# (Papers) ACET Paper May 2010 "ST6 – Finance and Investment B "

## (Papers) ACET Paper May 2010 "ST6 – Finance and Investment B "

** Q 1) **

(a) Alpha Limited has issued a Rs. 100 crores issue of floating-rate bonds on which it Pays an effective interest rate of 0.5% over the MIBOR rate annually. The bonds are selling at par value. The firm is worried that rates might be about to rise, and it would like to lock in a fixed interest rate on its borrowings. The firm sees that dealers in the swap market are offering swaps of MIBOR for 8%. The swaps available from the dealer have the same term as the floating-rate bonds. What interest rate swap will convert the firm’s interest obligation into one resembling a synthetic fixed rate loan? What interest rate will it pay on that synthetic fixed-rate loan?

(b) At the present time, one can enter 3-year swaps that exchange MIBOR for 6%. An off-market swap would then be defined as a swap of MIBOR for a fixed rate other than 6%. For example, a firm with 8% coupon debt outstanding might like to convert to synthetic floating-rate debt by entering a swap in which it pays MIBOR and receives a fixed rate of 8%. What up-front payment will be required to induce a counterparty to take the other side of the swap? Assume notional principal is Rs. 100 crores.

(c) If the yield curve is flat, prove that the duration of a coupon bond is

Where c is the coupon rate per annum with annual compounding (coupons are paid annually), y is the bond’s yield per annum with annual compounding, and T is the number of years after which the bond will expire.

(d) Pension funds pay life time annuities to recipients. If a firm will remain in business Indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of Rs. 120 crores per year to beneficiaries. The annual effective yield to maturity on all bonds is 12%.

(i) You decide to use 6-year maturity bonds with coupon rate of 10% (paid annually) and 21-year maturity bond with coupon rate 5% (paid annually) to immunize your obligation. How much each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation?

(ii) What will be the par value of your holding in the two coupon bonds?

**Q 2) **

(a) Suppose that a bank has a total of Rs. 4000 crores of a bond portfolio.

The 1-year probability of default averages 2% and the recovery rate averages 50%. The copula correlation parameter is 0.25. Using Gaussian copula model, estimate the 99% 1-year credit VaR.

(b) Consider a portfolio with a delta of 700, a gamma of -4100 and a kappa (vega) of - 2100. Two traded options are available on the portfolio. The first traded option is available with a delta of 0.60, a gamma of 1.20 and a kappa (vega) of 0.60. The second traded option is available with a delta of 0.30, a gamma of 0.80 and a kappa (vega) of 0.30. What is the position in the two traded options and in the underlying asset would make the portfolio delta, gamma, and kappa (vega) neutral?

**Q 3) **

It is November 30 2008. The cheapest to deliver bond in a March 2010 Treasury bond futures contract (which expires on March 31 2010) is a 10% (per annum with semiannual compounding) coupon bond and the delivery is expected to be made on March 31, 2010. Coupon payments on the bond are made on January 1 and July 1 each year.

The term structure is flat, and the risk-free rate of interest with continuous compounding is 8% per annum. The conversion factor for the bond is 1.3200. The current quoted bond price is Rs. 120 (face value of the bond is Rs. 100). Calculate the futures price for the contract.

**Q 4) **

(a) Demonstrate that an at-the-money call option on a given stock must be worth more than an at-the money put option on that stock with the same time to maturity. Assume that there are no dividends and that the risk-free rate is greater than zero.

(b) The agricultural price support system guarantees farmers a minimum price for their output. Describe the program provisions as an option. What is the asset? The exercise price?

(c) An executive compensation scheme might provide a manager a bonus of Rs. 500 for every rupee by which the company’s stock price exceeds some cutoff level. In what way is this arrangement equivalent to issuing the manager call options on the firm’s stock?

(d) The delta of an at-the-money money call option on Infosys stock is 0.5. The
delta of
an at-the-money put option on Infosys stock is -0.7. What is the delta of an
at-the

money straddle position on Infosys stock?

(e) Would you expect a one rupee increase in a vanilla call option’s exercise price to lead to a decrease in the option value of more or less than one rupee?

(f) If the stock price falls and call price increases, then what has happened to the call option’s implied volatility?

(g) What is the difference in cash flow between short-selling an asset and entering a short futures position?

(h) Are the following statements true or false?

(i) All else equal, the futures price on high beta stock should be higher than
the
futures price on low-beta stock.

(ii) The beta of a short position in the NSE Nifty futures contract is negative.