You are contemplating an investment project that has two phases. As currently planned, the first phase of the project requires an investment of $100,000 today. One year from now, the project will deliver either $120,000 or $80,000, with equal probabilities. When these Phase I payouts occur, you will be able to invest an additional $100,000 in Phase II One year later, Phase II will pay out either 20 percent more than Phase 1 Actually delivered or else 20 percent less, again with equal probabilities.

You may commit to both phases at the start, or you may commit to Phase 1 (and postpone a decision on Phase II) or you may invest in neither. If you commit to both phases at the start, there is really no reason to delay. Suppose that you can choose in that case to implement both phases virtually simultaneously, so that both investments are made today and all payouts occur one year from now. (Note however that the size of the Phase II payout still depends on the size of the Phase 1 Payout. Conceptually, you can think of the Phase II payout as occurring immediately after Phase 1 Payouts.)

a. Using an expected payoff criterion, and discounting at 10 percent, which of the alternatives (First, Both or Neither) is the optimal decision?

b. What is the breakeven discount rate at which neither is a better decision than first?

c. Suppose you have access to an additional, similar investment that resembles the original but is more volatile: for the same initial investment, it delivers a Phase I return of + 40 percent (that is, either $140,000 or $60,000) with equal probabilities. Similarly, it delivers a Phase II return of +40 percent of the Phase I payouts, again with equal probabilities. Show that this new investment is preferable to the original, with a discount rate of 10 percent

d. Evidently, the higher volatility of the investment (+40 percent as opposed to + 20 percent) makes the potential cash flows attractive. With the discount rate at 10 percent, what levels of volatility would lead to an expected value above zero?

Volatility cannot be directly observed for calculation purposes of the option pricing model. Therefore, it may be determined from:
historic volatility.
forward-looking volatility.
implied volatility.
any of the above.

1. Assume that the CAPM is a good description f stock price returns. The market expected return is 7% with 10% volatility and the risk-free rate is 3%. New news arrives that does not change any of these numbers but it does change the expected return of the following stocks:
Expected Return Volati

Suppose that he spot price of the Canadian dollar is US $0.75 and that the Canadian dollar/US dollar exchange rate has a volatility of 4% per annum. The risk-free rates of interest in Canada and the United States are 9% and 7% per annum, respectively.
Using the Black-Shole formula to calculate the value of a European call op

3. Using the values of St, K, rf , and T specified below, use your spreadsheet and trial and error (or Solver) to estimate the implied volatility (accurate to four decimal places) of a call with a price of $7.2568.
St = $60.00
K = $60.00
rf = 0.02
T = 0.3333 (3 months).

You calculate the black schoals value of a call option as $3.50 for a stock that doesnÃ¢??t pay dividends but the actual price is $3.75 . The most likely explanation is that either the option is_________or the volatility you input into the model is too_________
a. Overvalued and should be written; low
b. Undervalued and shou

AD 13: The Dow Jones Industrial Average on August 15, 2008 was 11,660 and the price of the December 117 call was $3.50. Assume the risk-free rate is 4.2%, the dividend yield is 2% and the option expires on December 25 (options markets are closed the day after Christmas).
Q1: Use Derivagem to calculate the implied volatility o

Can I please get help understanding the difference in the value of a call option with increase in maturity and volatility.
See the two questions below
The value of a call option increases or decreases with an increase in maturity?
The value of a call option increases or decreases with an increase in volatility?

The Dow Jones Industrial Average on January 12, 2009 was 8474 and the price of the March 84 call was $4.50. Assume the risk-free rate is 3.2%, the dividend yield is 2% and the option expires on March 20, 2009 (Note that the options are on the DJI dividend by 100.)
Q1: Use Derivagem to calculate the implied v

An investor puts $15,000 in each of four stocks, labeled A, B, C, and D. The table below contains means and standard deviations of the annual returns of these 4 stocks.
A: Mean = .15 Standard Deviation = .05
B: Mean = .18 Standard Deviation = .07
C: Mean = .14 Standard Deviation = .03
D: Mean = .17 Standard Deviation =