End Term Exam for April 2010 batch (Prof Mahendra Mehta)

SP Jain Center of Management, GMBA 2010 April, End Term Exam

Course: Financial Maths (Prof Mahendra Mehta)

Time: 2 hours, Max Marks: 45, Date: November 10, 2010

Instructions:

Ø Max marks for questions are respectively = 4,3,8,9,6,3,8,4

1) IQ scores are assumed to be normally distributed with a mean of 100 and a standard deviation of 15. In a random sample of 20,000, how many people will have IQ between

a. 90 and 100

b. 80 and 100

c. 120 and above

d. 80 and below

2) If 1 month later, interest rate of USD & SGD is 1% and 3% respectively and spot rate of USD / SGD is 1.2850, find the implied forward rate of USD / SGD (Use 1/12 for 1 month time). Which one of the 2 currencies in question is at discount

3) Find the daily, weekly, monthly and annual volatility of 6 stocks (given daily closing prices of stocks). Find also the correlation and covariance matrix along the 6 stocks (use natural log to compute correlation and covariance) (use 5 business days for a week, 22 business days for a month and 260 business days for a year). Interpret volatility, correlation and covariance results

4) Find the price of call and put option of a non-dividend paying stock, given the following

a. Spot Price – USD 100

b. Strike Price – USD 105 (Call)

c. Strike Price – USD 95 (Put)

d. Interest Rate – 2% per annum

e. Daily volatility of the stock 1.5% (use 260 days in a year to convert volatility)

f. Time to maturity – 6 months (use 182 days for 6 months and 360 as the day count basis)

i. Find also the call and put Delta of the stock and interpret it

5) Find the Value at risk of the following portfolio for 5 business days and at 95% confidence level

a. Buy USD against SGD, amount 2 MM at 1.2850, Volatility 15% (Annual)

b. Buy USD against JPY, amount 3 MM at 81.45, Volatility 12% (Annual)

c. Buy USD against CHF, amount 5 MM at 0.9610, Volatility 13% (Annual)

	SGD	JPY	CHF
SGD	1	0.30	0.35
JPY	0.30	1	0.25
CHF	0.35	0.25	1

6) The bid offer spread quoted by a dealer of USD / SGD is 1.2834 / 40. If you want to buy SGD, what rate would you get? (Hint: I buy SGD = I Sell USD = Bank buys USD = 1.2834)

7) Find the daily portfolio volatility (Stock data is given separately in an excel file. This data is also used in the problem 3, if we do the following transactions

a. But 100 ICICI Bank at INR 1270

b. Sell 200 HDFC at INR 740

c. Buy 300 HDFCBANK at INR 2390

d. Sell 400 Kotak BANK at INR 500

e. Buy 500 SBI at INR 3500

f. Sell 600 Axis Bank at INR 1550

Interpret the daily portfolio volatility result?

8) If you sell USD 10 MM against NOK at a spot rate 5.8500 and the annual volatility of the currency pair (USD / NOK) is 12%, what is your VaR (Value at risk) for 5 business days at 98% confidence level (assume returns of USD/NOK are normally distributed)