 9 dollars over a one year period, what is your holding period return (HPR)?

3. You would like to borrow $50,000 for a period of two years. You are deciding between a loan for $50,000, in which you pay an 8.25% interest rate compounded annually or a loan of $50,000, in which you pay an 8% interest rate compounded quarterly? On either loan you do not need to make any payments until 2 years time.

A) Calculate the final payment you will have to make in either case and state which loan you would prefer to use to borrow $50,000.

B) Construct a Market Weighted index, using these three stocks, use them to find the market weighted index return:

Stop inc. P0=40 Q0=200 P1=44 Q1=200

Drop Co. P0=20 Q0=500 P1=8 Q1=1000

Roll Tech. P0=5 Q0=1000 P1=3 Q1=3000

C. Explain what R- squared is, when used for a particular stock in contrast to the market? What relationship does R-squared have with firm specific risk for a particular security?

4. Use the following information for stock Hip and stock Cool:

E(rHip)=.09 SDhip=.15

E(rcool)=.12 SDcool=.2

rf=.03 Correlation coefficient= .25

A) Find the expected return and standard deviation of a portfolio with 30% allocated to stock Cool and 70% allocated to stock Hip.

B) Draw a graph that shows and labels the following:

X and Y axis (names), POS, Optimal risky portfolio, CAL, Optimal complete portfolio, risk free asset, and a tangent indifference curve

C) Explain why each item is drawn as it is and what this means, for:

POS, Optimal risky portfolio, CAL, Optimal complete portfolio, risk free asset and a tangent indifference curve(use the back of the paper if needed)

5. Worth 30 Points

A. if the optimal risky portfolio has an expected return of 15% and a standard deviation of 20%, write down your utility function you will need to maximize to determine the optimal complete portfolio using a risk free rate of .04. Take the derivative of this to maximize utility, show each step. Use this to come up with a formula for the optimal allocation to the optimal risky portfolio.

B. Solve for the Y value (as defined in class), if A=2 or 5 and give a thorough explanation what these optimal Y values mean and what your portfolio looks like.

C. Solve for the Sharpe ratio for when A=2 and A=5 in part C.

5. (Continued)

D. What if you can borrow at a 6% rate, now what is the optimal Y if A=2 or 5. What do these Y values mean and what would your portfolio look like.

E. Solve for the Sharpe ratio for when A=2 and A=5 in part D.

6. Assuming the assumptions of the CAPM, with E(rm)=.12 SDm=.2 and the rf=.03

A) If you have a stock, Aim High stock with beta=1.8. If e(raim high)=.20 what is Aim High’s Alpha?

B) Create a tracking portfolio to capture this gain. What is its expected return and Beta? Explain what your tracking portfolio is made up of.

C) Explain step by step how you will make a profit (initial and final selling and buying). What will your portfolio look like? Is the gain risk free, why or why not?

Midterm
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