In this document we will show how you can create a portfolio with two stocks which would have an ER of 8%, and what the SD of such a portfolio is. We also explain the concept of Efficient Markets Hypothesis and the difference between the Weak, Semi-Strong, and Strong forms of it. Finally we try to explain what short sales are and why they are dangerous for investors, which is also why governments often restrict their use. The efficient markets hypothesis is based on the idea that information is reflected in security prices. In fact, if investors had the information that buying a given stock will have a positive NPV, they will be tempted to buy it and it would then drive up the stock price. In a similar way, if investors are aware that selling given stocks will have a positive NPV, the price of the stocks will go down. The fact that competition among investors works to eliminate the positives NPV trading opportunities is known as the basis of the efficient markets hypothesis. This theory implies that securities are fairly priced based on their future cash flows and given all the information available for investors.
Sommaire
You have two stocks with the following Expected Returns (ER) and Standard Deviations (SD)
Show how you can create a portofolio 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%. What do you need to do to create this portfolio?
Explain the concept of Efficient Markets Hypothesis and what the difference is between the Weak, Semi-Strong, and Strong forms of it. Do you agree with 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
Calculate your annual return on the portfolio, if no other money was added or removed, and the value on December 31 was ?18,360
If inflation for the year was 4%, what was your real return on your portfolio? What does this mean?
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
Explain what the CAC40 is and how its value is calculated. (You may need to do a little outside research to answer this question)
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
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)
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
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?
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
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)?
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
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
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)
Show how you can create a portofolio 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%. What do you need to do to create this portfolio?
Explain the concept of Efficient Markets Hypothesis and what the difference is between the Weak, Semi-Strong, and Strong forms of it. Do you agree with 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
Calculate your annual return on the portfolio, if no other money was added or removed, and the value on December 31 was ?18,360
If inflation for the year was 4%, what was your real return on your portfolio? What does this mean?
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
Explain what the CAC40 is and how its value is calculated. (You may need to do a little outside research to answer this question)
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
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)
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
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?
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
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)?
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
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
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
[...] 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 If inflation for the year was what was your real return on your portfolio? What does this mean? 6 During the same year the CAC40 went from 2500 to 2565. Considering this, do you think your stock portfolio did well or did badly? [...]
[...] We choose also a stop loss order because we need to sell the stocks if the price falls to share. 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 To make this table, we know that we have bought the stock on margin and borrowed 50%. We purchased the stock at $35/share. [...]
[...] The time to maturity is the time that remains till the option is not valid anymore (deadline from now). Longer an option can be use in time, higher will be the premium, either for put or call option. So we can say that time to maturity is influencing a lot the premium. The interest rate is the amount of money that you have to pay to borrow money you don't owe. If the interest rate is increasing, the option premium can increase too. [...]
[...] In other terms, you don't have limits to your losses. It means that you can lose more than twice the initial amount you invest. In fact, the interest rate can lead you to very huge losses (because whatever happens, you have to pay back the shares you borrow and you have to pay the interest rate, at any moment when the lender is asking for. So if the price on the market is not good for you at the time you have to re-buy and return the shares, it can be a total disaster. [...]
[...] What do you need to do to create this portfolio? To create a portfolio with these two securities, we have to do the following: We know that = and ER = wbrb + wrfrrf We know that = so our Wrf will have to be negative if we want an ER of 13%. In fact, we can have the following table: So to have an ER of we will have to borrow 40% of our money (this will be in addition to the normal amount) = = = 1.4 x 0.1 = 14% Now, we calculate the ER of our portfolio in order to verify: ER = 1.4 x 0.1 + 0.4 x 0.025 ) ER = 0.14 0.01 which is the interest for borrowing. [...]
