### Holding period return-capital gains yield

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Problem 1: Your parents purchased 250 shares of a stock for \$51.21 per share at the beginning of the year. Due to your bills for school they sold them for \$45.69 per share after receiving \$150.00 dividend in total at the end of September. (Disregard the timing and TVM issue associated with dividends: Just assume that this is the total dividend received on this date!)

i. What is the holding period return (HPR) of their investment?

ii. What is the capital gains yield of their investment?

iii. What is the dividend yield of their investment?

iv. What is the total yield of their investment?

v. What is the annualized return of your parent's investment?

vi. Is there any problem with annualizing this way? Be precise.

Problem 2: As an equity analyst you observe the following annual rates of return for a mutual fund.

 Year Return 2007 5.49% 2008 -37.00% 2009 26.46% 2010 15.06% 2011 2.11% 2012 16.00%

i.  What is the annual arithmetic mean of the mutual fund?

ii. What is the geometric mean of the mutual fund?

iii. Suppose your parents invested in this mutual fund and made annual deposits to their account. Your parents are just buying and holding the mutual fund for future. Which return calculation method would be the best to evaluate their annual return, arithmetic or geometric? WHY? Show your work.

Problem 3: As an equity analyst you evaluate the following three newly formed three mutual funds with the following information:

 Mutual Fund Time since Inception Return since Inception X 200 days 7.45% Y 7 weeks 0.57% B 14 months 12.65%

i. Calculate each fund's annualized rate of return. Show your work.

ii. Is there any problem with annualizing this way? Be precise.

Problem 4: Suppose you invest \$7,500 and receive 4.5% interest per year.

i. If you invest for one year, how much money would you have in your account?

ii. If you invest for seven months, how much money would you have in your account?

iii. If you invest for 30 months, how much money would you have in your account?

Problem 5: Suppose you invest \$7,500 and receive 4.5% interest per year but compounded continuously. (Note that this is the same question as 4!)

iv. If you invest for one year, how much money would you have in your account?

v. If you invest for seven months, how much money would you have in your account?

vi. If you invest for 30 months, how much money would you have in your account?

vii. Compare your results in question-4. How much difference is there?

Problem 6: Suppose you go to Rocket Bank where they pay 5% interest continuously.

i. Your parents want to have \$1,000 in their account in exactly one year. How much money do they need to invest now in Rocket Bank?

ii. Your parents want to have \$5,000 in their account in 5 months. How much money do they need to invest now in Rocket Bank?

iii. Your parents want to have \$10,000 in their account in 20 months. How much money do they need to invest now in Rocket Bank?

Problem 7: Suppose that XYZ-Inc. stock price is \$31, and the exercise price of a 3-month European call and put options written on this stock is \$30. The risk-free interest rate is 10% per annum, the call and put option prices are \$3, and \$2.25, respectively.

Are these prices arbitrage free? If no, WHY?

And how can you take advantage of the arbitrage opportunity?

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