QUESTION 2 a) A call option matures in 6 months. The underlying stock price is $
ID: 2787880 • Letter: Q
Question
QUESTION 2
a) A call option matures in 6 months. The underlying stock price is $50 and the
standard deviation of stock’s return is 14 percent per year. The risk-free rate is
5 % per annum. The exercise price is $60. What is the price of the call option?
(5 marks)
b) What is a protective put strategy? How can it be duplicated? In light of your
answer, explain the put-call parity condition. (5 marks)
c) You are a financial manager and you have bonds worth $3,000,000 in your
portfolio which have a 7 percent coupon rate and will be maturing in 10 years
from now. What type of risk exposure do you face on these bonds? Suppose a
futures contract on these bonds is available with a standard contract size of
US$300,000 per contract. How will you hedge your exposure? If the market
interest rates change to 9 percent, what will be your position? (1+1+3 marks)
d) Explain why diversification per se is probably not a good idea for merger.
(5 marks
Explanation / Answer
a) First we need to list out the information given in terms of various variables that go into BS equation
Here, S = 50, K = 60, s = 14%, r = 5%, t = 6months = 0.5yrs
using above, d1 =[ ln(S/K) + (r+s^2/2)*t]/s*sqrt(t) = [ln(50/60)+(0.05+0.14^2/2)*0.5]/(0.14*sqrt(0.5) =[ -0.18232+(0.05+0.0098]/(0.14*sqrt(0.5))=-0.17742/0.098995 = -1.814
d2 = d1-s*sqrt(t) = -1.54474-0.14*sqrt(0.5) = -1.91299
Now, using BS formula, price of a call option, C = S*N(d1)- N(d2)*K*exp(-r*t) = 50*0.036548-0.029297*60*exp(-0.05*0.5)= 3.84 - 3.74 = 0.1$
b) A protective put strategy is to buy a put option on an underlyin that one already has in his portfolio so that value of investment is protected in case value of underlying goes down. Using put call parity, difference in price of a call and put option with same strike and maturity equals value of underlying and bond with strike K discounted to present value. To put his in equation, C - P = S - PV(K). Rearranging, S+ P = C +PV(K). LHS here is a protective Put (long underlying and long put) , which gets replicated as per RHS as long call and holding a bond with value K.
c)Major risk in holding long duration bonds is reinvestment risks of coupons that shall be paid every year and capital depreication due to increase in intrest rates
Since, you are long bond, you shall be selling futures to hedge your exposure. To completely hedge, you need to sell 10 contracts ($ 3 Million/ $300k )
If the market interest rate changes to 9%, price of bond shall fall as coupon rate is less than market rate. However, short futures shall have positive MTM as price of undelrying bond falls. if you are completely hedged, price decrease in bonds shall qual orice increase in short futures
d) Mergers typically create shareholder value to cost redcution achieved due to synergies and larger market share grabbed due to merger leading to increased pricing power. Diversification works in opposite way as mergin with a diverse business shall lead to increased cost due to dyssynergies and also firm operating in market different from its core competencies