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1. A 10-year maturity default-free bond has an annual coupon rate of 10% and makes semi-annual coupon payments. The annual yield to maturity of the bond equals 6%. The bond’s convexity equals 240.74.
What does the bond’s duration equal?
Duration = 6.996774
What would the price of the bond equal if there is an immediate (instantaneous) change in the yield from 6% to 5.75%? (assume the time until maturity stays at 10 years)
We can expect the Present value of the bond to increase to $ 1,319.83
Calculate the percentage change in the bond’s price if the yield to maturity changes from 6% to 5.75% using the prices you calculate at those to YTM’s?
(1319.83 - 1297.55)/ 1297.55 = 1.717 % increase
What is the predicted percentage change in the bond’s price if the YTM drops from 6% to 5.75% using the approximation that uses both duration and convexity?
-6.996774*(-.0025/1.06) = 0.01650183=1.650%
2. You purchase 500 shares of Fat Chance Co. stock on margin at a price of $ 45 per share. The initial margin requirement is 50% and the maintenance margin is 25%.
a. What is your margin loan amount?
Assets Liabilities and Account Equity
500@45= 22,500 Margin Loan = 11250
Equity = 11250
Total = 22500 Total = 22500
b. Suppose you sell the stock at a price of $ 50 per share. What is your return? (Ignore interest on the loan)
500@50 = 25,000 – 11250= 13750
c. What would your return have been had you purchased the stock without margin?
11250 /45 = 250 Shares
(12500-11250)/11250 = 11.11%
d. What is the threshold price at which you are just satisfying the maintenance margin requirement?
P=(11250/500)/(1-.25) = $30
3. You short sold 1,000 shares of stock at a price of $ 45 and an initial margin of 50 percent.
e. If the maintenance margin is 30 percent, at what share...
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