Advance corporate finance: exercises

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Advance corporate finance: exercises

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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%

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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?
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
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
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)

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Extraits

[...] As a conclusion, we can say that the more important the increase of CAC 40 is, the better the portfolio is doing. Explain what the CAC40 is and how its value is calculated. (You may need to do a little outside research to answer this question) What is the CAC40? The CAC 40 is the main stock market index for Paris. Created with 1000 base points in December 1987, it is determined on a base of 40 shares in the first market among 100 companies whose exchanges are the most important in the Euro next Paris. [...]

[...] ER calculation ER=Wa * ERa +Wc * ERc ER= 0,6 * 0,05 + 0,4 * 0,025 ER =0,04. 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. [...]

[...] The real rate of return represents in fact the exact gain of the portfolio during the year. It is a gain taking into account the purchasing power parity evolution over the year. By not doing that you do not take into account the value of the gain you just take into account the amount of money earned, and this is a really critical issue, especially when the country experienced a strong growth or enter in a strong recession (or at least non growth) period. [...]

[...] 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 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 You have bought stock on margin means that you bought it at the actual market price, so at T=0 the share price is $35. Here is a little overview of the situation. [...]

[...] The rate of the CAC 40 is the result of an average balanced by the capitalization of each value which composes the CAC 40. By this way, more the capitalization value is important, more its variation has an impact on the index. Although, a value cannot be more than 15% of balance into the CAC 40. Formula index value I of the CAC 40 index is calculated using the following formula: with t the day of calculation; N the number of constituent shares in the index (usually Qi,t the number of shares of company i on day Fi,t the free float factor of share fi,t the capping factor of share i (exactly 1 for all companies not subject to the 15% cap); Ci,t the price of share i on day Qi,0 the number of shares of company i on the index base date; Ci,0 the price of equity i on the index base date; and Kt the "adjustment coefficient for base capitalization" on day t (reflecting the switch from the French franc to the Euro in 1999).” Wikipedia You have purchased a stock for $35/share and it is now worth $50/share. [...]

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