Stock| E(r)| | Correlation Coefficients|
1| 0.06| 0.20| 1 with 2: -0.10|
2| 0.08| 0.10| 1 with 3: +0.60|
3| 0.15| 0.15| 2 with 3: +0.05|
A portfolio is formed as follows: sell short $1,000 of Stock 1; buy $1,500 of Stock 2; buy $1,500 of Stock 3. The investor uses $1,000 of his own equity, with the remaining amount borrowed at a risk-free interest rate of 4% (with continuous compounding). (a) Assuming that there are no restrictions on the use of short-sale proceeds, what is this investors expected rate of return? (b) What are some of the issues associated with short-selling, and what impact could these issues have on the expected return calculated in part (a).
(a) w1 = -1; w2 = 1.5; w3 = 1.5; wr = -1
E(r) = -1*0.06 + 1.5*0.08 + 1.5*0.15 + (-1)*0.04 = 24.5%
(b) short selling is restricted; unable to use proceeds from the short sale; fee for short selling reduces return. All of these restrictions could fundamentally change the return to the portfolio.
2. Consider a European call option on a stock. The stock price is $70, the time to maturity is 12 months, the risk free rate of interest is 10% per annum (with continuous compounding), the exercise price is $65, and the volatility is 32%. A dividend of $1 is expected in six months time. Determine the price of the option using the binomial method with 6-month steps.
3. The current price of silver is $9 per ounce. The storage costs are $0.24 per ounce per year payable quarterly in advance. Assuming that interest rates are 10% per annum for all maturities, calculate the futures price of silver for delivery in nine months. （所有的FORWARD 和FUTURE 都用CONTINEOUS COMPONDING 算R） ANSWER
4. The current price of a stock is $20 and over the next three months it is expected to move up to $22 or down to $19. If the continuously compounded three month risk free rate is 4.5%, what is the price of a three...