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Advance corporate finance: Exercises

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  1. You have two stocks with the following Expected Returns (ER) and Standard Deviations (SD)
    1. Show how you can create a portfolio with these two stocks which would have an ER of 8%. What is the SD of this portfolio?
    2. Now you also have a Risk-Free Asset with a return of 2.5%. Show how you can combine it with Stock A in order to create a portfolio with a SD of 3%. What is the ER of this portfolio?
    3. Now you want to create a portfolio with just the Risk-Free Asset and Stock B. Show how you can create a portfolio with these two securities that has an ER of 13%. What do you need to do to create this portfolio?
  2. You put 15000 euros into a group of French stocks on January 1. On June 30, your portfolio's value was 16,125 euros. The next day you added another 3000 euros to the portfolio
    1. Calculate your annual return on the portfolio, if no other money was added or removed, and the value on December 31 was 18,360 euros
    2. If inflation for the year was 4%, what was your real return on your portfolio? What does this mean?
    3. During the same year the CAC40 went from 2500 to 2565. Considering this, do you think your stock portfolio did well or did badly? Explain
    4. Explain what the CAC40 is and how its value is calculated
  3. You have purchased a stock for $35/share and it is now worth $50/share. You would like to wait until the stock reaches $60/share before you sell it, but you are worried that its price might fall suddenly
    1. What type of orders should you make to ensure that you sell it when it rises to $60/share or falls to $20/share? (market, limit, stop-loss)
    2. Assume that you have bought the stock on margin, and borrowed 50% of the purchase price. You purchased 100 shares. If the maintenance margin requirement is 30%, and the price of the stock falls to $22/share, will you receive a margin call ? i.e. will you have to add more money to your account? Explain your calculation
    3. If the price falls to $20/share and you sell your shares, which you purchased on margin at an 8% interest rate, calculate your percentage return on this investment?
    4. Explain what short sales are and why they are dangerous for investors. Also explain why governments often restrict their use
  4. You have decided to buy stock options
    1. Your first purchase is a call option on a stock, with an exercise price of $45/share and a premium of $3/share. If the stock rises in price to $57/share on the date of expiration, how much is your net profit/share (after subtracting the premium paid)?
    2. Now you have bought a put option on another stock, with an exercise price of $80/share, and a premium of $5/share. Calculate the breakeven price of this option, i.e. at what price would the stock have to be so that you have not gained or lost any money by buying this option
    3. If the stock of the put option above (with a premium of $5/share) is selling for $82/share, calculate the time value of this option
    4. Explain the five factors discussed in class that affect the premiums of put and call options (eg. time to maturity)

You have two stocks with the following Expected Returns (ER) and Standard Deviations (SD). Stock A: ER = 5%, SD = 5%. Stock B: ER = 10%, SD = 10%. The correlation coefficient is 0.5.

Show how you can create a portfolio with these two stocks which would have an ER of 8%. What is the SD of this portfolio?

First we have to calculate Wa and Wb. Afterwards we can enter the SD calculation.
Wa calculation - Let's use the following formula:
0.08 = 0.05Wa + 0.1Wb 0.08 = 0.05Wa x 0.1(1-Wa) 0.08 = 0.05Wa x 0.1-0.1Wa -0.02 = -0.05Wa 0.02 = 0.05Wa Wa = 0.02/0.05 Wa = 0.04
So we have Wa equal 40%

[...] In the 1970s, Fama published a review of both the theory and the evidence for the hypothesis. The paper extended and refined the theory, included the definitions for three forms of financial market efficiency: weak, semi- strong and strong. The weak form states that it is not possible to make money off the previous price. The semi strong form states that it is not possible to make money off public information because when the information becomes public it is too late to take advantage of the information. [...]


[...] Although one can make fast money in the stock market, like any action on the market it comes with risks. If the security price falls, the short-seller makes money on the difference between the prices at which he sold the borrowed securities and the price at which he purchased them back during the closing. ?However, if the security price rises, the short seller loses by having sold them for less than the price at which he later has to buy them. [...]


[...] value of Wc is 40%. ER calculation ER=Wa * ERa +Wc * ERc ER= 0.6 * 0.05 + 0.4 * 0.025 ER = The value of the ER is 40%. Now you want to create a portfolio with just the Risk-Free Asset and Stock B. Show how you can create a portfolio with these two securities that has an ER of 13%. What do you need to do to create this portfolio? We have to calculate the Wb and Wrf in order to create this portfolio. [...]

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