Quiz 2

Quiz – 2 (Financial Engineering – Prof. Mahendra Mehta)

You are running a global car company (eg: Ford). You are the CFO of the company. Your CEO wants you make a presentation to the board suggesting ways to lower the company’s cost of funding. The company has access to the capital markets. Background Capital Markets information is as follows:

Govt bond yield	3-month maturity	10 –year Maturity
US	0	3.5
EUR	1	4
JPY	0.5	1.5

The chief economist of your company believes that Yen and Euro are likely to weaken over 10 years. One choice is to issue fixed rate 10 year debt via corporate debt issuance.

Corporate spreads in US = 1%, EUR = 1.5% & in JPY = 2%.

Q1 – What rate can you issue 10-year fixed rate in each country?

Q2 – Fixed-for-floating 10 year spreads are: US = 10bp; EUR = 20bp; JPY = 50bp. If you swap your fixed rate bond to floating, what is your floating rate coupon in US, EUR and JPY?

Q3 – assume that short rates stay fixed for 10 years, what is the cost of debt in US, EUR and JPY?

Q4 – At the end of 10 year, your chief economist forecasts are as following: USD is weaker by 20%, JPY is weaker by 10%, EUR is same. If you issue debt now in these currencies, in 10 years time, you will have to pay back what % in real terms of USD, JPY and EUR notional?

Q5 – Give the specific funding cost and rank order the following choices in each of the 3 currencies: 10 year fixed rate debt; 10 year floating rate debt; foreign currency bond

Q6 – Given the 3 possibilities (Fixed 10 year, floating 10 year, foreign currency) which combination of financing structures do you suggest

Q7 – What are the risks of your recommendation? (All types of risk including but not limited to Business vs Financial mismatches)?

Q8 – If there were no financial intermediation, which option above would not be possible?

Q9 – Why do you think corporate spreads are so different in USD, EUR and JPY? Why is the fix to floating spreads so different in each country?

Q10 – Now assume that markets are liquid and all the options presented above are feasible. Who benefits and who loses from the various options?

Q11 – Do you think this type of financial engineering is useful to society at large? Why?

Q12 – Can you think of other innovative ideas to lower the funding cost of the company?

Quiz 4

Financial Engineering (Prof. Mahendra Mehta)

Quiz-3

You are planning to build a 5 star hotel in India. For financing the construction of the hotel, you have finalized loan arrangement with a consortium of banks. The loan amount is INR 5 billion. Agreed term of the loan at a floating rate and a spread of 250 bp and being given for a year of 10 years. Construction of the project would start from 1^st July, 2011. The loan would be drawn as per schedule given below. The construction of the hotel is likely to take 30 minutes (See Table 1)

Loan would be repaid starting from 5^th year (starting from 1^st July 2015) in 10 equal installments (see Table – 2). You are required to suggest at least 2 ways to hedge (interest rate risk) the financing risk efficiently. You are free to use any interest rate hedging instrument.

Table – 1 - Drawdown

Date	Millions
Jul-11	500
Oct-11	500
Jan-12	500
Apr-12	500
Jul-12	250
Oct-12	250
Jan-13	500
Apr-13	750
Jul-13	500
Oct-13	750
Total	5000

Table – 2 – Repayment Schedule

Date	Amount
Jul-15	100
Jan-16	200
Jul-16	300
Jan-17	400
Jul-17	500
Jan-18	600
Jul-18	700
Jan-19	800
Jul-19	900
Jan-20	500

Notes

Financial Engineering (Professor Mahendra Mehta)

· Designing a product with various financial concepts to exactly meet the objectives of the investor

· Most products available are generic

What drives financial innovation

· Regulation & Taxes

· Changing Needs

· Greed

· Competition

Inflation is a very risky phenomenon – increases interest rates and hence all the asset prices drop. Govt has only 2 weapons

· Increase CRR

· Increase Interest Rates to suck liquidity

· Open Market operations – Sell government bonds

Tier1 Cap+Tier2 Cap/Risk weighted Capital –Capital to be maintained by banks

· What is Tier 1 & Tier 2 – Based on liquidity and risk

Annual Volatility of indices – 20-30%

Commodity volatility – 25-30%

Market makers – gives 2 way quotes and is ready to buy or sell. He hence provides a lot of liquidity in the market and is called a market maker

Hedging

It is the process of mitigating risk. Risks have to be first identified, measured/estimated, analyzed (to see if it is within your risk appetite) and finally risk control. Risk Control can be done by reducing exposure, eliminating risk completely or accept if it is within your appetite. The risk has to be reported at 3 levels – Regulators, BoD, Senior Management, Shareholders (through the balance sheet). These steps are followed under normal market conditions. These risks are measured everyday.

· Credit Risk

o Obligor Risk/Issuer Risk (Default Risk) – defaults entire payment..

§ hedged through CDS

§ Measured by probability of default

§ The function is exponential and as the PD increases, the premium increases rapidly

§ Minimum PD is 3bps

o Settlement Risk (mainly for spot transactions) – doesn’t pay the exact amount. This and default risk can be classified as counterparty risk. So it is advisable to not use this term. This is a huge risk when you sell and buy currency because of the time zones. Hedged through operational Insurance

o Pre-Settlement Risk- If i do a forward contract with a customer for 1 year of buying $ and selling yen. After 6 months, the contract is in the money for me and hence the customer is likely to default. So you make alternative means for that amount and assume that the customer will default so you still have 6 months to find alternate means of generating the amount.

o Cross Border Risk – If you have invested in some other country and that country is in trouble.

· Market Risk -

o Price Risk – All financial Engineering products have to hedge all these risks. For a single product, all of the following risks wont be applicable, some will be depending on the underlying. This is measured using ‘Factor Sensitivity’ and VAR

§ Equity price risk

§ Interest rate risk

§ FX risk

§ Commodity risk

§ Volatility Risk

o Liquidity Risk

§ Measured with the bid offer spread.

§ Done through a qualitative measurement

o Basis Risk

§ If the hedge is not perfect

§ If the change in the price of the underlying is not the same as the change in the price of the hedge instrument, it is called basis risk.

· Operational Risk

o People-25%

o Process-65%

o System-2%

o Legal- 1%

o External elements – 6-7%

Hedging Risk

· Market factor sensitivity- Change in the portfolio per percent change in the value of the change of one share

· So to hedge, i will pick up some instrument with a factor sensitivity of -10.5 so that my net exposure is 0. If it is not 0, you will run a basis risk.

On the Balance sheet, a FE has different taks

Asset Side

Asset Allocation – Markovitz MPT, by maximizing Sharpe ratio

· Sharpe ratio is Mu/Sd * sqrt (260)

· Numerator is multiplied by 260 and denominator by sqrt(260) and hence it will cancel out and become sqrt(260)

· If the Sharpe is 1, the risk is higher than the return expected. If it is 2, the risk is reduced by half. Hence, the higher the Sharpe ratio the better because the risk is getting reduced. Hence, anything more than 3 is an excellent Sharpe ratio.

· It is negative when the returns are negative

Liability Side

· Minimizing the cost of the liability

Risk & return

· Look at the overall impact of the balance sheet and invoke an instrument that reduces the overall impact

· You can take a bunch of financial instruments and derivatives and combine them in a way to give you cash flows exactly as desired.

Market factor Sensitivity

Anything that is not in your control is a market factor

· Equity prices

· Commodity prices

· Interest rates

· FX rates etc

There are 100s of market factors in the market – each scrip will have a market factor.

Current portfolio : 1 reliance share of value 1050

· If i have a reliance share for 1050, my portfolio increases by 10.50rs for every +1% change in the reliance prices.

· Hence now the value becomes = 1050+10.5=1060.5

· MFS= Final value- Initial value

· VaR= Defeasance factor* MFS

· For a sd of 30, for 1 day

· VaR=10.5*normsinv(99%)*30*sqrt(1/260)=32.13299

· To hedge this

o You can buy a put on reliance. Either reliance or an underlying which is highly correlated with the underlying (>.8) with a strike = current spot of 1050. The upside is reduced parallel to the extent of the premium paid. However, if the stock price doesn’t increase by an amount greater than the premium, you will lose. Hence it is not a perfect hedge. Additional exposures have been created. With the stock, there is only one MFS. Here, you are exposing to more factors like volatility, interest rates etc

o You can sell a future. This is like shorting the stock, the upside on one is exactly compensated by the downside of the other. Although there is small exposure to interest rates, this makes for a good hedge and is perfectly hedged

o For banks, if the VAR is calculated, according to Basel, the bank has to show more than 3-4 times the VaR as capital to be able to take that much risk. This is the deciding factor of the confidence level that the bank takes to decide the VaR. The lower CL they take, the greater the probability of them needing to show 3 times rather than 4 times because they have more space to make mistakes in their back testing process. Also, at 99%, the dist is at the tail and the tail is never accurate. So it is safer to limit the confidence at a 95% where the results are more accurate.

o Expected Shortfall – you find the normsinv for 1%

Policy

· Appetite

o How do you decide the risk appetite ??

o Risk Appetite depends on

· Revenue

· Margin

· Debt

· USD/INR Volatility

· Quality of people

· Cash flows, liquid assets

o Generally start with a stringent number and then review it every 3 months

o It is generally a % of the revenue (PAT)

· Risk Identification

o Direct

o Indirect

· Risk measurement

o FS & VaR

o VaR is calculated for each currency by adding the separate VaRs and then portfolio VAR is calculated for different currencies

· Risk control

Some shit that i was absent for

Interest rate risk management

· FRA

o Risks : Interest rate risk, counter party risk

· IRS

o Risks : Interest rate risk, counter party risk

· STIR

o Exchange traded, only IRR

· Bond futures

o Exchange traded, only IRR

· Interest rate options – cap (call) and floor (put)

o OTC

o Series of caplets, every 6 months so if the interest rate goes above the strike interest

· Swaptions

o Swap+Option

o Option period must be less than the swap

o Once the strike price is breached, you can exercise the swaption and convert it into a swap contract

o Once it is converted to a swap, the strike will be the fixed rate and you are converting your obligation to floating

· Range Accrual

o It is an exotic product built using options

o The seller tells the buyer that he has to pay interest only if it remains between an agreed range (the actual rate in that case) or else, he doenst have to pay any interest

o This is calculated daily and amount to be paid is accrued and paid during settlement

Exotic Options

· Asian Options

o Average price option – payoff is average spot-strike

§ Volatility is much lower and hence the premium is also lower, profits are also lower

§ Exotic options aim to reduce the cost to customers rather than maximize the profit

§ Applied in ESOPs

§ It is easier to delta hedge. Delta approaches 0 as the option approaches maturity.

§ Similarly an average spot put

o Average strike call

§ Payoff : Spot on expiration – average spot of the asset

§ Similarly average strike put, where strike = average of spot

§ Average can be AM or GM

· Knock in/out and double knock in/out

o Becomes a vanilla option after breaching the barrier

o Objective is to again reduce the premium

· Lookback option

o Lookback call

§ Strike = minimum price of the asset

§ Payoff= spot at maturity-minimum stock value

o Lookback put

§ Strike=maximum price of the asset

§ Payoff=spot at maturity-maximum stock value

§ Premium will be very high

Sample Paper

Financial Engineering (Prof. Mahendra Mehta)

End Term Exam (2 Hours – Feb 3, 2011)

Open Notes, Closed Internet, Hard-Copy exam

Question 1 – Given the following bid/offer rates (2 marks)

ü USD/JPY – 82.34/38

ü USD/INR – 45.20/25

ü GBP/USD – 1.5620/25

Find the following cross rates – USD/GBP, INR/JPY, GBP/JPY, GBP/INR (Calculate up to 2 places of decimal for currency pairs involving JPY and up to 4 decimal places for other currency pairs)

Question 2 - USD/CHF spot rate is given as 0.9600/05. The 6 month USD interest rate is 1% and 6 month CHF interest rate is 1.5% per annum. The 6 month interest rate for USD/CHF is quoted to be 0.9705/0.9708 (1+2=3 Marks). Is the quoted rate appropriate? If yes, prove that by calculation. If no, can you arbitrage? If yes, what transactions would you carry out to arbitrage?

Question 3 – Given the following, find the INR interest rate for 3 months? (2 Marks)

ü USD/INR – Spot – 45.50

ü USD/INR – 3 Month Forward rate – 46.50

ü 3 Month USD interest rate is 1%

Question 4 – Answer the following with respect to an Interest Rate Swap (1+1+2=5 Marks)

ü What is the initial value of a single currency Interest Rate Swap?

ü If you are receiving fixed & paying floating, and the yield curve is going up, what will happen to the value of the swap?

ü What is the difference between a PAR value annual coupon paying and yearly swap rate?

Question 5 – Answer the following with respect to an option (2+2=4 Marks)

ü Define Put-Call parity. What does put call parity convey?

ü If the Put-Call parity equation is violated by the market place, how can you exploit the mispricing?

Question 6 – Explain carefully the difference between hedging, speculation & arbitrage (3 Marks)

Question 7 – What is the difference between entering into a long forward contract when the forward is $50 and taking long positions in a call option with a strike price of $50? (3 Marks)

Question 8 – Explain carefully the difference between selling a call option and buying a put option (3 Marks)

Question 9 – An investor enters into a sheet forward contract to sell 100,00 GBP for US dollar at an Exchange rate of 1.5000 USD per GBP. How much does the investor gain or lose if the exchange at the end of the contract is (1) 1.4900 and (2) 1.5200? (2+2=4 Marks)

Question 10 – Suppose that you write a put contract with a strike price of $40 and an expiration date in 3 months. The current stock price is $41 and the contract is on 100 shares. What have you committed yourself to? How much could you gain or lose? (1+2=3 Marks)

Question 11 – Suppose that you own 5,000 shares worth $25 each. How can put option be used to provide you with insurance against a decline in the value of your holding over the next 4 months? (2 Marks)

Question 12 – Suppose a June put option to sell a share for $60 costs $4 and is held until June. Under what circumstances will the seller of the option (i.e., the party with the short position) make a profit? Under what circumstances will the option are exercised? Draw a diagram illustrating how the profit from a short position in the option depends on the stock price at maturity of the option. (1+1+2=4 Marks)

Question 13 – The current price of a stock is $94, and 3-month European call option with a strike price of $95 currently sells for $4.70. An investor who feels that the price of the stock will increase is trying to decide between buying 100 shares and buying 2,000 call options (=20 Contracts). Both strategies involve an investment of $9,400. What advice would you give? How high does the stock price have to rise for the option strategy to be more profitable? (2+1=3 Marks)

Question 14 – A financial institution has entered into an interest rate swap with company X. Under the terms of the swap, it receives 10% per annum and pays 6-month LIBOR on a principle of $10 million for 5 years. Payments are made every 6 months. Suppose that company X defaults on the 6^th payment date -(at the end of the year 3) when the interest rate (with semi-annual compounding) is 8% per annum for all maturities. What is the loss to the financial institution? Assume that 6-month LIBOR was 9% per annum halfway through years. (2 Marks)

Question 15 – What does it mean to assert that the delta of a call option is 0.7? How can a short position in 1,000 options be made delta neutral when the delta of each option is 0.7? (1+1=2 Marks)