Advanced corporate finance

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Stock A: ER = 5%, SD = 5%; Stock B: ER = 10%, SD = 10%;
The correlation coefficient is 0.5.

a) 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?

Formula : √(Wa2 x oa2 + Wb2 x ob2 + 2 x Wa x Wb x oa x ob x pab)

Standard Deviation of the Portfolio = (Wa2 x 0.052 + Wb2 x 0.12 + 2 x Wa x Wb x 0.05 x 0.01 x 0.5)

Expected Return : ER = Wa x Ra + Wb + Rb
8% = 5% X + (1 - X) x 10%
5% x X + 10% - 8% - 10% x X = 0
- 5% x X = 2%
X = - 2/5 = - 40%

Wa = 40% and Wb = 60% (100 - 40)
We have to invest 40% of our money in Stock A and 60% of Stock B.

Standard Deviation of the Portfolio = √(Wa2 x 0.052 + Wb2 x 0.12 + 2 x Wa x Wb x 0.05 x 0.01 x 0.5) = √(0.42 x 0.052 + 0.62 x 0.12 + 2 x 0.4 x 0.6 x 0.05 x 0.01 x 0.5) = 7.21%

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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?
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?
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%.
Explain the concept of Efficient Markets Hypothesis and what the difference is between the Weak, Semi-Strong, and Strong forms of it.
You put ?15000 into a group of French stocks on January 1. On June 30, your portfolio's value was ?16,125. The next day you added another ?3000 to the portfolio.
1. Calculate your annual return on the portfolio
2. If inflation for the year was 4%, what was your real return on your portfolio?
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?
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?
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.

Extraits

[...] Advanced corporate finance You have two stocks with the following Expected Returns and Standard Deviations (SD). Stock ER = SD = Stock ER = SD = The correlation coefficient is 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? Formula : x oa2 + Wb2 x ob2 + 2 x Wa x Wb x oa x ob x pab) Standard Deviation of the Portfolio = (Wa2 x 0.052 + Wb2 x 0.12 + 2 x Wa x Wb x 0.05 x 0.01 x 0.5 ) Expected Return : ER = Wa x Ra + Wb + Rb = X + x x X + 10% - - 10% x X = 0 - x X = X = - 2/5 = - 40% Wa = 40% and Wb = 60% (100 40) We have to invest 40% of our money in Stock A and 60% of Stock B. [...]

[...] 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. Exercise price = $80 / share Premium price = / share Breakeven price formula = Exercise Price Premium Breakeven price = 80 5 = 75 $ The Breakeven price is $75 per share 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. [...]

[...] On June 30, your portfolio's value was €16,125. The next day you added another €3000 to the portfolio. Calculate your annual return on the portfolio, if no other money was added or removed, and the value on December 31 was €18,360. Formula of Average Annual Return = (Final Stock Price - Starting Stock price / Starting Stock price + Average Annual Return = ( ( 16125 15000 / 15000 + 1 ) x ( 18360 (16125 + 3000) / (16125 + 3000) + 1 = 1.075 x 0.96 1 = 0.032 = The annual rturn on the portfolio is 3,2%. [...]

[...] What does this mean? Formula = ( 1 + Nominal Rate ) = ( 1 + Real Rate ) x ( 1 + Inflation ) ( 1 + 0.032 ) = ( 1 + Real Rate ) x ( 1 + 0.4 ) 1.032 / 1.04 = 1 + Real Rate 0.99 1 = Real Rate Real Rate = - 0.01 (no changes) During the same year the CAC40 went from 2500 to 2565. Considering this, do you think your stock portfolio did well or did badly? [...]

[...] time to maturity). The factors which affect the premium of put and call options are : the current market price of the stock (the option price will rise if the price of the stock continues to rise), the time (the more time remaining until the options expiration date, the higher its premium will the volatility (If the price of the underlying security fluctuates substantially, the option is likely to command a heftier premium than an option for a security that normally trades in a narrow price range) and the risk free rate of return. [...]

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