Question 1
You expect the price of FBG stock to be $69.77 per share a year from now. Its current market price is $60, and you expect it to pay a annual dividend of $1.75 per share a year from now. What is the stock’s expected dividend yield? State your answer as a percentage rate rounded off to two digits after the decimal point, i.e. ‘x.xx’
The expected dividend yield \(= E(D_1)/P_0\)
The expected dividend yield is equal to \(1.75 / 60 = 0.029167 = 2.92\%\)
Question 2
Refer back to Question 1. What is your expected total return on FBG stock? State your answer as a percentage rate rounded to one digit after the decimal point, i.e ‘x.x’
The expected total return is equal to the expected dividend yield plus the expected rate of capital gain or loss.
The expected rate of capital gain \(= E(P_1 – P_0)/P_0\)
The expected rate of capital gain \(= (69.77 - 60)/60 = 0.1628 = 16.28\%\)
The expected total return is equal to \(E(D_1 + P_1 – P_0)/P_0\) or the sum of the expected dividend yield and the expected rate of capital gain or loss.
The expected total return \(= 16.28\% + 2.92\% = 19.2\%\).
Question 3
Which one of the following statements is true about the differences between debt and common stock?
Debt is ownership in a firm, but equity is not. No. Debt does not represent ownership in a firm. Equity does.
Creditors have voting power, while stockholders do not. No. Voting rights come with ownership, and therefore come with equity.
Periodic payments made to either class of security are tax deductible for the issuer. No. Only interest payments are tax-deductible for the issuer. Dividends to shareholders are paid out of after-tax earnings.
Interest payments are promised, while dividend payments are not. Yes, this is correct. The interest payments on a bond are promised and failure to make these payments is considered as default. Stocks, on the other hand, may or may not pay dividends. They are not promised.
Question 4
Two of the main indexes that equity investors keep track of are the Dow Jones Averages (DJIA) and the Standard & Poor’s Composite 500 (S&P 500). The difference between these two indexes is:
The DJIA is a price weighted average of the stocks of 30 companies and (S&P 500) is a market value weighted index of 500 companies. Yes, the main difference between DJIA is that it is a price weighted average whereas the S&P 500 is a market value weighted index.
The DJIA is more volatile than the Standard & Poor’s Composite 500 (S&P 500). No. Certainly, the volatility between these two indices can be different, but this is not how they are different.
None of the above.
Question 5
Scubaland, Inc. is experiencing a period of rapid growth. Earnings and dividends per share are expected to grow at a rate of 18 percent during the next two years, 15 percent in the third year, and 6 percent thereafter. Yesterday, Scubaland paid a dividend of $1.15. If the required rate of return on the stock is 12 percent, what is the price of a share of the stock today? Round off your final answer to three digits after the decimal point. State your answer as ‘x.xxx’
Recall that we can value a share of stock using the dividend discount model. The share price is equal to the present value of expected future dividends. There are three years of non-constant growth and the required rate of return is 12 %. Let’s calculate expected dividends for the first 4 years.
\(D_1 = 1.15(1 + 0.18) = 1.357\)
\(D_2 = 1.357(1 + 0.18) = 1.601\)
\(D_3 = 1.601(1 + 0.15) = 1.841\)
\(D_4 = 1.841(1 + 0.06) = 1.952\)
Next we calculate the stock price today \(P_0\), which is given by:
\(P_0 = 1.357/(1.12) + 1.601/(1.12)^2 + 1.841/(1.12)^3 + [1.952/(0.12-0.06)]/(1.12)^3 = 26.955\)
Question 6
A firm’s preferred stock often has a dividend yield that is lower than its bonds because:
Preferred stock generally carries a higher rating. No, preferred stock has similar features to both equity and debt, but it does not have a rating.
Owners of preferred stock have a prior claim on the firm’s earnings. No, preferred stock ranks after bonds in terms of the priority of its claim on distribution of payments.
Owners of preferred stock have a prior claim on a firm’s assets in the event of liquidation. No, preferred stock ranks after bonds in terms of the priority of its claims to the assets of the firm in the event of liquidation.
Corporations owning stock may exclude from income taxes most of the dividend income they receive. Yes, preferred stock often sells at lower yields than corporate bonds because of the value of the dividend exclusion from income taxes provided to corporations.
Question 7
Gemini Industries has just paid its annual dividend of $3 per share. Analysts expect the dividend to grow at a constant growth rate of 4% indefinitely. If the stock is currently trading at $54, what is the market’s required rate of return on this stock? Express your answer as a percentage rate rounded off to two digits after the decimal point, i.e. ‘x.xx’
You can back out the discount rate that will make the current market price equal to the present value of the expected future dividends:
\(P_0 = {E(Div) \over r-g}\)
\(54 = 3 \times (1.04)/(r - 0.04)\)
Solving for \(r = 0.097778 = 9.78\%\)
Question 8
If GE stock is trading at $19.72 and the last quarterly dividend payment was $0.17 per share, what is GE’s annual dividend yield? Express your answer as a percentage rate rounded off to two digits after the decimal point, i.e. ‘x.xx’
The annual dividend yield is defined as the annual dividend per share divided by the share price. If the quarterly dividend payment was $0.17, that corresponds to an annual dividend payment of $0.17 x 4 = $0.68.
This implies that the annual dividend yield is $0.68 / $19.72 = 0.3448 = 3.45%
Question 9
What is the value of a preferred stock that pays a fixed dividend of $2 per share if the discount rate is 8%? Round off your final answer to the nearest dollar.
Preferred stock that pays a constant dividend can be valued using the constant growth dividend discount model. This basically is valuing a perpetuity of $2.
\(P_0 = 2 / 0.08 = 25\)
Question 10
Suppose that the company XYZ has just won a major contract. This lucrative contract will enable it to increase the growth rate of its dividends from 5% to 6% without affecting the projected current dividend of $3.00 per share. If the current share price is $57.14, what will happen to the share price upon announcement of this good news?
The price will jump by 6%.
The price will jump by 1%.
The price will increase to $62.28
The price will increase to $70.59
We can first back out the discount rate using the current price:
\(P_0 = {E(Div) \over r-g} = 57.14= {3 \over r - 5\%}\)
Solving for r = 10.25%
We can now and the new price using the new growth rate:
\({E(Div) \over r-g} = 3 / (10.25\% - 6\%) = 70.59\)
Question 1
A derivative security is:
A type of financial asset that is traded frequently in money markets. No. Money market instruments are very short-term debt obligations.
A type of fixed income instrument similar to bonds and commercial paper traded in capital markets. No. A derivative security is not a fixed income instrument. Bonds and commercial paper are examples of fixed income instruments.
A type of financial asset whose value depends on the value of another underlying asset such as stock, commodity, index, reference rates. Yes, that is correct. A derivative security is a financial instrument whose value depends on the value of an underlying asset such as stock, commodity, index, reference rates. Remember the name derivative gives a hint that the value of this financial asset is derived from the value of an underlying asset.
Question 2
Select which of these securities are examples of derivatives securities.
A. Options and futures Yes. Options and futures contracts are examples of derivative securities. Are there any others?
B. Swaps and forwards contracts Yes. Swap and forward contracts are examples of derivative securities. Are there any others?
C. Stocks and bonds No. Stocks and bonds are not derivative securities. Stocks are examples of equity instruments, and bonds are examples of fixed income instruments. They are often used as the underlying assets of derivative securities.
A and B Correct. Both options A and B are both correct since they are the most common types of derivatives as was explained in the videos. Option C is incorrect. Bonds and stocks can often be used as the underlying asset for derivative securities, but they are not derivative securities themselves.
Question 3
The difference between derivatives traded on exchanges and in the over the counter (OTC) market is:
A. On an exchange, an investor can obtain a derivative contract that is tailored to his needs. No, this is not correct. Derivative contracts that are traded on exchanges are standardized.
B. Exchnage-traded contracts are standardized and defined by the exchange, but in over the counter derivatives (OTC) contracts are customized and transactions costs are higher. Yes, this is true. In exchange traded markets, the specific features of the contracts are determined by exchanges. In contrast, an investor can obtain a contract that is tailored to her needs in the over-the counter market. Since it would be harder to find a counterparty willing to provide such a contract, transaction costs are higher in OTC derivatives contracts. Anything else?
C. In exchange traded markets there is no counterparty risk since there exists a clearinghouse. Yes, this is true. The clearinghouse acts as the counter party to both parties. The clearinghouse guarantees that the derivative trade will take place according to the conditions that were originally negotiated.
B and C. Correct. Options b and c are both true statements and explain the difference between the OTC and exchange-traded markets.
Question 4
Which of the following positions do you think would be the most risky transaction to take in the stock index option markets if the stock market is expected to increase substantially after you complete the transaction?
A short call option Yes. This is the riskiest. If you have a short call option, that means you have sold or written a call option. This call option will be exercised again you if the stock market increases. The option holder has the right to buy the index at the exercise price which is less than the current market level. You have potentially unlimited losses.
A short put option No. If you have a short put option, that means you have sold or written put option. If the stock market is expected to increase substantially, this option will not be exercised as there is no positive payoff to the option holder
A long call option No. If you have a long call option position you have purchased a call option. If the stock market increases substantially, your option will be in the money and you will profit by exercising your option.
A long put option No. If you have a long put position, that means you purchased a put option. If the stock market increases substantially, the put option will be out of the money and will not be exercised. You will at most lose the premium you paid for the option.
Question 5
Suppose RIO stock has both currently call and put options traded. What would your profit at the expiration date be if you buy the 3-month call option with an exercise price of $60 for $4 and at the same time buy the 3-month put option with the same exercise price for $6 today if the RIO stock trades for $48 in three months?
Recall that a call option gives you the right but not the obligation to buy the underlying at the exercise price \(X\). The call option will be exercised if \(S_T > X\), and the payoff will be \(S_T − X\).
A put option gives you the right but not the obligation to see the underlying at the exercise price \(X\). The put option will be exercised if \(S_T < X\), and the payoff will be \(X − S_T\).
Profit is the option payoff less the option premium.
If the stock price is $48 at expiration date, the call option will be out of the money. The payoff to the long call option is max(48 - 60, 0) = 0. However, the put option will be in the money. Your payoff from exercising the put option will be \(\max(X − S_T ,0) = 60 - 48 = 12\). Your profit is your total payoff less what you paid for the options. \(12 - 6 - 4 = 2\).
Question 6
The main difference between a futures and a forward contract is:
A. Forward contracts are traded over the counter and are customized, but futures are standardized contracts and are traded on organized exchanges. True. This is the main difference between these two types of derivatives.
B. Future contracts can take only financial assets as the underlying asset. No. Future contracts can take a variety of commodities as underlying asset: pork belly, live cattle, sugar lumber, copper, etc.
None of the above. No. There is a correct answer.
A and B. No the correct answer is only a. Answer b is not correct. Future contracts can take a variety of commodities as underlying asset: pork belly, live cattle, sugar lumber, copper, etc.
Question 7
Which of these options on the same stock should sell at a greater price?
A 6-month call option with an exercise price of $40 No. Think about how the exercise price is likely to affect the likelihood of exercise and option value.
A 6-month call option with an exercise price of $35 Correct. A call option with a lower exercise price is more likely to finish in the money and be exercised. Therefore, a call option with an exercise price of $35 should sell at a greater price than a call option with the same expiration date but a higher exercise price.
Question 8
Suppose that a trader enters into a long corn futures position for 5000 bushels with a delivery date on December 2017 and a future price of $3.902 per bushel. What is the payoff to this position if on the delivery date, the spot price of corn is $4.0995 per bushel? Round off your final answer to the nearest dollar.
Recall that the payoff to the long futures is given by \((P_T−F_0)\)
where \(P_T\) is the spot price per bushel at delivery date and \(F_0\) is the future bushel.
In this case:
\(P_T = 4.0995\)
\(F_0 = 3.902\)
(4.0995 - 3.902) * 5000 = 987.5 ~ 988
Question 9
Assuming all other relevant features of the stocks and options are identical, which of these options should sell at a lower price?
A put option on a stock with a market price of $50 No, that is not correct. Recall that a put option gives the right to sell the underlying at the exercise price and it will be exercised if the market price is less than exercise price. For a given exercise price, the lower the market price of the underlying stock, the greater is the likelihood that the put option will be in the money at expiration. So the option should be worth more.
A put option on a stock with a market price of $60 Yes, that is correct. Recall that a put option gives the right to sell the underlying at the exercise price and it will be exercised if the market price is less than exercise price. For a given exercise price, the higher the market price of the underlying stock, the less is the likelihood that the put option will be in the money at expiration. So the option would be worth less.
Question 10
You are a portfolio manager who uses options positions to custom the risk profile of your clients. Your portfolio’s performance to date is up 16%. Your client’s objective is to earn at least 15%. You expect that there is a good chance of large losses between now and the end of the year. What strategy is best given your client’s objective?
Long put options Yes, that is correct. Put options give you the right but not the obligation to sell at the exercise price. Put options therefore provide protection.
Short call options No. A short call option position means that you have written a call option. Think about how this would affect your client’s objective if you expect the market to decline.
Long call options No. A long call option position means that you have bought a call option. Think about how this would affect your client’s objective if you expect the market to decline.
Question 11
Suppose you will receive your bonus next month. You hope to invest it in long-term corporate bonds. You believe that bonds are currently selling at quite attractive yields How would you use financial futures to hedge your risk?
Go long in bond futures Yes, this is correct. A long hedge eliminates the risk of uncertain purchase price.
Go short in bond futures No. This is not correct. A short hedge eliminates the risk of uncertain sales price.
Question 12
Suppose you have just received 10,000 shares of your company stock as part of your compensation package. The stock currently sells $30 a share. You would like to defer selling the stock until the next tax year. In January, however, you will have to liquidate your holdings in order to provide a down payment on your new house. You are therefore worried about the price risk associated with keeping your shares of stock. If the value of your stock holdings fall below $250,000, your ability to come up with the necessary down payment would be jeopardized. On the other hand, if the stock value rises to $350,000, then you might be able to maintain a small cash reserve even after making your down payment. Which of these investment strategies would you choose?
Writing January call options on your company shares with an exercise price $35. These are currently selling for $3 each. Think about what this position generates. Essentially you have your shares plus a short call position on the shares. If the stock price increases above $35, then the call option will be exercised and the stock will be called away. You will have $350,000 plus $30,000 in option premium. If the stock price remains below $35 then the option will not be exercised. You will have your shares plus the premium. Note that this position does not provide any downside protection if the value of your stock holdings fall below $250,000.
Buying put options with an exercise price of $25. These options are also selling for $3 each. Think about what this position generates. Essentially, you have your shares plus a long put option on the shares. If the stock price does decline below $25 then you will exercise the option and sell your shares for $250,000. You will have $250,000 less the $30,000 in premium you paid. If the stock price is above $25, then the put options will not be exercised.
Establishing a zero-cost collar position by writing the January calls and buying the January puts. Yes. Think about what this position generates. Essentially, you have your shares plus a zero-cost collar position which enables to guarantee to have the value of your holdings between $250,000 and $350,000. The premium you receive for the call options will pay for the put options. You are able to obtain the downside protection represented by the put option by selling your claim to any upside potential beyond the exercise price of the call.
Question 13
You have a client who believes that the shares of MexCon, currently trading at $48 per share, could move significantly in either direction in response to an expected court ruling involving the company. Your client currently owns no MexCon shares but asks you for advice to implement a strangle strategy to profit from the possible price movement. A strangle is a portfolio of a put and a call with a higher exercise price but with the same expiration date. Currently, MexCon stock has a 3-month call option with an exercise price of $50 selling for $4, and a 3-month put option with an exercise price of $45 selling for $3. Which of the two strategies would you recommend your client?
A long strangle strategy Yes. That is correct. As long as the stock price moves substantially in either direction, this will generate a positive payoff.
A short strangle strategy No. Think about the payoffs to a short strangle strategy. When would it yield a positive payoff?
Question 14
Suppose you are an oil distributor planning to sell 100,00 barrels of oil eight months from now. You would like to hedge against a possible decline in oil prices. Which position would you take?
A short hedge taking a short futures position
Yes, that is correct. A short futures position offsets the risk in the sale of price of the underlying.
The revenue from the sale of oil eight months from now is \(100,000 \times P_T\).
The profit from the short futures position is \(100,000 \times (F_0− P_T)\)
Total proceeds will be \(100,000 \times F_0\)
A long hedge taking a long futures position No. A long hedge is a hedge for someone who wishes to eliminate the risk of uncertain purchase price.
Question 15
Why does a speculator who wants to bet on the direction of the price of an underlying asset buy a futures contract instead of buying the underlying asset itself?
A. Futures contracts require only a fraction of the value to be deposited compared to the value of the asset underlying the contract. This is correct, but not the only one. Because they only have to pay up only a fraction of the value, futures trading provides much greater leverage to speculators than trading in the underlying asset.
B. Speculators are attracted to futures because the futures market appears more sophisticated. No. This is not correct.
C. Speculators are not allowed to trade in the underlying asset. No. This is not correct.
D. Transaction costs in the futures markets are far smaller. Yes, this is correct, but it is not the only one.
A and D Yes. Both a and d are reasons why futures trading is often preferred to trading in the underlying for speculators.
Question 1
Earnings and dividends per share at G3-Biz Inc. are expected to grow at a rate of 18 percent over the next two years, then at 15 percent in the third year, and then at 6 percent thereafter. G3- Biz just paid a dividend of $1.15. If the required rate of return on the stock is 12 percent, what is the price of a share of G3-Biz stock today? Round off to two decimal points. (i.e. “x.xx”)
There are three years of non-constant growth and the required rate of return is 12 %.
Let’s calculate expected dividends for the first 4 years.
\(D_1\) = 1.15 * (1 + 0.18) = 1.357
\(D_2\) = 1.357 * (1 + 0.18) = 1.601
\(D_3\) = 1.601 * (1 + 0.15) = 1.841
\(D_4\) = 1.841 * (1 + 0.06) = 1.952
Next we calculate the stock price today \(P_0\), which is given by:
\(P_0 = [1.357 / (1 + 0.12) ^ 1] + [1.601 / (1 + 0.12) ^ 2] + [1.841 / (1 + 0.12) ^3] + [1.952 / (0.12-0.05) ] * (1 + 0.12) ^ {-3} = 26.95\)
D1 = 1.15 * (1 + 0.18)
D2 = D1 * (1 + 0.18)
D3 = D2 * (1 + 0.15)
D4 = D3 * (1 + 0.06)
P0 = D1 / 1.12 + D2 / 1.12 ** 2 + D3 / 1.12 ** 3 + D4 / (0.12 - 0.06) / 1.12 ** 3
round(P0, 2)## 26.95Question 2
Suppose that the company XYZ is going to pay a dividend of $1.50 per share next year, and the dividend is expected to grow by 10% forever. If investors require a 13%, what should the value of XYZ’s stock be?
55
50
62
65
Recall the dividend discount model with constant growth rate.
\(P_0 = E(Div)/(r-g) = 1.5/(0.13 - 0.10) = 50\)
Question 3
Suppose that the stock of the company CFAA is currently trading on April 15 at a price of $70. A call option with a strike price of $70 and an expiration date on October 15 is trading at $4. What is your profit if the stock price at expiration date is $80? Remember that each option contract is for 100 shares.
Profit of a call option \(= (S_T - X) - P = (80-70)*100- 400 = 600\)
\(S_T = 80\) (Stock price at expiration date \(T\))
\(X = 70\) (Exercise price of each share)
\(P = 4*100=400\) Premium (cost) of the option contract.
Since \(S_T > X\) – that is, since the price of the stock is greater than the exercise price, the option is in the money and it would make sense for the call option holder to exercise the option. Note that we still have to deduct the premium from the option’s payoff to find the profit.
Question 4
Suppose that a trader enters into a long futures position for 1000 oil barrels with a delivery date on December 2016 and a future price of $40 per barrel. Suppose that on delivery date, the spot price of oil is $45 per barrel. What is the payoff to the long position?
Payoff of the future contract (long position) \(= (P_T - F_0) = (45-40)*1000 = 5000\)
\(P_T = 45\) (Spot price per barrel at maturity date \(T\))
\(F_0 = 40\) (Future price of each barrel)
Question 5
Suppose your research shows that technology stocks currently provide an expected rate of return 12%. BMI, a large computer company, is expected to pay a dividend of $2 per share at the end of the year. If the stock is currently selling at $48 per share, what is the market’s expectation of growth at BMI?
6.53%
7.83%
4.17%
None of the above
Recall that \(P_0 = E(Div)/(r-g)\)
In this case, \(P_0 = 48\), \(Div = 2\), \(r = 12\%\) and we can solve for \(g\).
\(g = 7.83\%\)
Question 6
An investor purchases a stock for $28 and a put on the stock for $0.40 with a strike price of $24. She also sells a call on the same underlying stock for $0.40 with a strike price of $30 and with the same expiration date. What is the value of her portfolio, net of the proceeds from the options, if the stock price ends up at $35 on the expiration date?
Write down the payoff associated with each position. She has a long position in the stock, a short position in the put, and a long position in the call. What is the payoff associated with each? Which options will be exercised if the stock price ends up at $35?
Note that the premium for the puts will be offset by the premium she receives for the calls.
If the stock price ends up at $35, the puts will be out of the money. The calls, however, will be in the money and will be called away. So the value of her portfolio is given by \(S_T + -( S_T − X) = (35) + - (35-30) = 30\).
Question 7
Which of the following is correct about the over-the-counter markets?
a. The counterparty risk is eliminated. No. Over-the-counter markets is subject to counterparty risk.
b. There is no clearing house. Yes, that is correct. An important distinction between exchanges and over the counter market is the clearing house. Its absence in the OTC markets is why investors are subject to counterparty risk.
c. Futures are traded in OTC markets. No, futures contracts are traded on organized exchanges.
d. Both b and c are correct. No. While it is correct that there is no clearing house in OTC markets, it is not correct that futures are traded in OTC markets. Futures are traded on organized exchanges.
Question 8
A spread is a combination of two or more call options on the same stock with differing exercise prices or times to maturity. Some options are bought, and others are sold. Consider a bullish spread option strategy where you buy a call option with a $35 exercise price priced at $4 and sell a call option with a $50 exercise price priced at $2.50. If the price of the underlying stock increases to $60 at expiration and each option is exercised on the expiration date, what is your net profit?
8.50
13.50
16.50
23.50
Think about the profit associated with each position.
Long call: \(S_T − X- \text{premium}\) when \(S_T > X\)
Short call: \(-(S_T − X) + \text{premium}\) when \(S_T > X\)
Long call: your profit is \((60 - 35) - 4 =21\)
Short call: your profit is \((50 - 60) + 2.5 = -7.5\)
Your total net profit \(= 21 - 7.5 = 13.5\)
Question 9
Suppose you are a U.S. investor who is harmed when the dollar depreciates. Specifically, suppose that your profits decrease by $200,000 for every $0.05 rise in the dollar/pound exchange rate. If the pound futures contract on the Chicago Mercantile Exchange calls for delivery of 62,500 pounds, how many contacts will you need to enter to hedge? Will you take the long or the short side of the contracts?
64 contracts short
64 contracts long
32 contracts short
32 contracts long
Because you do poorly when the dollar depreciates, you can hedge it with a futures contract that will provide a payoff in that scenario. So think about what position in pound futures will earn profits when the futures price increases. Then think about how many contracts you will need to hedge.
If the profit on a long future contract would increase by $0.05 x 62,500 = $3,125, you would need $200,000 / $3,125 = 64 contracts.
Question 10
You know that many corporate bonds are issued with call provisions that allow the issuer to buy bonds back from the bondholders at some time in the future at a specified call price. Which of the following is correct?
This is similar to the bond issuer holding a call option with an exercise price equal to the price at which the bond can be repurchased. Yes, this is correct. The option inherent in a callable bond is like a call option held by the bond issuer and that allows the bond issuer to repurchase the bonds if the issuer chooses to exercise that option.
This is similar to the bondholder owning a call option with an exercise price equal to the price at which the bond can be repurchased.
No this is not correct. Think about the option inherent in a callable bond. Who gets to exercise it?
The option inherent in a callable bond is like a call option held by the bond issuer and that allows the bond issuer to repurchase the bonds if the issuer chooses to exercise that option.
This is similar to the bond issuer holding a put option with an exercise price equal to the price at which the bond can be repurchased.
No this is not correct. Think about the option inherent in a callable bond. Who gets to exercise it? And what is the exercise?
The option inherent in a callable bond is like a call option held by the bond issuer and that allows the bond issuer to repurchase the bonds if the issuer chooses to exercise that option.
This is similar to the bondholder owning a put option with an exercise price equal to the price at which the bond can be repurchased.
No this is not correct. Think about the option inherent in a callable bond. Who gets to exercise it? And what is the exercise?
The option inherent in a callable bond is like a call option held by the bond issuer and that allows the bond issuer to repurchase the bonds if the issuer chooses to exercise that option.