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The below is a sample

Sample 1

The cost of capital for the project is different to that of the cost of capital for an overall company. The cost of capital for this project has been calculated with the help of a capital budgeting technique of Internal Rate of Return (IRR) analysis (Chapman, Hopwood, & Shields, 2007). The Internal Rate of Return determines the discounting rate to be applicable in the computation of the present value of the project with its cash inflows.


Particulars Cash Inflows Discount rate Present value Discount rate Present value
Year 1 1000000 10% 909090.9091 11% 900900.9009
Year 2 1000000 10% 826446.281 11% 811622.4332
Year 3 1500000 10% 1126972.201 11% 1096787.072
Year 4 1500000 10% 1024520.183 11% 988096.4612
Year 5 1800000 10% 1117658.382 11% 1068212.391
Salvage value 100000 10% 62092.13231 11% 59345.13281
Total Cash Inflows 5066780.088 4924964.391
Initial Outlay 5000000 5000000
Net Present Value 66780.0883 -75035.60937


In order to determine the IRR value of the project by calculation, a trial and error method has been deployed to determine the Net Present value (NPV) of the investment to be Zero. The above table shows the NPV calculated with the discount rates 10 percent and 11 percent which provides with a positive and negative value denoting that the IRR to be somewhere in between (Mittal, 2006). Therefore, an interpolation technique has been used to determine the IRR and the project demonstrated an IRR value of 10.47 percent which is well beyond the WACC of the overall company. Hence, the project would be profitable for the company.


Chapman, C. S., Hopwood, A. G., & Shields, M. D. (2007). Handbook of Management Accounting Research. The Netherlands: Elsevier.

Mittal, R. (2006). Management Accounting and Financial Management. India: V.K. Enterprises.

Sample 2 : Financial Risk Management


Many affiliate the economical industry mostly with the value industry. The economical industry is, of course, far broader, covering ties, forex trading, property, products, and numerous other resource sessions and economical equipment. A section of the industry has fast become its most important one: types. Mixture items originally appeared, as securing devices against variations in product expenses and commodity-linked types stayed the only form of such items for almost three century. The economical types came into highlight in post-1970 period due to growing uncertainty in the marketplaces. However, since their appearance, these items have become very popular and by 90’s, they included about two-thirds of total dealings in derivative items. Recently, the industry for economical types has grown extremely both in terms of variety of equipment available, their complexness and also revenues. In the class of value types, futures trading and options on stock spiders have obtained more popularity than on personal shares, especially among institutional traders, who are major users of index-linked types. (Stulz, 2014)

The following factors have been the reason for growth of economical derivatives:

  • Increased movements in resource expenses in marketplaces,
  • Increased incorporation of national marketplaces with the worldwide marketplaces,
  • Marked enhancement in interaction features and distinct decrease in their expenses,
  • Development of more innovative threat control tools, providing economic agents a broader choice of threat control strategies, and
  • Innovations in the marketplaces, which properly merge the threats and profits over a huge number of economic resources, leading to higher profits, reduced threat as well as trans-actions expenses as compared to personal economical resources.(Campello, 2011)

Derivatives have widely been used as they accomplish securing, that is, they enable finance mangers of an actual resource profile to transfer some parts of the chance of price changes to others who are willing to bear such threat.




The problem in hand is related to the any downside in the market in near future which may affect the portfolio. From a fund manager perspective, protecting the fund from any downside is the foremost criteria and hence proper hedging strategy needs to be built to protect the fund.


Financial Exposure:


The fund size is of $50 million, and hence the whole of the fund is exposed to the downside risk. Any fall in the market will affect the fund. With Beta of 0.87, the fund will fall by 8.7%, if the market (S&P) falls by 10%.


Fundamental Analysis:


Fundamental analysis deals with macro-economic factors and also the financial of the company. For S&P, the individual stock present in the S&P will affect the movement of index.

The Derivative Instruments process consists of the following activities:

  • Entering into Trades
  • Valuation of Derivative Instruments
  • Review & Recording
  • Monthly Reconciliation Process
  • Hedge Accounting for Derivative Instruments

The main thing to look into the futures contract while hedging is the expiry month of the contract. If the need is for short term, then immediate or nearest expiry month should be considered. Or rollover strategy can be used to roll the contract over next month.

Another important asset class to hedge the portfolio is option. Options are fundamentally different from futures contracts. While in a future contract both the contracting parties have an obligation to honor the contract, in case of options, the seller has an obligation and buyer has the right in the contract, which he may or may not exercise. The party taking a long position is called the buyer/holder of the options and the party selling the option is called the seller/writer of the options. (Kozhan, 2013)

Options can be categorized as call or put options depending upon the right conferred on the buyer. An option, which gives the buyer a right to buy the underlying asset, is called a call option and the option that gives the buyer the right to sell is called as put option. Further an option that can be exercised at any time on or before the expiry date/day is called an American option and the option that can be exercised only at the expiry is called the European option. The price at which option is being traded is called as strike price or the exercise price. The date/day at which the option ceases to exist is called as expiration date/day. (Kozhan, 2013)

The price that an option buyer pays to the option writer is called as option premium. An option premium is the inflow to the option writer irrespective of whether the option holder exercises his option or not.

An option has no obligation in an option contract and he will exercise this right only when he is likely to benefit by doing so. For example, if he holds a call option on a particular stock he will exercise his option only when the market price of that stock is trading at a higher rate so that he profits from the difference between the market price and strike price. Thus the profit potential of the option buyer is unlimited. If however the stock price falls then he will not exercise the contract in which case he will loosed only the premium paid. Therefore the option buyer bears the limited amount of risk but his profit potential is unlimited. Conversely, as the profit/loss of an option buyer reflects the loss/profit of option seller, the seller carries an unlimited risk with a limited return potential. Thus the risk and return of the option contracts is asymmetric unlike that of that of a futures contract. (Kozhan, 2013)


Technical Analysis:


From a fundamental analysis point of view, future market goes hand in hand with the S&P index, and the trend of S&P shows downtrend. Technical analysis deals with movements in the price based on short term news and based on historical prices. From futures market perspective, the timing of the expiry also plays an important role in the pricing.

Another important kind of hedging which is fruitful from technical perspective is Dynamic hedging. It is a technique that is widely used to hedge gamma or vega exposures. Because it involves adjusting the position hedge as the underlying moves—often several times a day—it is “dynamic.”

Dynamic hedging is delta hedging of a non-linear position with linear instruments like futures or forwards or spot positions. The delta value of the non-linear position offset the linear hedge position which yields a zero value delta from overall perspective. However, as the underlying value moves to and fro, the delta value of the non-linear position does change but the value of linear hedge does not change. The deltas no longer offset each other, so the linear hedge has to be adjusted (increased or decreased) to restore the delta hedge. The continual adjustment of the position to maintain a delta hedge is called dynamic hedging. (Basak, 2012)

The continual readjustment of the delta hedge ensures that the portfolio always has a zero delta—and that it loses only a little value each time the underlying stock price moves. Note however, that the portfolio always loses value. It never gains it. A delta-hedged negative gamma portfolio loses money irrespective of whether the underlying value rises or falls. Each time the underlying moves, the portfolio suffers a small loss. The dealer readjusts the delta hedge, locking in that loss. The underlying moves again, causing another loss. The dealer readjusts the delta hedge again, locking in that loss as well. The process continues until the option expires and the dealer can stop dynamic hedging.


Position in derivative market:


For our portfolio, as we have long position in the cash market so it is better to short future to get the hedging position.

Now in order to perform the hedging operation it is necessary to know exactly how many contracts of S&P has to be sell and what will be the net impact of this combined position in the cash and future markets. The following formula will help to determine the number of contracts that need to be sold in order to achieve perfect hedging against the systematic risk using S&P. This number is called as hedge ratio.

Number of contracts for perfect hedge= Vp*βp/Vi

Vp-> Value of the portfolio

βp -> beta of the portfolio

Vi-> value of the index futures contract

Value of S&P Futures Index for December 14 expiry is $1976.

Now hence by applying the formula we get:

$50 million * 0.87/1976 = 22014.17

As S&P lot size is of 250, so it comes out to be around 88 lots.

Hence we need to short 88 lots of S&P at $1976 in order to protect our portfolio from systematic risk.

So, the net outgo for buying 88 lots of S&P future will be = 1976*88*250 = $43.472 million

The 3 month risk free interest rate is 0.02% (Anon., 2014)

The 3 month bank prime loan is 3.25% (Anon., 2014)

Thus the net outgo will be 43.472*3.25/4 = $0.35321 million

The index has provides a dividend of 3%. So, over 3 month period, the net income will be

$43.472 million * 3%/4 = $0.32604 million.

Hence, the net cash outgo will be = $0.35321 – $0.32604 = $27170


Reassessment of the portfolio:


The portfolio has been reassessed at the end of October 26. The prices for the S&P and its future are given below


Date Open Close
26-Sep-14 1,966.22 1,982.85
29-Sep-14 1,978.96 1,977.80
30-Sep-14 1,978.21 1,972.29
1-Oct-14 1,971.44 1,946.16
2-Oct-14 1,945.83 1,946.17
3-Oct-14 1,948.12 1,967.90
6-Oct-14 1,970.01 1,964.82
7-Oct-14 1,962.36 1,935.10
8-Oct-14 1,935.55 1,968.89
9-Oct-14 1,967.68 1,928.21
10-Oct-14 1,925.63 1,906.13
13-Oct-14 1,905.65 1,874.74
14-Oct-14 1,877.11 1,877.70
15-Oct-14 1,874.18 1,862.49
16-Oct-14 1,855.95 1,862.76
17-Oct-14 1,864.91 1,886.76
20-Oct-14 1,885.62 1,904.01
21-Oct-14 1,909.38 1,941.28
22-Oct-14 1,941.29 1,927.11
23-Oct-14 1,931.02 1,950.82
24-Oct-14 1,951.59 1,964.58

Source – (Anon., 2014)


S&P Futures
Date Open Close
26-Sep-14 1961 1976
29-Sep-14 1974.75 1969.5
30-Sep-14 1968.75 1965.5
1-Oct-14 1961 1940.75
2-Oct-14 1940.75 1938.5
3-Oct-14 1938.5 1960.25
6-Oct-14 1961 1956
7-Oct-14 1953.25 1928
8-Oct-14 1926.25 1961.75
9-Oct-14 1961.5 1925
10-Oct-14 1917 1894.25
13-Oct-14 1892 1865.5
14-Oct-14 1866.25 1874.75
15-Oct-14 1878.25 1846.75
16-Oct-14 1846.75 1850.5
17-Oct-14 1853 1881
20-Oct-14 1884 1900
21-Oct-14 1903.5 1938
22-Oct-14 1938.25 1925
23-Oct-14 1924.5 1946
24-Oct-14 1946 1959.75

Source – (Anon., 2014)


The S&P has fallen from 1980 to 1964 in this 1 month, which is almost 0.92% fall.

The S&P future has fell from 1976 to 1959.75 which is 0.82% fall.

The cash position of the portfolio would have reduced by

= 0.87*0.92% = 0.8%

So, the net loss in the portfolio would be = 0.8% * $50 million = 0.4002 million

So, has we not hedge the portfolio, the new loss would be $400,200.

Now, we will see the effect of hedging.

The short position on the index has increase due the price decrease in index futures.

The increase is = 0.82% * $43.472 million = $0.35647 million

So, the short position in the index future would give profit of $356,740.4

Thus, the total gain/loss would be = $400,200 – $356,740.4 = $43,729.6

Taking into consideration the interest, we would get = $43,730 + $27,170 = $70,899.6

So, on percentage basis, the total loss in the portfolio is = 0.142%.

Had, the hedging been not done, the loss would have been 0.8%. Thus through hedging, the portfolio had been saved with loss in tune of $329,300.4 or almost $0.329 million.




Derivatives have always been used to hedge the position in cash market. Hedging means minimizing risk and it does not guarantee any profit. The different strategies used only tries to minimize the risk due to the movement in the market. But over a long term they do provide profit in the position.

Risk management underscores the fact that the survival of an individual depends heavily on his capabilities to anticipate and prepare for the change rather than just waiting for the change and act on it. The main objective of risk management is neither to prohibit nor prevent risk taking activity, but on the contrary it is to ensure that the risks are taken with complete knowledge, crystal clear purpose and proper understanding so that it can be properly measured and mitigated. It also prevents an individual from suffering unacceptable loss. Derivative can be efficiently used to manage risk. Here offsetting position can be created which leads to a much smoother cash flow in the portfolio. Hedging can be done by using both futures and options. While in future one is locked at a price and he cannot benefit if market movement is positive, in option hedging upward profit is not limited and if market is favorable than he will be having profit that movement.


Anon., 2014. Federal Reserve. [Online]
Available at: http://www.federalreserve.gov/releases/H15/update/

Anon., 2014. Investing. [Online]
Available at: http://www.investing.com/indices/us-spx-500-futures-historical-data

Basak, S. &. C. G., 2012. Dynamic hedging in incomplete markets: a simple solution.. Review of financial studies, Volume hhs050..

Campello, M. L. C. M. Y. &. Z. H., 2011. The real and financial implications of corporate hedging. The Journal of Finance, , pp. 66(5), 1615-1647..

Kozhan, R. N. A. &. S. P., 2013. The skew risk premium in the equity index market. Review of Financial Studies, , pp. 26(9), 2174-2203..

Stulz, R., 2014. How Companies Can Use Hedging to Create Shareholder Value (Digest Summary).. CFA Digest, , p. 44(7).

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