The Hindu Business Line : How to protect the portfolio using index futures

ON SEPTEMBER 9, the BSE Sensex touched 8060. You wish to fully cover your portfolio worth Rs 36,49,000 using index futures, the size of the contract being 100 indices. If the beta of the portfolio is 0.7, what is the number of contracts to be traded?

Consider another issue: On December 31 you buy units of a mutual fund at Rs 60. The cheque got paid out of your bank account on the next day. You received dividends of Rs 3 and capital gains distribution of Rs 5 on March 6. On March 14 you exited out of the fund, and the cheque for Rs 70 that MF issued was credited by your bankers on the following day. If interest earnings on a SB account with a bank is 5 per cent per annum, how many times are you better off? (4 + 4 = 8 marks)

Solution (part 1): Number of contracts to be traded = Portfolio value / contract size x beta of portfolio = 36,49,000/(100 x 8060) x 0.7

36,49,000/8060 = 4.527295

= 4.527295 x 0.7 = 3.169, rounded off to next higher number = 4

= Number of contracts to be traded = Four

Solution (part ii): Return on the investment is computed as: (Total return on funds invested / funds invested) x (365 / number of days funds deployed) x 100

Return comprises of: i) Dividend = Rs 3; ii) capital gains, Rs 5 (amount distributed);

iii) profit on exit, Rs 70 - 60 = 10; iv) total return, Rs 10 + 5 + 3 = 18

Funds invested = Rs 60

Cash outflow for days 73 (31 in January + 28 in February + 14 in March)

= 18/60 x 365/73 x 100 = annualised return is, therefore, 150 per cent

If SB interest is 5 per cent per annum, the investor in MF is better off by 30 times.

CFO's dilemma

A YEAR ago, ABC Ltd incurred Rs 160 lakh in a project. As of now, a small amount of additional expenditure is required to be incurred to complete the project. Once this expenditure is incurred, project completion can be achieved during this year and cash inflows will begin from next year as shown in Table 1.

i) Beta of the industry is 1.60, Rf is 9 per cent, and market expectation of returns is 14 per cent. What is the cut-off amount beyond which additional expenditure cannot be incurred in order that the project is viable?

ii) The chief financial officer (CFO) has invited bids from prospective contractors to undertake and complete the contract. If none of the proposals of the contractors is below the cut-off amount, what alternative does the CFO have? Should the project be abandoned? (8 + 4 = 12 marks)

Solution: Step 1: Deriving the discount rate for evaluating the project.

By applying CAP-Model, we can derive the discount rate: Rf + beta (Rm - Rf)

= Rf + beta (Rm - Rf)

= 9 + 1.60 (14 - 9)

Discount rate = 9 + 8 = 17 per cent

Step 2: Determining Project outlay: It is noted that initial outlay is taking place in two stages, namely, a year ago and in the current year. Cash outflows of past-year have to be converted into present values by applying a compounding factor of 1.17 (Table 2).

Step 3: Determining PV of project cash inflows at a discount rate 17 of per cent (Table 3).

Step 4: Determining the cut-off amount (Table 4).

Part (a): For the project to be viable, additional expenditure should be below the cut-off amount of Rs 15.95 lakh.

Part (b): The answer to this part of the question can vary and, hence, subjective. The important alternatives are:

i) The CFO can re-evaluate the cash flows to identify specific areas of cost savings or revenue increase, so that the project inflows are improved.

ii) The PV of cash outflows pertaining to last year has been compounded at an imputed rate of 17 per cent. An enquiry is to be made whether the actual cost of funds invested in the project last year was lower than the increase of Rs 27.20 lakh (that is, 187.20 less 160), assumed above. If the actual costs were lower by, say, Rs 16 lakh, the project implementation can be reconsidered.

iii) If abandoned, it would be as shown in Table 5.

Even if additional expenditure exceeds the cut-off amount, the loss can be curtailed, in situations where the present value (PV) of loss arising from abandonment is higher than the PV of loss arising from the implementation of project.

Buyback impact

SHARES of a leading company closed on the BSE at Rs 454.60 on September 6. September 7 was a holiday for the Mumbai market. You find in the morning papers on September 8, that the management of the company has made a public offer for buyback of shares at a fixed price of Rs 568.25. Explain, with reasons, the likely impact of this buyback offer on the market price. (4 marks)

Solution: It is seen that the offer at Rs 568.25 is 25 per cent over the last closing price. Generally a share repurchase is viewed as a signal to the effect that: i) the

management desires to avoid excess cash, or ii) the management desires to increase the gearing level (debt/equity); or iii) the stock is good value even at 25 per cent above the current share price.

If any one or all of these factors are appropriate for the business-risk in question, the share prices will, in all likelihood, go up and will touch the signal-level.

On the other hand, i) if the repurchases so made will make the firm substantially more risky, ii) if the managers were having their own shares repurchased, or iii) if the action was interpreted as an inability to find positive NPV projects for the future, then the share price might either remain unchanged or decrease.

Call option contract

A SHARE with a current market price (CMP) of Rs 100 per share is expected either to move up to Rs 120 per share or move down to Rs 94 per share in six months from now. You wish to enter into a call option contract with an exercise price of Rs 96. If the risk-free interest rate is 12 per cent per annum, what would you pay for this option under the replication model for valuing options? (4 marks)

Solution: Contract period — six months; effective rate (12 per cent p.a.) for six months — 6 per cent; if on exercise date, the price is Rs 120, option value is Rs 24; if on exercise date, the price is Rs 94, option value is NIL; number of shares purchased — (120 - 94/24 - 0) = 26/24 = 1.0833

Certainty Equivalent Co-efficient

CERTAINTY Equivalent Factor (CEF) is the ratio of assured cash flows to uncertain cash flows. Under this approach, the cash flows expected in the project are converted into risk-less equivalent amounts. The adjustment factor used is called Certainty Equivalent Co-efficient (CEC).

CEF varies between 0 and 1. A coefficient of one indicates that the cash flows are certain. The greater the risk in a cash inflows, the smaller will be certainty equivalent factor for `receipts', and greater will be the certainty equivalent factor for `payments'. While employing this method, the decision-maker estimates the sum he must be assured of receiving, in order that he is indifferent between an assured sum, and the expected value of a risky sum.

A CEF problem

A PROJECT carries a forecast cash flow of Rs 1.12 crore in Year-1, and 1.2544 crore in Year-2. Interest rate is 6 per cent. Estimated risk premium on the market is 12 per cent. The project-asset carries a beta value of 0.5. If you use, a constant risk-adjusted discount rate: i) What is the PV of the project; ii) What are the Certainty Equivalent cash flows in Years 1 and 2; iii) Ratio of Certainty Equivalent Cash Flows to the expected cash flows in Years 1 and 2. (2+4+2 = 8 marks)

Solution: Step 1. Deriving the Risk-adjusted discount Rate: Using CAP-Model, the risk-adjusted discount rate can be computed as under:

Discount rate = Rf + beta (Rm - Rf)

= 6 + 0.5 (12) = 12 per cent

This rate is the constant risk-adjusted discount rate. Applying this discount rate, we can compute the PV of the project.

Part (i) PV of the project is presented in Table 7.

Part (ii) Certainty Equivalent Cash flows (CE cash flows) in Years 1 and 2

For computing CE cash flows, the risk-free rate is to be taken as the discount rate. The solution lies in the fact that CE cash flows should provide the same PV, by using the CE-discount factor.

Therefore, let the CE cash flows be = X-1 and X-2

X-1 equals = X{-1}/1.06{+1} = 1.12/(1+0.12){+1} = and

X-2 equals= X{-2}/1.062 = 1.254/(1+0.12){+2} = 1.236

Therefore, CE cash flows for Year 1 and Year 2 are shown in Table 8.

Part (iii), ratio of CE cash flows to expected cash flows is presented in Table 9.

Cost of carry model

THE price of PQR Ltd as at the close of September 22, 2005, was quoted at Rs 400, when three-month futures on the same stock were quoted at Rs 410. During this period, an interim dividend of Rs 10 is expected to be paid out by PQR Ltd. If the interest rate was 16 per cent, compute:

i) Applying the cost of carry model, what should be the futures price, and

ii) Is there is any arbitrage opportunity? (4 + 4 = 8 marks)

Solution: Part (i) The time to expiration is three months, that is, 1/4th (0.25) of the year. Futures price is computed as:

= CMP + (Appropriate Interest cost on current price) - (div)

= 400 + {lcub}(400*0.25*0.16) - (10){rcub}

= 400 + (16 - 10) = 400 + 6 = Rs 406

Futures price = Rs 406

Part (ii) Arbitrage: As per cost of carry model, the futures price would be Rs 406. As against this, the futures are quoted at Rs 410. This gives rise to arbitrage opportunities in order that ultimately, the prices will converge.

The process of arbitrage will be: a) Buy PQR Stock in spot market now. For this purpose, borrow money; b) Sell PQR futures in futures market now, at going futures price; and c) Out of sale proceeds received, repay the loan along with interest. Excess of proceeds over repayment is the gain (see Table 10).

Question 6 (b)

Kakotkars Ltd. has its main activity in Mumbai. It has a manufacturing outfit in Berlin that imports components from its HO in Mumbai, and sells its entire output to customers in Berlin.

Mukerjees Ltd. has its main activity in Kolkatta. It also has a manufacturing outfit in Berlin that procures its materials entirely locally from various suppliers in and around Berlin. The output is exported to Kolkatta.

Explain how each company is likely to be affected by a rise in the value of Euro against INR, and how can they hedge the risks through `forward market'.

(5 marks)

Revenue of Kakotkars is in Euros, and expenses are in INR. If the value of Euro rises, its profit will increase. In the short run, Kakotkars can hedge this exchange risk by entering into a forward contract to

(Source: Prime Academy, Chennai.)

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