Imagine you are a provider of portfolio insurance. You are establishing a four-year program. The portfolio you manage is currently worth $100 million, and you promise to provide a minimum return of 0%. The equity portfolio has a standard deviation of 25% per year, and T-bills pay 5% per year. Assume for simplicity that the portfolio pays no dividends (or that all dividends are reinvested). a. What fraction of the portfolio should be placed in bills? What fraction in equity? b. What should the manager do if the stock portfolio falls by 3% on the first day of trading?

A corporation plans to issue $10 million of 10-year bonds in three months. At current yields the bonds would have modified duration of eight years. The T-note futures contract is selling at F0 = 100 and has modified duration of six years. How can the firm use this futures contract to hedge the risk surrounding the yield at which it will be able to sell its bonds? Both the bond and the contract are at par value.

How does U.S. debt compare to Japan's debt as a percentage of GDP?

A corporation plans to issue $\$ 10$ million of 10 -year bonds in three months. At current yields the bonds would have modified duration of eight years. The T-note futures contract is selling at $F_0=100$ and has modified duration of six years. How can the firm use this futures contract to hedge the risk surrounding the yield at which it will be able to sell its bonds? Both the bond and the contract are at par value.

A collar is established by buying a share of stock for $50, buying a six-month put option with exercise price$45, and writing a six-month call option with exercise price $55. Based on the volatility of the stock, you calculate that for an exercise price of$45 and maturity of six months, N(d1) = .60, whereas for the exercise price of $55, N(d1) = .35. a. What will be the gain or loss on the collar if the stock price increases by$1? b. What happens to the delta of the portfolio if the stock price becomes very large? c. Very small?

A collar is established by buying a share of stock for $\$ 50$, buying a six-month put option with exercise price $\$ 45$, and writing a six-month call option with exercise price $\$ 55$. Based on the volatility of the stock, you calculate that for an exercise price of $\$ 45$ and maturity of six months, $N\left(d_1\right)=.60$, whereas for the exercise price of $\$ 55, N\left(d_1\right)=.35$.

a. What will be the gain or loss on the collar if the stock price increases by $1?

b. What happens to the delta of the portfolio if the stock price becomes very large? Very small?

Suppose the market can be described by the following three sources of systematic risk. Each factor in the following table has a mean value of zero (so factor values represent realized surprises relative to prior expectations), and the risk premiums associated with each source of systematic risk are given in the last column. $$ \begin{matrix} \text{Systematic Factor} & \text{Risk Premium}\\ \text{Industrial production, IP} & \text{6\\%}\\ \text{Interest rates, INT} & \text{2}\\ \text{Credit risk, CRED} & \text{4}\\ \end{matrix} $$ The excess return, R, on a particular stock is described by the following equation that relates realized returns to surprises in the three systematic factors: R = 6% + 1.0 IP + .5 INT + .75 CRED + e. Find the equilibrium expected excess return on this stock using the APT. Is the stock overpriced or underpriced?

Suppose there are two independent economic factors, M1 and M2. The risk-free rate is $7\%$, and all stocks have independent firm-specific components with a standard deviation of $50\%$. Portfolios A and B are both well diversified.

Portfolio	Beta on M1	Beta on M2	Expected Return (%)
A	1.8	2.1	40
B	2.0	-0.5	10

Assuming the following Adjusted Trial Balance, create the Post-Closing Trial Balance that would result, after all closing journal entries were made and posted:

$$\begin{array}{c} \textbf{Adjusted Trial Balance} \end{array}$$

$$\begin{array}{lcc} &\textbf{Debit}&\textbf{Credit}\\[5pt] \text{Cash}&\text{\$\hspace{5pt}22,900}\\ \text{Prepaid Insurance}&\text{\hspace{15pt}4,000}\\ \text{Fixed Assets}&\text{\hspace{10pt}44,000}\\ \text{Notes Payable}&&\text{\$\hspace{5pt}40,000}\\ \text{Common Stock}&&\text{\hspace{10pt}25,000}\\ \text{Retained Earnings}&&\text{\hspace{10pt}48,350}\\ \text{Dividends}&\text{\hspace{10pt}22,000}\\ \text{Sales Revenue}&&\text{\hspace{5pt}150,000}\\ \text{Automobile Expense}&\text{\hspace{10pt}26,500}\\ \text{Insurance Expense}&\text{\hspace{10pt}20,000}\\ \text{Salaries Expense}&\text{\hspace{5pt}122,500}\\ \text{Supplies Expense}&\underline{\text{\hspace{15pt}1,450}}&\underline{\text{\hspace{39pt}}}\\ &\underline{\underline{\text{\$\hspace{1pt}263,350}}}&\underline{\underline{\text{\$\hspace{1pt}263,350}}}\\ \end{array}$$

The common stock of the C.A.L.L. Corporation has been trading in a narrow range around $50 per share for months, and you believe it is going to stay in that range for the next three months. The price of a three-month put option with an exercise price of$50 is $4, and a call with the same expiration date and exercise price sells for$7. a. What would be a simple options strategy using a put and a call to exploit your conviction about the stock price’s future movement? b. What is the most money you can make on this position? c. How far can the stock price move in either direction before you lose money? d. How can you create a position involving a put, a call, and riskless lending that would have the same payoff structure as the stock at expiration? The stock will pay no dividends in the next three months. e. What is the net cost of establishing that position now?

You buy a share of stock, write a one-year call option with X = $10, and buy a one-year put option with X =$10. Your net outlay to establish the entire portfolio is $9.50. What is the payoff of your portfolio? What must be the risk-free interest rate? The stock pays no dividends.

A put option on a stock with a current price of $33 has an exercise price of$35. The price of the corresponding call option is $2.25. According to put-call parity, if the effective annual risk-free rate of interest is 4% and there are three months until expiration, what should be the price of the put?

One Chicago has just introduced a new single stock futures contract on the stock of Brandex, a company that currently pays no dividends. Each contract calls for delivery of 1,000 shares of stock in one year. The T-bill rate is 6% per year. a. If Brandex stock now sells at $120 per share, what should the futures price be? b. If the Brandex stock price drops by 3%, what will be the change in the futures price and the change in the investor’s margin account? c. If the margin on the contract is$12,000, what is the percentage return on the investor’s position?

Use the formula $A=\frac{P\left[\left(1+\frac{r}{n}\right)^{n t}-1\right]}{\left(\frac{r}{n}\right)}$. Round all computations to the nearest dollar. Suppose that you drive 15,000 miles per year and gas averages $3.50 per gallon. a. What will you save in annual fuel expenses by owning a hybrid car averaging 60 miles per gallon rather than an SUV averaging 15 miles per gallon? b. If you deposit your monthly fuel savings at the end of each month into an annuity that pays 5.7% compounded monthly, how much will you have saved at the end of six years?