# (Papers) ACET Paper May 2010 "CT8 – Financial Economics"

## (Papers) ACET Paper May 2010 "CT8 – Financial Economics"

Q. 1) The fund manager of Alpha Asset Management Company Limited has a well diversified portfolio that mirrors the performance of the BSE-SENSEX and is worth 8000 crores. The current value of the SENSEX is 16000 points. The fund manager would like to hedge the risk against a reduction of more than 10% in the value of the portfolio over the next six months. The risk free rate of interest is 6% per annum (with continuous compounding) and the volatility of the SENSEX is 25% per annum (with continuous compounding).

a) What would the hedging cost be if the fund manager decides to
hedge the risk using traded European put options on BSE-SENSEX?

b) What are the alternate strategies available to the fund manager using traded
European call options on BSE-SENSEX? Show that this strategy leads to the same
result as strategy used in part (a)

c) If the fund manager decides to hedge the risk by keeping part of the
portfolio in the risk free securities, what should the initial position be?

Q. 2)

a) Explain the difference between hedging, speculation and
arbitrage.

b) Show that, if c is the price of an European call option on a future contract
when the strike price is K and the maturity is T, and p is the price of an
European put option on the same futures contract with the same strike price (K)
and expiration date (T), then

c) Suppose that a one-year futures price on Infosys stock is currently Rs.100. A one year call option and a one year put option on the futures (one-year futures on Infosys) with a strike price of Rs.95 are both currently priced at Rs.8 in the market. The risk free interest rate is 6% per annum (with continuous compounding). Identify an arbitrage opportunity available to an arbitrageur.

Q. 3) A stock price is currently at Rs.100. Over the next two three-month periods it is expected to go up by 4% or down by 3%. The risk free rate of interest is 6% per annum with continuous compounding.

(a) What is the value of a six-month European call option with a
strike price of Rs.102?

(b) What is the value of a six-month European put option with a strike price of
Rs.102?

(c) Verify that the European call and European put prices satisfy the put-call
parity.

(d) If the put option in part (b) were American, would it be ever be optimal to
exercise it early at any of the nodes on the tree? (3)

Q. 4)

(a) What is a one-factor terms structure model?

(b) What are the limitations of the one-factor terms structure models?

(c) The cash prices of six-month and one-year zero coupon bonds are Rs. 94 and
Rs. 89 respectively. A 1.5 year bond that will pay coupons of Rs. 4 every six
months currently sells for Rs. 94.84. A two-year bond that will pay coupons of
Rs. 5 every six months currently sells for 97.12. Calculate the six-month,
one-year, 1.5-year and two-year spot (zero) rates. All bonds have face value of
Rs. 100.

Q. 5)

(a) What are different ways in which a credit default impacts
the contracted payment stream?

(b) Define the term credit event.