a) A call option gives its holder the right to purchase an asset for a specified price, called the exercise or strike price, on or before the specified expiration date. The price that the writer of a call option receives to sell the option is called the premium.
b) Forward contracts are formalized and standardized.
c) Consider two bonds, A and B. Both bonds presently are selling at their par value of $1,000. Each pays interest of $120 annually. Bond A will mature in five years, while bond B will mature in six years. If the yields to maturity on the two bonds change from 12% to 10%, both bonds will decrease in value, but bond B will decrease more
than bond A.
d) Suppose that Boeing has an expected rate of return of 0.08. It has a beta of 0.92. The risk-free rate is 0.04 and the market expected rate of return is 0.10. According to the Capital Asset Pricing Model, this security is overpriced.
e) A two-asset portfolio with a standard deviation of zero can be formed when the assets have a correlation coefficient equal to zero.
f) You invest $1,000 in a risky asset with an expected rate of return of 0.17 and a standard deviation of 0.40 and a T-bill with a rate of return of 0.04. The slope of the capital allocation line formed with the risky asset and the risk-free asset is equal to 0.325.
g) You sold short 100 shares of common stock at $45 per share. The initial margin is 50%. Your initial investment was $9,000.
h) With regard to a futures contract, the short position is held by the trader who commits to delivering the commodity on the delivery date.
i) Callable bonds give the bondholder the option to convert each bond into a stipulated number of shares of stocks.
j) The clearinghouse guarantees that a futures contract will be fulfilled.
2. Suppose that Air New Zealand is currently selling at $2.80 per share.
a) You believe that the stock price of Air New Zealand will increase. So you decide to buy 10,000 shares by using $15,000 of your own money and borrowing the remainder ($13,000) of the purchase price from your broker.
(i) What is the rate of return on your margined position if the price becomes:
(1) $2.50; (2) $2.80; (3) $3.10?
(ii) If the maintenance margin is 25%, how low can Air New Zealand’s stock price fall before you get a margin call?
(iii) How would your answer to the question (ii) in section a), change if you had financed the initial purchase with $20,000 of your own money?
b) Suppose that your friend Alex is pessimistic about Air New Zealand’s stock performance. Then he sells short 5,000 shares of Air New Zealand at $2.80 per share, and gives his broker $8,000 to establish his margin account.
(i) If Alex earns no interest on the funds in the margin account, what will be his rate of return after 1 year if Air New Zealand stock is selling at: (1) $2.50; (2) $2.80;
(ii) If the maintenance margin is 25%, how high can Air New Zealand’s price rise before Alex gets a margin call?
(iii) Redo part (ii) in section b), but now assume that Air New Zealand also has paid a year-end dividend of 4.3 cents per share (1 cent = $0.01).
a) What is the alpha of each stock?
b) Conclude whether each stock is fairly priced, over-priced, or under-priced. According to the CAPM, which stock is a better buy?
If the required return is 12 percent and the company just paid a dividend of $2.50, what is the current share price?
We assume that investors use mean-variance utility: U = E(r)−0.5×Aσ where E(r) is the expected return, A is the risk aversion coefficient and σ is the variance of returns.
b) What is the reward-to-volatility ratio (Sharpe ratio) of your risky portfolio? What is the reward-to-volatility ratio (Sharpe ratio) of your client’s complete portfolio?
c) Your client’s degree of risk aversion is A = 3.5.
(i) What proportion, y, of the total investment should be invested in your risky fund?
(ii) If your client’s degree of risk aversion increases from A = 3.5 to A = 4.5. What proportion, y , of the total investment should be invested in your risky fund?
(iii) What do you conclude about the relationship between the proportion y and your client’s attitude toward risk?
a) Explain the differences between the short and long positions in call options transaction.
b) Two bonds, Bond A and Bond B, have identical times to maturity, coupon rates and face value. Bond A is callable at $105. Bond B is a straight bond that has no special features compared to callable or forwardable bonds with embedded options. Bond B is selling for $110. Which bond should have a higher yield to maturity? Why?
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